Daily Papers

3D convolution neural networks (CNNs) have been the prevailing option for video recognition. To capture the temporal information, 3D convolutions are computed along the sequences, leading to cubically growing and expensive computations. To reduce the computational cost, previous methods resort to manually designed 3D/2D CNN structures with approximations or automatic search, which sacrifice the modeling ability or make training time-consuming. In this work, we propose to automatically design efficient 3D CNN architectures via a novel training-free neural architecture search approach tailored for 3D CNNs considering the model complexity. To measure the expressiveness of 3D CNNs efficiently, we formulate a 3D CNN as an information system and derive an analytic entropy score, based on the Maximum Entropy Principle. Specifically, we propose a spatio-temporal entropy score (STEntr-Score) with a refinement factor to handle the discrepancy of visual information in spatial and temporal dimensions, through dynamically leveraging the correlation between the feature map size and kernel size depth-wisely. Highly efficient and expressive 3D CNN architectures, \ie entropy-based 3D CNNs (E3D family), can then be efficiently searched by maximizing the STEntr-Score under a given computational budget, via an evolutionary algorithm without training the network parameters. Extensive experiments on Something-Something V1\&V2 and Kinetics400 demonstrate that the E3D family achieves state-of-the-art performance with higher computational efficiency. Code is available at https://github.com/alibaba/lightweight-neural-architecture-search.

Long-horizon reasoning in recent LLMs demands that the model switch between distinct skills inside a reasoning chain, such as first doing a math derivation, then using the result to plan a schedule. We call such problems cross-skill long-horizon tasks: multi-step tasks whose steps require different reasoning skills and depend on earlier outputs. Existing benchmarks often evaluate individual skills, lacking a principled way to measure how well a model switches between skills. We address this gap from both the evaluation and training sides. We introduce Skill Entropy, a measure of the difficulty of switching from one skill to another. We then propose Skill^2-Bench, a benchmark of cross-skill long-horizon tasks built over 558 skills across 9 verifiable and open-ended domains. Each task is assigned a task-level skill-entropy score and grouped into three difficulty levels. Evaluating 8 frontier and 4 open-source models on Skill^2-Bench reveals a skill-switching gap: accuracy decreases on higher-entropy tasks. We then turn skill entropy from a benchmark scale into a training signal. We propose Skill-Entropy RL, an RL framework where the model predicts not only the answer at each step but also the skill used to produce it. The reward combines step-level correctness with a skill-entropy reward that measures the alignment between the model-predicted skill sequence and the gold skill sequence. On Qwen3-4B-Instruct and Qwen3-1.7B, Skill-Entropy RL improves the Skill^2-Bench score from 34.4% to 68.4% and from 14.6% to 40.1%, respectively, outperforming competitive baselines. The same pipeline can be applied to off-the-shelf training data such as OpenR1-Math, indicating that skill entropy is a reusable training signal. Code available at: https://github.com/Gen-Verse/Skill-Entropy-RL

Traditional evaluations of multimodal large language models (LLMs) have been limited by their focus on single-image reasoning, failing to assess crucial aspects like contextual understanding, reasoning stability, and uncertainty calibration. This study addresses these limitations by introducing a novel benchmark that integrates multi-image reasoning tasks with rejection-based evaluation and positional bias detection. To evaluate these dimensions, we further introduce entropy as a novel metric for quantifying reasoning consistency across reordered answer variants. We applied this benchmark to assess Grok 3, ChatGPT-4o, ChatGPT-o1, Gemini 2.0 Flash Experimental, DeepSeek Janus models, Qwen2.5-VL-72B-Instruct, QVQ-72B-Preview, and Pixtral 12B across eight visual reasoning tasks, including difference spotting and diagram interpretation. Our findings reveal ChatGPT-o1 leading in overall accuracy (82.5\%) and rejection accuracy (70.0\%), closely followed by Gemini 2.0 Flash Experimental (70.8\%). QVQ-72B-Preview demonstrated superior rejection accuracy (85.5\%). Notably, Pixtral 12B (51.7\%) showed promise in specific domains, while Janus models exhibited challenges in bias and uncertainty calibration, reflected in low rejection accuracies and high entropy scores. High entropy scores in Janus models (Janus 7B: 0.8392, Janus 1B: 0.787) underscore their susceptibility to positional bias and unstable reasoning, contrasting with the low entropy and robust reasoning of ChatGPT models. The study further demonstrates that model size is not the sole determinant of performance, as evidenced by Grok 3 underperformance despite its substantial parameter count. By employing multi-image contexts, rejection mechanisms, and entropy-based consistency metrics, this benchmark sets a new standard for evaluating multimodal LLMs, enabling a more robust and reliable assessment of next-generation AI systems.

The use of CLIP embeddings to assess the alignment of samples produced by text-to-image generative models has been extensively explored in the literature. While the widely adopted CLIPScore, derived from the cosine similarity of text and image embeddings, effectively measures the relevance of a generated image, it does not quantify the diversity of images generated by a text-to-image model. In this work, we extend the application of CLIP embeddings to quantify and interpret the intrinsic diversity of text-to-image models, which is responsible for generating diverse images from similar text prompts. To achieve this, we propose a decomposition of the CLIP-based kernel covariance matrix of image data into text-based and non-text-based components. Using the Schur complement of the joint image-text kernel covariance matrix, we perform this decomposition and define the matrix-based entropy of the decomposed component as the Schur Complement Entropy (SCE) score, a measure of the intrinsic diversity of a text-to-image model based on data collected with varying text prompts. Additionally, we demonstrate the use of the Schur complement-based decomposition to nullify the influence of a given prompt in the CLIP embedding of an image, enabling focus or defocus of embeddings on specific objects or properties for downstream tasks. We present several numerical results that apply our Schur complement-based approach to evaluate text-to-image models and modify CLIP image embeddings. The codebase is available at https://github.com/aziksh-ospanov/CLIP-DISSECTION

Reasoning capability has advanced rapidly in large language models (LLMs), leading to an increasing size of key-value (KV) cache in both prefilling and decoding stages. Existing KV cache compression methods mainly rely on attention weights to estimate token importance. While attention effectively captures contextual relevance, it overlooks complementary information-theoretic signals related to predictive uncertainty and token informativeness. In this paper, we revisit token importance from a forward-looking perspective and introduce Forward Influence, a metric that measures how compressed tokens affect future contexts. Our analysis reveals that tokens selected by attention scores mainly influence nearby contexts, whereas tokens associated with high predictive uncertainty exhibit substantially stronger influence on distant future contexts. Based on the observation, we propose InfoKV, an entropy-aware KV cache compression framework that incorporates information-theoretic signals. It combines token-level predictive uncertainty with layer-wise representation evolution and integrates the resulting entropy scores with attention scores during reasoning. Experiments on long-context reasoning benchmarks with Llama-3.1, Llama-3.2, and DeepSeek-R1 demonstrate that InfoKV consistently outperforms existing attention-based KV compression methods in both long prefilling and decoding scenarios.

Multimodal Large Language Models (MLLMs) are increasingly deployed in fine-tuning-as-a-service (FTaaS) settings, where user-submitted datasets adapt general-purpose models to downstream tasks. This flexibility, however, introduces serious security risks, as malicious fine-tuning can implant backdoors into MLLMs with minimal effort. In this paper, we observe that backdoor triggers systematically disrupt cross-modal processing by causing abnormal attention concentration on non-semantic regions--a phenomenon we term attention collapse. Based on this insight, we propose Believe Your Eyes (BYE), a data filtering framework that leverages attention entropy patterns as self-supervised signals to identify and filter backdoor samples. BYE operates via a three-stage pipeline: (1) extracting attention maps using the fine-tuned model, (2) computing entropy scores and profiling sensitive layers via bimodal separation, and (3) performing unsupervised clustering to remove suspicious samples. Unlike prior defenses, BYE equires no clean supervision, auxiliary labels, or model modifications. Extensive experiments across various datasets, models, and diverse trigger types validate BYE's effectiveness: it achieves near-zero attack success rates while maintaining clean-task performance, offering a robust and generalizable solution against backdoor threats in MLLMs.

Imitation learning (IL) with generative models, such as diffusion and flow matching, has enabled robots to perform complex, long-horizon tasks. However, distribution shifts from unseen environments or compounding action errors can still cause unpredictable and unsafe behavior, leading to task failure. Early failure prediction during runtime is therefore essential for deploying robots in human-centered and safety-critical environments. We propose FIPER, a general framework for Failure Prediction at Runtime for generative IL policies that does not require failure data. FIPER identifies two key indicators of impending failure: (i) out-of-distribution (OOD) observations detected via random network distillation in the policy's embedding space, and (ii) high uncertainty in generated actions measured by a novel action-chunk entropy score. Both failure prediction scores are calibrated using a small set of successful rollouts via conformal prediction. A failure alarm is triggered when both indicators, aggregated over short time windows, exceed their thresholds. We evaluate FIPER across five simulation and real-world environments involving diverse failure modes. Our results demonstrate that FIPER better distinguishes actual failures from benign OOD situations and predicts failures more accurately and earlier than existing methods. We thus consider this work an important step towards more interpretable and safer generative robot policies. Code, data and videos are available at https://tum-lsy.github.io/fiper_website.

Despite the remarkable performance of score distillation in text-to-3D generation, such techniques notoriously suffer from view inconsistency issues, also known as "Janus" artifact, where the generated objects fake each view with multiple front faces. Although empirically effective methods have approached this problem via score debiasing or prompt engineering, a more rigorous perspective to explain and tackle this problem remains elusive. In this paper, we reveal that the existing score distillation-based text-to-3D generation frameworks degenerate to maximal likelihood seeking on each view independently and thus suffer from the mode collapse problem, manifesting as the Janus artifact in practice. To tame mode collapse, we improve score distillation by re-establishing in entropy term in the corresponding variational objective, which is applied to the distribution of rendered images. Maximizing the entropy encourages diversity among different views in generated 3D assets, thereby mitigating the Janus problem. Based on this new objective, we derive a new update rule for 3D score distillation, dubbed Entropic Score Distillation (ESD). We theoretically reveal that ESD can be simplified and implemented by just adopting the classifier-free guidance trick upon variational score distillation. Although embarrassingly straightforward, our extensive experiments successfully demonstrate that ESD can be an effective treatment for Janus artifacts in score distillation.

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by 25-75\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around 6-8times better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with 32times fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

We show that the three movements of Beethoven's "Moonlight Sonata" (Op. 27 No. 2) instantiate three distinct machine learning architectures -- not by analogy, but by structural correspondence. Through computational analysis of the score (entropy, Jensen-Shannon divergence, dissonance, hand distributional overlap, self-similarity matrices, temporal memory decay, and contextual pitch embeddings), we establish four counterintuitive findings: (1) perceived musical "temperature" is governed by throughput, not distributional width; (2) the lightest movement carries the highest dissonance; (3) the movements implement streaming, recurrent, and periodic positional encoding memory architectures; and (4) the same pitch class acquires different contextual identities across movements, analogous to contextual vs.static embeddings in NLP -- and unsupervised clustering recovers the tonal structure without music-theoretic input. We construct a reverse sonification (decoding analytical features back into MIDI) and quantify the chirality of the encode-decode cycle: what distributions preserve and sequential ordering destroys. Prompted by a listener's observation that the decoded piece sounds like "mirror isomers that can't be superimposed," the chirality measurement reveals reconstruction loss increasing monotonically with n-gram order. Bootstrap baselines and subsample checks confirm all movements carry sequential information above noise, though raw values are confounded by sample size. Cross-domain comparison shows natural language has higher chirality than music, reflecting stronger sequential constraints.

Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the pretrained distribution. Feynman-Kac sequential Monte Carlo (SMC) makes this correction exact in principle, but its prescribed weights routinely degenerate when the proposal dynamics are misaligned with the tilt, capping the practical gains from additional particles. We introduce FluxLite, a lightweight, training-free proposal-control framework for discrete diffusion. On the sparse directed graph of pretrained reverse rates, any sparse jump-rate perturbation can be exactly compensated by a q_t-weighted graph-divergence term in the Feynman-Kac potential; the target path is therefore preserved while the residual reweighting variance becomes a local convex objective. We instantiate this principle as two practical samplers: a one-hop local reallocation rule (HEU) and a small nonnegative quadratic program over pretrained-rate bases (D-VCG). We further prove population stability under the standard score-entropy training loss, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman-Kac recursion. Empirically, FluxLite improves over standard Feynman-Kac SMC baselines by up to two orders of magnitude in terminal KL on an analytically tractable finite-state CTMC benchmark, and reduces row-correlation MSE on 2D Ising sampling by 5-7x in geometric mean and up to 55x at peak.

Dual-encoder retrievers depend on the principle that relevant documents should score higher than irrelevant ones for a given query. Yet the dominant Noise Contrastive Estimation (NCE) objective, which underpins Contrastive Loss, optimizes a softened ranking surrogate that we rigorously prove is fundamentally oblivious to score separation quality and unrelated to AUC. This mismatch leads to poor calibration and suboptimal performance in downstream tasks like retrieval-augmented generation (RAG). To address this fundamental limitation, we introduce the MW loss, a new training objective that maximizes the Mann-Whitney U statistic, which is mathematically equivalent to the Area under the ROC Curve (AUC). MW loss encourages each positive-negative pair to be correctly ranked by minimizing binary cross entropy over score differences. We provide theoretical guarantees that MW loss directly upper-bounds the AoC, better aligning optimization with retrieval goals. We further promote ROC curves and AUC as natural threshold free diagnostics for evaluating retriever calibration and ranking quality. Empirically, retrievers trained with MW loss consistently outperform contrastive counterparts in AUC and standard retrieval metrics. Our experiments show that MW loss is an empirically superior alternative to Contrastive Loss, yielding better-calibrated and more discriminative retrievers for high-stakes applications like RAG.

Discrete diffusion models have recently gained significant attention due to their ability to process complex discrete structures for language modeling. However, fine-tuning these models with policy gradient methods, as is commonly done in Reinforcement Learning from Human Feedback (RLHF), remains a challenging task. We propose an efficient, broadly applicable, and theoretically justified policy gradient algorithm, called Score Entropy Policy Optimization (SEPO), for fine-tuning discrete diffusion models over non-differentiable rewards. Our numerical experiments across several discrete generative tasks demonstrate the scalability and efficiency of our method. Our code is available at https://github.com/ozekri/SEPO.

Large Vision-Language Models (LVLMs) have adopted visual token pruning strategies to mitigate substantial computational overhead incurred by extensive visual token sequences. While prior works primarily focus on either attention-based or diversity-based pruning methods, in-depth analysis of these approaches' characteristics and limitations remains largely unexplored. In this work, we conduct thorough empirical analysis using effective rank (erank) as a measure of feature diversity and attention score entropy to investigate visual token processing mechanisms and analyze the strengths and weaknesses of each approach. Our analysis reveals two insights: (1) Our erank-based quantitative analysis shows that many diversity-oriented pruning methods preserve substantially less feature diversity than intended; moreover, analysis using the CHAIR dataset reveals that the diversity they do retain is closely tied to increased hallucination frequency compared to attention-based pruning. (2) We further observe that attention-based approaches are more effective on simple images where visual evidence is concentrated, while diversity-based methods better handle complex images with distributed features. Building on these empirical insights, we show that incorporating image-aware adjustments into existing hybrid pruning strategies consistently improves their performance. We also provide a minimal instantiation of our empirical findings through a simple adaptive pruning mechanism, which achieves strong and reliable performance across standard benchmarks as well as hallucination-specific evaluations. Our project page available at https://cvsp-lab.github.io/AgilePruner.

The robustness of machine learning models can be compromised by spurious correlations between non-causal features in the input data and target labels. A common way to test for such correlations is to train on data where the label is strongly tied to some non-causal cue, then evaluate on examples where that tie no longer holds. This idea is well established for classification tasks, but for semantic segmentation the specific failure modes are not well understood. We show that a model may achieve reasonable overlap while assigning the wrong semantic label, swapping one plausible foreground class for another, even when object boundaries are largely correct. We focus on this semantic label-flip behaviour and quantify it with a simple diagnostic (Flip) that counts how often ground truth foreground pixels are assigned the wrong foreground identity while remaining predicted as foreground. In a setting where category and scene are correlated during training, increasing the correlation consistently widens the gap between common and rare test conditions and increases these within-object label swaps on counterfactual groups. Overall, our results motivate assessing segmentation robustness under distribution shift beyond overlap by decomposing foreground errors into correct pixels, flipped-identity pixels, and missed-to-background pixels. We also propose an entropy-based, ground truth label-free `flip-risk' score, which is computed from foreground identity uncertainty, and show that it can flag flip-prone cases at inference time. Code is available at https://github.com/acharaakshit/label-flips.

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.

Transferring knowledge from a cross-encoder teacher via Knowledge Distillation (KD) has become a standard paradigm for training retrieval models. While existing studies have largely focused on mining hard negatives to improve discrimination, the systematic composition of training data and the resulting teacher score distribution have received relatively less attention. In this work, we highlight that focusing solely on hard negatives prevents the student from learning the comprehensive preference structure of the teacher, potentially hampering generalization. To effectively emulate the teacher score distribution, we propose a Stratified Sampling strategy that uniformly covers the entire score spectrum. Experiments on in-domain and out-of-domain benchmarks confirm that Stratified Sampling, which preserves the variance and entropy of teacher scores, serves as a robust baseline, significantly outperforming top-K and random sampling in diverse settings. These findings suggest that the essence of distillation lies in preserving the diverse range of relative scores perceived by the teacher.

Large Language Models (LLMs) are known to have limited extrapolation ability beyond their pre-trained context window, constraining their application in downstream tasks with lengthy inputs. Recent studies have sought to extend LLMs' context window by modifying rotary position embedding (RoPE), a popular position encoding method adopted by well-known LLMs such as LLaMA, PaLM, and GPT-NeoX. However, prior works like Position Interpolation (PI) and YaRN are resource-intensive and lack comparative experiments to assess their applicability. In this work, we identify the inherent need for LLMs' attention entropy (i.e. the information entropy of attention scores) to maintain stability and introduce a novel extension to RoPE which combines adjusting RoPE's base frequency and scaling the attention logits to help LLMs efficiently adapt to a larger context window. We validate the superiority of our method in both fine-tuning performance and robustness across different context window sizes on various context-demanding tasks. Notably, our method extends the context window of LLaMA-2-7B-Chat to 16,384 with only 100 samples and 6 training steps, showcasing extraordinary efficiency. Finally, we also explore how data compositions and training curricula affect context window extension for specific downstream tasks, suggesting fine-tuning LLMs with lengthy conversations as a good starting point. We release our code and SFT data at https://github.com/GAIR-NLP/Entropy-ABF.

Large Language Models (LLMs) are predominantly trained and aligned in ways that reinforce Western-centric epistemologies and socio-cultural norms, leading to cultural homogenization and limiting their ability to reflect global civilizational plurality. Existing benchmarking frameworks fail to adequately capture this bias, as they rely on rigid, closed-form assessments that overlook the complexity of cultural inclusivity. To address this, we introduce WorldView-Bench, a benchmark designed to evaluate Global Cultural Inclusivity (GCI) in LLMs by analyzing their ability to accommodate diverse worldviews. Our approach is grounded in the Multiplex Worldview proposed by Senturk et al., which distinguishes between Uniplex models, reinforcing cultural homogenization, and Multiplex models, which integrate diverse perspectives. WorldView-Bench measures Cultural Polarization, the exclusion of alternative perspectives, through free-form generative evaluation rather than conventional categorical benchmarks. We implement applied multiplexity through two intervention strategies: (1) Contextually-Implemented Multiplex LLMs, where system prompts embed multiplexity principles, and (2) Multi-Agent System (MAS)-Implemented Multiplex LLMs, where multiple LLM agents representing distinct cultural perspectives collaboratively generate responses. Our results demonstrate a significant increase in Perspectives Distribution Score (PDS) entropy from 13% at baseline to 94% with MAS-Implemented Multiplex LLMs, alongside a shift toward positive sentiment (67.7%) and enhanced cultural balance. These findings highlight the potential of multiplex-aware AI evaluation in mitigating cultural bias in LLMs, paving the way for more inclusive and ethically aligned AI systems.

Vision-language models (VLMs) have made significant progress in image classification by training with large-scale paired image-text data. Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones.

Scaling laws provide important insights that can guide the design of large language models (LLMs). Existing work has primarily focused on studying scaling laws for pretraining (upstream) loss. However, in transfer learning settings, in which LLMs are pretrained on an unsupervised dataset and then finetuned on a downstream task, we often also care about the downstream performance. In this work, we study the scaling behavior in a transfer learning setting, where LLMs are finetuned for machine translation tasks. Specifically, we investigate how the choice of the pretraining data and its size affect downstream performance (translation quality) as judged by two metrics: downstream cross-entropy and BLEU score. Our experiments indicate that the size of the finetuning dataset and the distribution alignment between the pretraining and downstream data significantly influence the scaling behavior. With sufficient alignment, both downstream cross-entropy and BLEU score improve monotonically with more pretraining data. In such cases, we show that it is possible to predict the downstream BLEU score with good accuracy using a log-law. However, there are also cases where moderate misalignment causes the BLEU score to fluctuate or get worse with more pretraining, whereas downstream cross-entropy monotonically improves. By analyzing these observations, we provide new practical insights for choosing appropriate pretraining data.

Large language models (LLMs) are increasingly used as judges to replace costly human preference labels in pairwise evaluation. Despite their practicality, LLM judges remain prone to miscalibration and systematic biases. This paper proposes SCOPE (Selective Conformal Optimized Pairwise Evaluation), a framework for selective pairwise judging with finite-sample statistical guarantees. Under exchangeability, SCOPE calibrates an acceptance threshold such that the error rate among non-abstained judgments is at most a user-specified level α. To provide SCOPE with a bias-neutral uncertainty signal, we introduce Bidirectional Preference Entropy (BPE), which queries the judge under both response positions, aggregates the implied preference probabilities to enforce invariance to response order, and converts the aggregated probability into an entropy-based uncertainty score. Across MT-Bench, RewardBench, and Chatbot Arena, BPE improves uncertainty quality over standard confidence proxies, providing a stronger selection signal that enables SCOPE to consistently meet the target risk level while retaining good coverage across judge scales. In particular, at α= 0.10, SCOPE consistently satisfies the risk bound across all benchmarks and judge scales (empirical risk approx 0.097 to 0.099), while retaining substantial coverage, reaching 0.89 on RewardBench with Qwen-14B and 0.98 on RewardBench with Qwen-32B. Compared to naïve baselines, SCOPE accepts up to 2.4times more judgments on MT-Bench with Qwen-7B under the same target risk constraint, demonstrating that BPE enables reliable and high-coverage LLM-based evaluation.

The growth of IoT devices in shared environments has outpaced our ability to identify them, posing urgent risks to privacy, safety, and accountability. This challenge is especially pronounced in open-world environments, where network traffic metadata is often sparse, noisy, or adversarial. To address this problem, we introduce a semantic inference pipeline that reframes device identification as a language modeling task over real-world network metadata. As this approach depends on reliable supervision, we first construct high-fidelity vendor labels for the IoT Inspector dataset, the largest real-world corpus of its kind, using an ensemble of large language models guided by mutual-information and entropy-based stability scores. We then instruction-tune a quantized LLaMA 3.1 8B model on this dataset using curriculum learning to support generalization under sparsity and long-tail vendor distributions. Our model achieves 98.69% top-1 and 90.73% macro accuracy across 2,015 vendors, while remaining robust to missing fields, protocol drift, and adversarial manipulation. We also evaluate the model on an independent IoT testbed dataset, assess explanation quality, and conduct adversarial tests to probe robustness under spoofed and obfuscated input. These results position instruction-tuned LLMs as a scalable, interpretable foundation for trustworthy device identification at scale.

Semi-supervised semantic segmentation (SSSS) faces persistent challenges in effectively leveraging unlabeled data, such as ineffective utilization of pseudo-labels, exacerbation of class imbalance biases, and neglect of prediction uncertainty. Current approaches often discard uncertain regions through strict thresholding favouring dominant classes. To address these limitations, we introduce a holistic framework that transforms uncertainty into a learning asset through four principal components: (1) fuzzy pseudo-labeling, which preserves soft class distributions from top-K predictions to enrich supervision; (2) uncertainty-aware dynamic weighting, that modulate pixel-wise contributions via entropy-based reliability scores; (3) adaptive class rebalancing, which dynamically adjust losses to counteract long-tailed class distributions; and (4) lightweight contrastive regularization, that encourage compact and discriminative feature embeddings. Extensive experiments on benchmarks demonstrate that our method outperforms current state-of-the-art approaches, achieving significant improvements in the segmentation of under-represented classes and ambiguous regions.

Transfer entropy measures directed information flow in time series, and it has become a fundamental quantity in applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.

Diversity is an important criterion for many areas of machine learning (ML), including generative modeling and dataset curation. Yet little work has gone into understanding, formalizing, and measuring diversity in ML. In this paper, we address the diversity evaluation problem by proposing the Vendi Score, which connects and extends ideas from ecology and quantum statistical mechanics to ML. The Vendi Score is defined as the exponential of the Shannon entropy of the eigenvalues of a similarity matrix. This matrix is induced by a user-defined similarity function applied to the sample to be evaluated for diversity. In taking a similarity function as input, the Vendi Score enables its user to specify any desired form of diversity. Importantly, unlike many existing metrics in ML, the Vendi Score doesn't require a reference dataset or distribution over samples or labels, it is therefore general and applicable to any generative model, decoding algorithm, and dataset from any domain where similarity can be defined. We showcased the Vendi Score on molecular generative modeling, a domain where diversity plays an important role in enabling the discovery of novel molecules. We found that the Vendi Score addresses shortcomings of the current diversity metric of choice in that domain. We also applied the Vendi Score to generative models of images and decoding algorithms of text and found it confirms known results about diversity in those domains. Furthermore, we used the Vendi Score to measure mode collapse, a known limitation of generative adversarial networks (GANs). In particular, the Vendi Score revealed that even GANs that capture all the modes of a labeled dataset can be less diverse than the original dataset. Finally, the interpretability of the Vendi Score allowed us to diagnose several benchmark ML datasets for diversity, opening the door for diversity-informed data augmentation.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEE

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

The Optical Character Recognition (OCR) task is important for evaluating Vision-Language Models (VLMs) and providing high-quality data sources for LLM training data. While state-of-the-art VLMs show improved average OCR accuracy, they still struggle with sample-level quality degradation and lack reliable automatic detection of low-quality outputs. We introduce Consensus Entropy (CE), a training-free post-inference method that quantifies OCR uncertainty by aggregating outputs from multiple VLMs. Our approach exploits a key insight: correct VLM OCR predictions converge in output space while errors diverge. We develop a lightweight multi-model framework that effectively identifies problematic samples, selects the best outputs and combines model strengths. Experiments across multiple OCR benchmarks and VLMs demonstrate that CE outperforms VLM-as-judge approaches and single-model baselines at the same cost and achieves state-of-the-art results across multiple metrics. For instance, our solution demonstrates: achieving 15.2% higher F1 scores than VLM-as-judge methods in quality verification, delivering 6.0% accuracy gains on mathematical calculation tasks, and requiring rephrasing only 7.3% of inputs while maintaining overall performance. Notably, the entire process requires neither training nor supervision while maintaining plug-and-play functionality throughout.

Masked Diffusion Models (MDMs) have emerged as a promising non-autoregressive paradigm for generative tasks, offering parallel decoding and bidirectional context utilization. However, current sampling methods rely on simple confidence-based heuristics that ignore the long-term impact of local decisions, leading to trajectory lock-in where early hallucinations cascade into global incoherence. While search-based methods mitigate this, they incur prohibitive computational costs (O(K) forward passes per step). In this work, we propose Backward-on-Entropy (BoE) Steering, a gradient-guided inference framework that approximates infinite-horizon lookahead via a single backward pass. We formally derive the Token Influence Score (TIS) from a first-order expansion of the trajectory cost functional, proving that the gradient of future entropy with respect to input embeddings serves as an optimal control signal for minimizing uncertainty. To ensure scalability, we introduce ActiveQueryAttention, a sparse adjoint primitive that exploits the structure of the masking objective to reduce backward pass complexity. BoE achieves a superior Pareto frontier for inference-time scaling compared to existing unmasking methods, demonstrating that gradient-guided steering offers a mathematically principled and efficient path to robust non-autoregressive generation. We will release the code.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

We propose ERA, a new paradigm that constrains the sampling entropy above given thresholds by applying specially designed activations to the outputs of models. Our approach demonstrates broad effectiveness across different domains: 1) for large language models(LLMs), boosting the AIME 2025 score for Qwen2.5-Math-7B by 37.4%; 2) for continuous control reinforcement learning agents, improving performance by more than 30% over strong baselines such as SAC on the challenging HumanoidBench; 3) for image classification, enhancing ImageNet top-1 accuracy by 0.69% for ResNet-50. These gains are achieved with a computational overhead of less than 7%. Our work validates output activation as a powerful tool for entropy control, opening a new direction for designing simpler and more robust algorithms.

As TLS 1.3 encryption limits traditional Deep Packet Inspection (DPI), the security community has pivoted to Euclidean Transformer-based classifiers (e.g., ET-BERT) for encrypted traffic analysis. However, these models remain vulnerable to byte-level adversarial morphing -- recent pre-padding attacks reduced ET-BERT accuracy to 25.68%, while VLESS Reality bypasses certificate-based detection entirely. We introduce AEGIS: an Adversarial Entropy-Guided Immune System powered by a Thermodynamic Variance-Guided Hyperbolic Liquid State Space Model (TVD-HL-SSM). Rather than competing in the Euclidean payload-reading domain, AEGIS discards payload bytes in favor of 6-dimensional continuous-time flow physics projected into a non-Euclidean Poincare manifold. Liquid Time-Constants measure microsecond IAT decay, and a Thermodynamic Variance Detector computes sequence-wide Shannon Entropy to expose automated C2 tunnel anomalies. A pure C++ eBPF Harvester with zero-copy IPC bypasses the Python GIL, enabling a linear-time O(N) Mamba-3 core to process 64,000-packet swarms at line-rate. Evaluated on a 400GB, 4-tier adversarial corpus spanning backbone traffic, IoT botnets, zero-days, and proprietary VLESS Reality tunnels, AEGIS achieves an F1-score of 0.9952 and 99.50% True Positive Rate at 262 us inference latency on an RTX 4090, establishing a new state-of-the-art for physics-based adversarial network defense.

This paper presents TEVR, a speech recognition model designed to minimize the variation in token entropy w.r.t. to the language model. This takes advantage of the fact that if the language model will reliably and accurately predict a token anyway, then the acoustic model doesn't need to be accurate in recognizing it. We train German ASR models with 900 million parameters and show that on CommonVoice German, TEVR scores a very competitive 3.64% word error rate, which outperforms the best reported results by a relative 16.89% reduction in word error rate. We hope that releasing our fully trained speech recognition pipeline to the community will lead to privacy-preserving offline virtual assistants in the future.

Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each attention head during the course of training, which is a proxy for model sharpness. We identify a common pattern across different architectures and tasks, where low attention entropy is accompanied by high training instability, which can take the form of oscillating loss or divergence. We denote the pathologically low attention entropy, corresponding to highly concentrated attention scores, as entropy collapse. As a remedy, we propose sigmaReparam, a simple and efficient solution where we reparametrize all linear layers with spectral normalization and an additional learned scalar. We demonstrate that the proposed reparameterization successfully prevents entropy collapse in the attention layers, promoting more stable training. Additionally, we prove a tight lower bound of the attention entropy, which decreases exponentially fast with the spectral norm of the attention logits, providing additional motivation for our approach. We conduct experiments with sigmaReparam on image classification, image self-supervised learning, machine translation, automatic speech recognition, and language modeling tasks, across Transformer architectures. We show that sigmaReparam provides stability and robustness with respect to the choice of hyperparameters, going so far as enabling training (a) a Vision Transformer to competitive performance without warmup, weight decay, layer normalization or adaptive optimizers; (b) deep architectures in machine translation and (c) speech recognition to competitive performance without warmup and adaptive optimizers.

Simultaneous Speech Translation (SimulST) systems stream in audio while simultaneously emitting translated text or speech. Such systems face the significant challenge of balancing translation quality and latency. We introduce a strategy to optimize this tradeoff: wait for more input only if you gain information by doing so. Based on this strategy, we present Regularized Entropy INformation Adaptation (REINA), a novel loss to train an adaptive policy using an existing non-streaming translation model. We derive REINA from information theory principles and show that REINA helps push the reported Pareto frontier of the latency/quality tradeoff over prior works. Utilizing REINA, we train a SimulST model on French, Spanish and German, both from and into English. Training on only open source or synthetically generated data, we achieve state-of-the-art (SOTA) streaming results for models of comparable size. We also introduce a metric for streaming efficiency, quantitatively showing REINA improves the latency/quality trade-off by as much as 21% compared to prior approaches, normalized against non-streaming baseline BLEU scores.

Realistic and diverse traffic simulation is essential to autonomous driving development. Yet prevailing benchmarks predominantly reward realism, and recent methods have optimized accordingly, leaving diversity underexplored. We introduce Flow-ERD, a multi-agent simulator that pursues realism and diversity jointly. Its backbone, Agent-Type Aware Flow Matching (AFM), couples flow matching's multi-modal expressiveness with type-specific kinematic execution. It preserves fine-grained diversity while keeping motions consistent with each agent type. A second stage, Entropy-Regularized Distillation (ERD), fine-tunes the closed-loop rollout distribution with an entropy-regularized reverse-KL objective. This mitigates covariate shift while explicitly preventing collapse onto high-density modes. We evaluate Flow-ERD with a log-free diversity metric alongside standard realism scores. Flow-ERD ranks first on the WOSAC test benchmark and dominates the realism--diversity Pareto front among reproducible baselines. Our project page is available https://seulbinhwang.github.io/flow-erd-project-page/{here}.

Solutions based on large language models (LLMs) often rely on temperature sampling to improve accuracy and stability by aggregating multiple samples from the completion distribution. However, this memoryless approach is inherently suboptimal: because it lacks awareness of prior generations and their evaluations, it produces an increasing proportion of semantically duplicate answers as more samples are drawn, leading to diminishing returns. To address this limitation, we introduce FLEET, a novel method that integrates a memory mechanism into the generation process. FLEET represents each generation as a sparse trajectory through states whose entropy exceeds a predefined threshold and uses these trajectories to infer per-token utility scores that adjust the logits. Benchmark evaluations demonstrate that FLEET achieves the same accuracy as the repeated sampling baseline, with a 3x speedup, and substantially improves accuracy on complex coding tasks (LiveCodeBench Pass@32 increases from 59.9% to 66.2%) under the same budget. Furthermore, in the greedy-decoding configuration evaluated here, the approach is deterministic and uses a single calibration pass to derive its principal hyperparameters, requiring only minimal modifications to existing LLM pipelines.

A wide range of deep learning-based machine learning techniques are extensively applied to the design of high-entropy alloys (HEAs), yielding numerous valuable insights. Kolmogorov-Arnold Networks (KAN) is a recently developed architecture that aims to improve both the accuracy and interpretability of input features. In this work, we explore three different datasets for HEA design and demonstrate the application of KAN for both classification and regression models. In the first example, we use a KAN classification model to predict the probability of single-phase formation in high-entropy carbide ceramics based on various properties such as mixing enthalpy and valence electron concentration. In the second example, we employ a KAN regression model to predict the yield strength and ultimate tensile strength of HEAs based on their chemical composition and process conditions including annealing time, cold rolling percentage, and homogenization temperature. The third example involves a KAN classification model to determine whether a certain composition is an HEA or non-HEA, followed by a KAN regressor model to predict the bulk modulus of the identified HEA, aiming to identify HEAs with high bulk modulus. In all three examples, KAN either outperform or match the performance in terms of accuracy such as F1 score for classification and Mean Square Error (MSE), and coefficient of determination (R2) for regression of the multilayer perceptron (MLP) by demonstrating the efficacy of KAN in handling both classification and regression tasks. We provide a promising direction for future research to explore advanced machine learning techniques, which lead to more accurate predictions and better interpretability of complex materials, ultimately accelerating the discovery and optimization of HEAs with desirable properties.

Jailbreak attacks reveal a persistent weakness in aligned Large Language Models: carefully crafted prompts can elicit policy-violating responses despite safety training. While most defenses operate at the prompt or output level, it remains unclear how harmful intent is encoded within the model's internal representations. We investigate this question by analyzing token-level predictive entropy trajectories across layers of a frozen LLM using the logit lens. We find that static aggregate statistics of prompt-level entropy (e.g., mean, variance) carry little discriminative signal, whereas features capturing how entropy evolves across token positions, such as monotonic rank-based trend scores, are substantially more informative. Importantly, this signal is not uniform across model depth: it is concentrated in intermediate layers and degrades at the final layer, indicating that jailbreak-relevant structure is most pronounced in mid-network representations rather than at the output head. Across multiple models (Llama, Qwen, Gemma) and adversarial benchmarks, these entropy dynamics provide architecture-consistent separation without additional training. Together, our findings show that jailbreak behavior is reflected in structured intermediate uncertainty dynamics, clarifying both which entropy-derived features encode harmful intent and where in the network that signal is most pronounced.

Measuring the distance between machine-produced and human language is a critical open problem. Inspired by empirical findings from psycholinguistics on the periodicity of entropy in language, we propose FACE, a set of metrics based on Fourier Analysis of the estimated Cross-Entropy of language, for measuring the similarity between model-generated and human-written languages. Based on an open-ended generation task and the experimental data from previous studies, we find that FACE can effectively identify the human-model gap, scales with model size, reflects the outcomes of different sampling methods for decoding, correlates well with other evaluation metrics and with human judgment scores.

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that unifies semantic segmentation, classification, and image generation within a single model. Using a symmetric learning objective, SymmFlow models forward and reverse transformations jointly, ensuring bi-directional consistency, while preserving sufficient entropy for generative diversity. A new training objective is introduced to explicitly retain semantic information across flows, featuring efficient sampling while preserving semantic structure, allowing for one-step segmentation and classification without iterative refinement. Unlike previous approaches that impose strict one-to-one mapping between masks and images, SymmFlow generalizes to flexible conditioning, supporting both pixel-level and image-level class labels. Experimental results on various benchmarks demonstrate that SymmFlow achieves state-of-the-art performance on semantic image synthesis, obtaining FID scores of 11.9 on CelebAMask-HQ and 7.0 on COCO-Stuff with only 25 inference steps. Additionally, it delivers competitive results on semantic segmentation and shows promising capabilities in classification tasks. The code will be publicly available.

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models suffers from two critical challenges: (1) the inherent noise in preference datasets, which degrades model performance, and (2) the inefficiency of conventional training methods, which ignore the differences in sample difficulty. In this paper, we identify a strong correlation between response entropy and accuracy, indicating that entropy can serve as a reliable and unsupervised proxy for annotation noise and sample difficulty. Based on this insight, we propose a novel Entropy-Guided Training (EGT) approach for multimodal reasoning reward models, which combines two strategies: (1) entropy-guided data curation to mitigate the impact of unreliable samples, and (2) an entropy-guided training strategy that progressively introduces more complex examples. Extensive experiments across three benchmarks show that the EGT-trained model consistently outperforms state-of-the-art multimodal reward models.

This paper introduces EnergyFlow, a framework that unifies generative action modeling with inverse reinforcement learning by parameterizing a scalar energy function whose gradient is the denoising field. We establish that under maximum-entropy optimality, the score function learned via denoising score matching recovers the gradient of the expert's soft Q-function, enabling reward extraction without adversarial training. Formally, we prove that constraining the learned field to be conservative reduces hypothesis complexity and tightens out-of-distribution generalization bounds. We further characterize the identifiability of recovered rewards and bound how score estimation errors propagate to action preferences. Empirically, EnergyFlow achieves state-of-the-art imitation performance on various manipulation tasks while providing an effective reward signal for downstream reinforcement learning that outperforms both adversarial IRL methods and likelihood-based alternatives. These results show that the structural constraints required for valid reward extraction simultaneously serve as beneficial inductive biases for policy generalization. The code is available at https://github.com/sotaagi/EnergyFlow.

Black-box adversarial attacks that minimize only the ground-truth confidence suffer from class drift: perturbations wander through the feature space without committing to a specific adversarial class, wasting queries on diffuse, undirected progress. We introduce Opportunistic Target Selection (OTS), a lightweight wrapper that switches an untargeted attack to a targeted objective early in its trajectory, locking onto whichever non-true class currently leads. OTS requires no architectural modification to the underlying attack, no gradient access, and no a priori target-class knowledge. We validate OTS on three score-based attacks (SimBA, Square Attack with cross-entropy loss, and Bandits) across five standard ImageNet classifiers (4,500 runs). On random-search attacks, OTS closely tracks oracle performance, with gains up to +27 pp in success rate and 43% relative reduction in censored-mean iterations on ResNet-50. On gradient-estimation attacks (Bandits) and attacks with margin loss, OTS is redundant, a negative result that reinforces our interpretation of OTS as a margin-loss surrogate. On adversarially-trained models, a bimodal difficulty distribution eliminates the regime where targeting helps.

We present a novel dataset collected by ASOS (a major online fashion retailer) to address the challenge of predicting customer returns in a fashion retail ecosystem. With the release of this substantial dataset we hope to motivate further collaboration between research communities and the fashion industry. We first explore the structure of this dataset with a focus on the application of Graph Representation Learning in order to exploit the natural data structure and provide statistical insights into particular features within the data. In addition to this, we show examples of a return prediction classification task with a selection of baseline models (i.e. with no intermediate representation learning step) and a graph representation based model. We show that in a downstream return prediction classification task, an F1-score of 0.792 can be found using a Graph Neural Network (GNN), improving upon other models discussed in this work. Alongside this increased F1-score, we also present a lower cross-entropy loss by recasting the data into a graph structure, indicating more robust predictions from a GNN based solution. These results provide evidence that GNNs could provide more impactful and usable classifications than other baseline models on the presented dataset and with this motivation, we hope to encourage further research into graph-based approaches using the ASOS GraphReturns dataset.

Machine translation tests masked diffusion language models (dLLMs) because every source token must be rendered faithfully, while fixed canvas decoding must choose target length before denoising. Existing masked diffusion decoding work mainly studies token unmasking order, leaving this length decision under-explored despite its direct effect on coverage and redundancy. We introduce Entropy-Valley (EV), a training-free length selector that scores candidate target canvases by mean predictive entropy from all-mask forward passes and selects the canvas the backbone is most prepared to fill. Relative to a baseline using training corpus length statistics, EV recovers 64.9%, 65.3%, and 33.0% of the COMET-22 gain from reference target lengths on EntoZh, ZhtoEn, and EntoDe. Our diagnostics show that denoising-friendly lengths need not match reference lengths. Evaluation by three translation experts supports the EnleftrightarrowZh adequacy gains, with stronger evidence on ZhtoEn. Compared with a LLaMA-3-8B autoregressive (AR) model trained on the same fine-tuning data, the EV system ties on EntoZh and leads on ZhtoEn; an oracle-length diagnostic further shows that, in this masked diffusion MT setting, deciding which tokens to reveal first matters less than how the target length is supplied.

With the remarkable generation performance of large language models, ethical and legal concerns about using them have been raised, such as plagiarism and copyright issues. For such concerns, several approaches to watermark and detect LLM-generated text have been proposed very recently. However, we discover that the previous methods fail to function appropriately with code generation tasks because of the syntactic and semantic characteristics of code. Based on Kirchenbauer2023watermark, we propose a new watermarking method, Selective WatErmarking via Entropy Thresholding (SWEET), that promotes "green" tokens only at the position with high entropy of the token distribution during generation, thereby preserving the correctness of the generated code. The watermarked code is detected by the statistical test and Z-score based on the entropy information. Our experiments on HumanEval and MBPP show that SWEET significantly improves the Pareto Frontier between the code correctness and watermark detection performance. We also show that notable post-hoc detection methods (e.g. DetectGPT) fail to work well in this task. Finally, we show that setting a reasonable entropy threshold is not much of a challenge. Code is available at https://github.com/hongcheki/sweet-watermark.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

We present a discriminative multimodal reward model that scores all candidate responses in a single forward pass. Conventional discriminative reward models evaluate each response independently, requiring multiple forward passes, one for each potential response. Our approach concatenates multiple responses with separator tokens and applies cross-entropy over their scalar scores, enabling direct comparative reasoning and efficient N-way preference learning. The multi-response design also yields up to Ntimes wall-clock speedup and FLOPs reduction over conventional single-response scoring. To enable N-way reward evaluation beyond existing pairwise benchmarks, we construct two new benchmarks: (1) MR^2Bench-Image contains human-annotated rankings over responses from 8 diverse models; (2) MR^2Bench-Video is a large-scale video-based reward benchmark derived from 94K crowdsourced pairwise human judgments over video question-answering spanning 19 models, denoised via preference graph ensemble. Both benchmarks provide 4-response evaluation variants sampled from the full rankings. Built on a 4B vision-language backbone with LoRA fine-tuning and a lightweight MLP value head, our model achieves state-of-the-art results on six multimodal reward benchmarks, including MR^2Bench-Image, MR^2Bench-Video, and four other existing benchmarks. Our model outperforms existing larger generative and discriminative reward models. We further demonstrate that our reward model, when used in reinforcement learning with GRPO, produces improved policy models that maintain performance across standard multimodal benchmarks while substantially improving open-ended generation quality, outperforming a single-response discriminative reward model (RM) baseline by a large margin in both training stability and open-ended generation quality.

As large language models (LLMs) are deployed in multilingual settings, their safety behavior in culturally diverse, low-resource languages remains poorly understood. We present the first systematic evaluation of LLM safety across 12 Indic languages, spoken by over 1.2 billion people but underrepresented in LLM training data. Using a dataset of 6,000 culturally grounded prompts spanning caste, religion, gender, health, and politics, we assess 10 leading LLMs on translated variants of the prompt. Our analysis reveals significant safety drift: cross-language agreement is just 12.8\%, and SAFE rate variance exceeds 17\% across languages. Some models over-refuse benign prompts in low-resource scripts, overflag politically sensitive topics, while others fail to flag unsafe generations. We quantify these failures using prompt-level entropy, category bias scores, and multilingual consistency indices. Our findings highlight critical safety generalization gaps in multilingual LLMs and show that safety alignment does not transfer evenly across languages. We release IndicSafe, the first benchmark to enable culturally informed safety evaluation for Indic deployments, and advocate for language-aware alignment strategies grounded in regional harms.

Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.

Many NLP tasks such as tagging and machine reading comprehension are faced with the severe data imbalance issue: negative examples significantly outnumber positive examples, and the huge number of background examples (or easy-negative examples) overwhelms the training. The most commonly used cross entropy (CE) criteria is actually an accuracy-oriented objective, and thus creates a discrepancy between training and test: at training time, each training instance contributes equally to the objective function, while at test time F1 score concerns more about positive examples. In this paper, we propose to use dice loss in replacement of the standard cross-entropy objective for data-imbalanced NLP tasks. Dice loss is based on the Sorensen-Dice coefficient or Tversky index, which attaches similar importance to false positives and false negatives, and is more immune to the data-imbalance issue. To further alleviate the dominating influence from easy-negative examples in training, we propose to associate training examples with dynamically adjusted weights to deemphasize easy-negative examples.Theoretical analysis shows that this strategy narrows down the gap between the F1 score in evaluation and the dice loss in training. With the proposed training objective, we observe significant performance boost on a wide range of data imbalanced NLP tasks. Notably, we are able to achieve SOTA results on CTB5, CTB6 and UD1.4 for the part of speech tagging task; SOTA results on CoNLL03, OntoNotes5.0, MSRA and OntoNotes4.0 for the named entity recognition task; along with competitive results on the tasks of machine reading comprehension and paraphrase identification.

Latent Video Diffusion Models (LVDMs) achieve high-quality generation but are sensitive to imperfect conditioning, which causes semantic drift and temporal incoherence on noisy, web-scale video-text datasets. We introduce CAT-LVDM, the first corruption-aware training framework for LVDMs that improves robustness through structured, data-aligned noise injection. Our method includes Batch-Centered Noise Injection (BCNI), which perturbs embeddings along intra-batch semantic directions to preserve temporal consistency. BCNI is especially effective on caption-rich datasets like WebVid-2M, MSR-VTT, and MSVD. We also propose Spectrum-Aware Contextual Noise (SACN), which injects noise along dominant spectral directions to improve low-frequency smoothness, showing strong results on UCF-101. On average, BCNI reduces FVD by 31.9% across WebVid-2M, MSR-VTT, and MSVD, while SACN yields a 12.3% improvement on UCF-101. Ablation studies confirm the benefit of low-rank, data-aligned noise. Our theoretical analysis further explains how such perturbations tighten entropy, Wasserstein, score-drift, mixing-time, and generalization bounds. CAT-LVDM establishes a principled, scalable training approach for robust video diffusion under multimodal noise. Code and models: https://github.com/chikap421/catlvdm

Recent advances in agentic Reinforcement Learning (RL) have substantially improved the multi-turn tool-use capabilities of large language model agents. However, most existing methods assign credit over coarse heuristic units, such as tool-call boundaries or fixed workflows, making it difficult to identify which intermediate decisions influence downstream outcomes. In this work, we study agentic RL from two perspectives: where to branch and how to assign credit after branching. Our pilot analysis shows that influential decision points are broadly distributed throughout the generated sequence rather than concentrated at tool calls, while token entropy alone does not reliably reflect their impact on final outcomes. Motivated by these observations, we propose Agentic Procedural Policy Optimization (APPO), which shifts branching and credit assignment from coarse interaction units to fine-grained decision points in the sequence. APPO selects branching locations using a Branching Score that combines token uncertainty with policy-induced likelihood gains of subsequent continuations, enabling more targeted exploration while filtering out spurious high-entropy positions. It further introduces procedure-level advantage scaling to better distribute credit across branched rollouts. Experiments on 13 benchmarks show that APPO consistently improves strong agentic RL baselines by nearly 4 points, while keeping efficient tool-calls and maintaining behavior interpretability.

On-policy distillation (OPD) provides dense teacher supervision on student-generated trajectories, but standard reverse-KL training can assign insufficient probability to other plausible continuations. Teacher entropy alone does not reveal whether uncertainty is concentrated among a few plausible next tokens or dispersed over a long probability tail, nor whether the student already represents those candidates well. Moreover, local teacher probabilities may not predict downstream success. We introduce Sparse Probing and Outcome-calibrated Targets OPD (SPOT), which addresses two coupled decisions, where to probe and what to distill, through an acquisition--exploration--exploitation procedure. During acquisition, a position-level score combines normalized teacher entropy, the probability mass captured by a small top-k candidate set, and student--teacher mismatch to allocate a limited probing budget. During exploration, SPOT evaluates teacher-proposed candidates through verifier-scored student continuations. During exploitation, these outcomes produce a closed-form, KL-regularized target that favors candidates with better downstream outcomes while remaining anchored to the teacher distribution. Extensive experiments across multiple student models and reasoning benchmarks demonstrate the effectiveness of SPOT in improving reasoning performance while balancing solution quality and coverage.

In most machine learning tasks, we evaluate a model M on a given data population S by measuring a population-level metric F(S;M). Examples of such evaluation metric F include precision/recall for (binary) recognition, the F1 score for multi-class classification, and the BLEU metric for language generation. On the other hand, the model M is trained by optimizing a sample-level loss G(S_t;M) at each learning step t, where S_t is a subset of S (a.k.a. the mini-batch). Popular choices of G include cross-entropy loss, the Dice loss, and sentence-level BLEU scores. A fundamental assumption behind this paradigm is that the mean value of the sample-level loss G, if averaged over all possible samples, should effectively represent the population-level metric F of the task, such as, that E[ G(S_t;M) ] approx F(S;M). In this paper, we systematically investigate the above assumption in several NLP tasks. We show, both theoretically and experimentally, that some popular designs of the sample-level loss G may be inconsistent with the true population-level metric F of the task, so that models trained to optimize the former can be substantially sub-optimal to the latter, a phenomenon we call it, Simpson's bias, due to its deep connections with the classic paradox known as Simpson's reversal paradox in statistics and social sciences.

The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six different reasoning benchmarks, we find that step-level uniformity not only provides a strong theoretical lens but also yields practical performance benefits; for example, selecting reasoning traces with more uniform information density at the step-level improves accuracy by 10-32\% relative gains over baselines at AIME2025. Our analysis further reveals that correct reasoning traces tend to avoid sharp information density spikes, while incorrect traces exhibit irregular information bursts. These results demonstrate that UID-inspired information density measures outperform alternative internal signals as predictors of reasoning quality. Results highlight the uniformity of the information density as a robust diagnostic and selection criterion for building more reliable and accurate reasoning systems.

Risk decision systems in fraud detection and credit scoring operate under structural label absence: ground truth arrives weeks to months after decisions are made. During this blind period, model performance may degrade silently, eroding the governance evidence that justifies automated decisions. Existing drift detection methods either require labels (supervised detectors) or detect statistical change without distinguishing harmful degradation from benign distributional evolution (unsupervised detectors). No existing framework integrates drift detection with governance evidence assessment and operational response. This paper presents a label-free governance monitoring extension to the Governance Drift Toolkit that produces governance alerts rather than statistical alarms. The monitoring architecture applies composite multi-proxy monitoring across four proxy monitors (score distribution, feature drift, prediction entropy, confidence distribution), with governance-calibrated thresholds. Empirical evaluation on the Lending Club credit scoring dataset (1.37M loans, 11 years) demonstrates three findings. First, raw proxy metrics (Feature PSI delta up to 1.84, Score PSI delta up to 0.92) distinguish injected covariate degradation from natural temporal drift in an offline evaluation setting. Second, pure concept drift in P(Y|X) produces exactly zero delta across all proxy metrics in all windows, confirming the irreducible blind spot of label-free monitoring as a structural verification. Third, the composite score provides monotonic severity progression as more monitors trigger (0.583 to 0.833 to 1.000), enabling graduated governance response. Cross-domain comparison with IEEE-CIS fraud detection results shows the detectable/undetectable boundary is consistent across both domains. The toolkit and evaluation code are available as open-source artifacts.

This paper presents the first empirical demonstration of controllable locality in transformer language models, a novel architectural framework that enables continuous control over the degree of representation localization through a tunable locality dial parameter. Unlike traditional language models that rely exclusively on distributed representations, our approach allows dynamic interpolation between highly interpretable localist encodings and efficient distributed representations without requiring model retraining. We conducted experiments on the WikiText corpus using a two-layer transformer architecture, systematically varying the locality parameter λ across the full spectrum from 1.0 (fully localist) to 0.0 (fully distributed). Our results demonstrate that localist configurations achieve dramatically lower attention entropy, with λ = 1.0 yielding 5.36 bits compared to 7.18 bits at λ = 0.0, while maintaining substantially higher pointer fidelity scores reflecting stronger alignment with rule-specified targets. Prediction experiments reveal that intermediate locality values optimize the tradeoff between interpretability and performance, with λ = 0.6 achieving test perplexity of 4.65 and accuracy of 84.7%. These findings establish that localist language models provide a practical framework for applications in regulated domains requiring both transparency and capability, offering precise mathematical control over the interpretability-performance spectrum through explicit penalty thresholds and information-theoretic design principles.

Modern embodied agents achieve impressive success rates, yet their actual instruction-following ability is far weaker than these numbers suggest. We trace this illusion to a structural property we term low scene entropy: when a visual scene admits only one valid task, language becomes redundant and a policy can score highly while barely using it. We introduce RoboFollow, a diagnostic benchmark with three principles: (1) High Scene Entropy: each training scene supports multiple kinematically distinct task branches, making vision alone insufficient and forcing reliance on language. (2) Hierarchical Diagnostic Protocol: a four-level protocol (L0--L3) progressively perturbs visual layout and semantics, probing whether equivalent instructions yield consistent behavior and distinct ones yield discriminable behavior across spatial relations, attributes, trajectory constraints, and logic. (3) Confound-Controlled Diagnosis: we simplify interaction objects, restrict actions to the trained repertoire and report stage-wise Intent and Execution scores, isolating comprehension from motor execution. Evaluation of nine VLA and WAM policies shows that strong L0 performance, where attained, does not reliably transfer to L1--L3 under our fine-tuning setup. Representative mitigations, including stronger VLM backbones, QA co-training, LangForce, and Classifier-Free Guidance, all fail to close this gap. RoboFollow exposes genuine instruction following as a critical, overlooked bottleneck. Code and dataset are available at https://github.com/AutoLab-SAI-SJTU/RoboFollow and https://huggingface.co/datasets/AutoLab-SJTU/robofollow-data.

Neural sentence embedding models for dense retrieval typically rely on binary relevance labels, treating query-document pairs as either relevant or irrelevant. However, real-world relevance often exists on a continuum, and recent advances in large language models (LLMs) have made it feasible to scale the generation of fine-grained graded relevance labels. In this work, we propose BiXSE, a simple and effective pointwise training method that optimizes binary cross-entropy (BCE) over LLM-generated graded relevance scores. BiXSE interprets these scores as probabilistic targets, enabling granular supervision from a single labeled query-document pair per query. Unlike pairwise or listwise losses that require multiple annotated comparisons per query, BiXSE achieves strong performance with reduced annotation and compute costs by leveraging in-batch negatives. Extensive experiments across sentence embedding (MMTEB) and retrieval benchmarks (BEIR, TREC-DL) show that BiXSE consistently outperforms softmax-based contrastive learning (InfoNCE), and matches or exceeds strong pairwise ranking baselines when trained on LLM-supervised data. BiXSE offers a robust, scalable alternative for training dense retrieval models as graded relevance supervision becomes increasingly accessible.

Large vision transformers present impressive scalability, as their performance can be well improved with increased model capacity. Nevertheless, their cumbersome parameters results in exorbitant computational and memory demands. By analyzing prevalent transformer structures, we find that multilayer perceptron (MLP) modules constitute the largest share of the model's parameters. In this paper, we propose an Adaptive MLP Pruning (AMP) method to substantially reduce the parameters of large vision transformers without obvious performance degradation. First, we adopt Taylor based method to evaluate neuron importance of MLP. However, the importance computation using one-hot cross entropy loss ignores the potential predictions on other categories, thus degrading the quality of the evaluated importance scores. To address this issue, we introduce label-free information entropy criterion to fully model the predictions of the original model for more accurate importance evaluation. Second, we rank the hidden neurons of MLP by the above importance scores and apply binary search algorithm to adaptively prune the ranked neurons according to the redundancy of different MLP modules, thereby avoiding the predefined compression ratio. Experimental results on several state-of-the-art large vision transformers, including CLIP and DINOv2, demonstrate that our method achieves roughly 40\% parameter and FLOPs reduction in a near lossless manner. Moreover, when the models are not finetuned after pruning, our method outperforms other pruning methods by significantly large margin. The source code and trained weights are available at https://github.com/visresearch/AMP.

Machine unlearning has emerged as a critical capability for addressing privacy, safety, and regulatory concerns in large language models (LLMs). Existing methods operate at the sequence level, applying uniform updates across all tokens despite only a subset encoding the knowledge targeted for removal. This introduces gradient noise, degrades utility, and leads to suboptimal forgetting. We propose TokenUnlearn, a token-level attribution framework that identifies and selectively targets critical tokens. Our approach combines knowledge-aware signals via masking, and entropy-aware signals to yield importance scores for precise token selection. We develop two complementary strategies: hard selection, applying unlearning only to high-importance tokens, and soft weighting, modulating gradient contributions based on importance scores. Both extend existing methods to token-level variants. Theoretical analysis shows token-level selection improves gradient signal-to-noise ratio. Experiments on TOFU and WMDP benchmarks across three model architectures demonstrate consistent improvements over sequence-level baselines in both forgetting effectiveness and utility preservation.

Sequential recommendation models often struggle to capture latent periodic patterns in user interests, primarily due to the noise inherent in time-domain behavioral data. While frequency-domain analysis offers a global perspective to address this, existing approaches typically treat user sequences in isolation, overlooking the crucial context of the target item. In this work, we present a novel empirical observation: user attention scores exhibit distinct spectral entropy distributions when conditioned on positive versus negative target items. Specifically, true user interests manifest as highly concentrated spectral patterns with lower entropy in the frequency domain, whereas irrelevant behaviors appear as high-entropy noise. Leveraging this insight, we propose the Frequency-Enhanced Deep Interest Network (FEDIN). FEDIN introduces a frequency-domain branch that utilizes a target-aware spectrum filtering mechanism to isolate these periodic interest signals. Extensive experiments on three public datasets demonstrate that FEDIN consistently outperforms state-of-the-art sequential recommendation baselines, demonstrating superior robustness against noise. We have released our code at: https://github.com/otokoneko/FEDIN.

Reinforcement learning is crucial for aligning large language models to perform complex reasoning tasks. However, current algorithms such as Group Relative Policy Optimization suffer from coarse grained, sequence level credit assignment, which severely struggles to isolate pivotal reasoning steps within long Chain of Thought generations. Furthermore, the standard unbounded Kullback Leibler divergence penalty induces severe gradient instability and mode seeking conservatism, ultimately stifling the discovery of novel reasoning trajectories. To overcome these limitations, we introduce Distribution Guided Policy Optimization, a novel critic free reinforcement learning framework that reinterprets distribution deviation as a guiding signal rather than a rigid penalty. DGPO replaces the volatile KL divergence with the bounded Hellinger distance to safely quantify token level exploration without the risk of gradient explosion. To effectively distinguish genuine reasoning breakthroughs from hallucinatory noise, we propose an entropy gating mechanism that scales this deviation by the policy`s epistemic uncertainty. By dynamically redistributing the coarse sequence-level advantage to individual tokens based on these gated scores, DGPO heavily incentivizes critical exploratory steps while suppressing unwarranted, low-entropy deviations. Consequently, DGPO completely eliminates the traditional token-level KL penalty and achieves fine-grained credit reallocation without the computational overhead of an additional value network. Extensive empirical evaluations demonstrate that DGPO sets a new state-of-the-art for critic free alignment. Notably, on the Qwen2.5-32B architecture, DGPO achieves 60.0% Avg@32 accuracy and 46.0% Avg@32 accuracy on the challenging AIME2024 and AIME2025 benchmarks respectively, substantially outperforming competitive baselines like DAPO.

The S{\o}rensen--Dice Coefficient has recently seen rising popularity as a loss function (also known as Dice loss) due to its robustness in tasks where the number of negative samples significantly exceeds that of positive samples, such as semantic segmentation, natural language processing, and sound event detection. Conventional training of polyphonic sound event detection systems with binary cross-entropy loss often results in suboptimal detection performance as the training is often overwhelmed by updates from negative samples. In this paper, we investigated the effect of the Dice loss, intra- and inter-modal transfer learning, data augmentation, and recording formats, on the performance of polyphonic sound event detection systems with multichannel inputs. Our analysis showed that polyphonic sound event detection systems trained with Dice loss consistently outperformed those trained with cross-entropy loss across different training settings and recording formats in terms of F1 score and error rate. We achieved further performance gains via the use of transfer learning and an appropriate combination of different data augmentation techniques.

Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for hallucination detection that analyzes the evolution of hidden-state semantics across transformer layers. Unlike prior methods that rely on multiple sampling passes or external verification sources, LSD operates intrinsically within the model's representational space. Using margin-based contrastive learning, LSD aligns hidden activations with ground-truth embeddings derived from a factual encoder, revealing a distinct separation in semantic trajectories: factual responses preserve stable alignment, while hallucinations exhibit pronounced semantic drift across depth. Evaluated on the TruthfulQA and synthetic factual-hallucination datasets, LSD achieves an F1-score of 0.92, AUROC of 0.96, and clustering accuracy of 0.89, outperforming SelfCheckGPT and Semantic Entropy baselines while requiring only a single forward pass. This efficiency yields a 5-20x speedup over sampling-based methods without sacrificing precision or interpretability. LSD offers a scalable, model-agnostic mechanism for real-time hallucination monitoring and provides new insights into the geometry of factual consistency within large language models.

The growing complexity of machine learning (ML) models in big data analytics, especially in domains such as environmental monitoring, highlights the critical need for interpretability and explainability to promote trust, ethical considerations, and regulatory adherence (e.g., GDPR). Traditional "black-box" models obstruct transparency, whereas post-hoc explainable AI (XAI) techniques like LIME and SHAP frequently compromise accuracy or fail to deliver inherent insights. This paper presents a novel framework that combines type-2 fuzzy sets, granular computing, and clustering to boost explainability and fairness in big data environments. When applied to the UCI Air Quality dataset, the framework effectively manages uncertainty in noisy sensor data, produces linguistic rules, and assesses fairness using silhouette scores and entropy. Key contributions encompass: (1) A type-2 fuzzy clustering approach that enhances cohesion by about 4% compared to type-1 methods (silhouette 0.365 vs. 0.349) and improves fairness (entropy 0.918); (2) Incorporation of fairness measures to mitigate biases in unsupervised scenarios; (3) A rule-based component for intrinsic XAI, achieving an average coverage of 0.65; (4) Scalable assessments showing linear runtime (roughly 0.005 seconds for sampled big data sizes). Experimental outcomes reveal superior performance relative to baselines such as DBSCAN and Agglomerative Clustering in terms of interpretability, fairness, and efficiency. Notably, the proposed method achieves a 4% improvement in silhouette score over type-1 fuzzy clustering and outperforms baselines in fairness (entropy reduction by up to 1%) and efficiency.

Multi-teacher on-policy distillation (MOPD) integrates specialized capabilities into a single student, but existing practice typically hard-routes each prompt to a domain-matched teacher for the entire rollout. This dependence on prompt-level domain labels restricts using unlabeled training mixtures and leaves complementary signals from other teachers unused. We introduce MOPD-Router, a framework that routes supervision over the full teacher pool at each token, without domain labels or training a separate routing model. Its plug-in interface supports different metrics for selecting and weighting teacher-specific OPD signals. Within this interface, we propose ExpertAlign, which scores each teacher by whether its correction to the student at the current token expresses the specialization that teacher acquired during post-training, and compare it against two reference metrics built on teacher confidence (Entropy) and teacher-student discrepancy (Novelty). Experiments on unlabeled and domain-labeled training mixtures under strong-to-weak and same-size distillation scenarios show that ExpertAlign achieves the strongest overall performance in all four settings. On unlabeled data, it improves the overall score by 5.88 (+12.3%) points over Mean aggregation; on domain-labeled data, it outperforms standard MOPD by 3.95 (+7.8%) points without using available domain labels. These results demonstrate token-level routing can exploit cross-domain complementary supervision, and reduce exclusive reliance on prompt-level domain assignment. Code is available at: https://github.com/TURLEing/MOPD-Router.

On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation. The same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD^2 and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

Synthesizing human's movements such as dancing is a flourishing research field which has several applications in computer graphics. Recent studies have demonstrated the advantages of deep neural networks (DNNs) for achieving remarkable performance in motion and music tasks with little effort for feature pre-processing. However, applying DNNs for generating dance to a piece of music is nevertheless challenging, because of 1) DNNs need to generate large sequences while mapping the music input, 2) the DNN needs to constraint the motion beat to the music, and 3) DNNs require a considerable amount of hand-crafted data. In this study, we propose a weakly supervised deep recurrent method for real-time basic dance generation with audio power spectrum as input. The proposed model employs convolutional layers and a multilayered Long Short-Term memory (LSTM) to process the audio input. Then, another deep LSTM layer decodes the target dance sequence. Notably, this end-to-end approach has 1) an auto-conditioned decode configuration that reduces accumulation of feedback error of large dance sequence, 2) uses a contrastive cost function to regulate the mapping between the music and motion beat, and 3) trains with weak labels generated from the motion beat, reducing the amount of hand-crafted data. We evaluate the proposed network based on i) the similarities between generated and the baseline dancer motion with a cross entropy measure for large dance sequences, and ii) accurate timing between the music and motion beat with an F-measure. Experimental results revealed that, after training using a small dataset, the model generates basic dance steps with low cross entropy and maintains an F-measure score similar to that of a baseline dancer.

As large language models (LLMs) like GPT-4 and Llama 3 become integral to educational contexts, concerns are mounting over the cultural biases, power imbalances, and ethical limitations embedded within these technologies. Though generative AI tools aim to enhance learning experiences, they often reflect values rooted in Western, Educated, Industrialized, Rich, and Democratic (WEIRD) cultural paradigms, potentially sidelining diverse global perspectives. This paper proposes a framework to assess and mitigate cultural bias within LLMs through the lens of applied multiplexity. Multiplexity, inspired by Senturk et al. and rooted in Islamic and other wisdom traditions, emphasizes the coexistence of diverse cultural viewpoints, supporting a multi-layered epistemology that integrates both empirical sciences and normative values. Our analysis reveals that LLMs frequently exhibit cultural polarization, with biases appearing in both overt responses and subtle contextual cues. To address inherent biases and incorporate multiplexity in LLMs, we propose two strategies: Contextually-Implemented Multiplex LLMs, which embed multiplex principles directly into the system prompt, influencing LLM outputs at a foundational level and independent of individual prompts, and Multi-Agent System (MAS)-Implemented Multiplex LLMs, where multiple LLM agents, each representing distinct cultural viewpoints, collaboratively generate a balanced, synthesized response. Our findings demonstrate that as mitigation strategies evolve from contextual prompting to MAS-implementation, cultural inclusivity markedly improves, evidenced by a significant rise in the Perspectives Distribution Score (PDS) and a PDS Entropy increase from 3.25\% at baseline to 98\% with the MAS-Implemented Multiplex LLMs. Sentiment analysis further shows a shift towards positive sentiment across cultures,...

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

Large Language Models (LLMs) have achieved remarkable progress across reasoning, generation, and decision-making tasks, yet deploying them on mobile, embedded, and edge devices remains particularly challenging. On-device LLM inference is heavily constrained by the memory and bandwidth overhead of the key-value (KV) cache, which grows linearly with context length and often dominates decoding cost. Existing KV-cache quantization schemes typically rely on fixed precision or hand-crafted heuristics, thereby wasting bits on low-impact tokens while over-compressing informative ones, leading to avoidable accuracy degradation. Inspired by Huffman coding's principle of variable-length allocation, we propose adaptive KV-cache quantization, a learned policy that assigns bit-width proportional to token importance, minimizing expected memory and latency without sacrificing competitive accuracy. Our framework extracts lightweight token-level features, including token frequency, quality score, attention variance, and entropy-based uncertainty, and feeds them into a compact data-driven controller that dynamically selects KV precision from {2-bit, 4-bit, 8-bit, FP16} during decoding. This adaptive precision policy reduces KV memory footprint and latency while improving accuracy compared to static KV quantization and rule-based baselines, and maintaining competitive accuracy close to FP16 inference across standard LLM benchmarks. Extensive experiments across multiple commonsense reasoning benchmarks using SmolLM-135M, SmolLM-360M, and SmolLM-1.7B demonstrate that our controller consistently improves the accuracy-latency trade-off. For instance, with SmolLM-360M on HellaSwag, our method reduces decoding latency (ms/token) by 17.75% relative to static KV quantization, improves accuracy by 7.60 points, and remains within only 0.30 points of FP16 inference.

Reinforcement learning with verifiable rewards (RLVR) broadcasts a single response-level reward to every token, while on-policy distillation (OPD) scores each token against a stronger teacher for a dense advantage but caps performance at teacher quality and discourages exploration beyond it. Their complementarity makes combining RLVR and OPD promising, but we find that fusing the two advantages with a fixed coefficient triggers entropy collapse from two miscalibrations: a magnitude mismatch, where token-level OPD advantages can spike far beyond the bounded RLVR advantage and erase its signal, and a temporal mismatch, where sustained full-strength OPD keeps pulling the student toward the teacher and limits exploration needed to surpass it. We propose SAF, a Stable Advantage Fusion framework that resolves both issues via a lightweight, four-stage pipeline applied only to the OPD advantage: a sparsify-then-compress mechanism for magnitude control paired with a warm-up-then-anneal mechanism for temporal control, with each stage independently switchable and adding negligible overhead. Instantiating RLVR with GRPO, we evaluate SAF across seven mathematical reasoning and code generation benchmarks with Qwen3-1.7B/4B/8B: SAF avoids entropy collapse and consistently outperforms fixed-coefficient GRPO+OPD fusion, improving the aggregate score by 0.51-2.70% across all six model-domain settings while achieving more stable training.

In the deep learning (DL) era, parsing models are extremely simplified with little hurt on performance, thanks to the remarkable capability of multi-layer BiLSTMs in context representation. As the most popular graph-based dependency parser due to its high efficiency and performance, the biaffine parser directly scores single dependencies under the arc-factorization assumption, and adopts a very simple local token-wise cross-entropy training loss. This paper for the first time presents a second-order TreeCRF extension to the biaffine parser. For a long time, the complexity and inefficiency of the inside-outside algorithm hinder the popularity of TreeCRF. To address this issue, we propose an effective way to batchify the inside and Viterbi algorithms for direct large matrix operation on GPUs, and to avoid the complex outside algorithm via efficient back-propagation. Experiments and analysis on 27 datasets from 13 languages clearly show that techniques developed before the DL era, such as structural learning (global TreeCRF loss) and high-order modeling are still useful, and can further boost parsing performance over the state-of-the-art biaffine parser, especially for partially annotated training data. We release our code at https://github.com/yzhangcs/crfpar.

Tokenization is fundamental to Natural Language Processing (NLP), directly impacting model efficiency and linguistic fidelity. While Byte Pair Encoding (BPE) is widely used in Large Language Models (LLMs), it often disregards morpheme boundaries, leading to suboptimal segmentation, particularly in morphologically rich languages. We introduce MorphBPE, a morphology-aware extension of BPE that integrates linguistic structure into subword tokenization while preserving statistical efficiency. Additionally, we propose two morphology-based evaluation metrics: (i) Morphological Consistency F1-Score, which quantifies the consistency between morpheme sharing and token sharing, contributing to LLM training convergence, and (ii) Morphological Edit Distance, which measures alignment between morphemes and tokens concerning interpretability. Experiments on English, Russian, Hungarian, and Arabic across 300M and 1B parameter LLMs demonstrate that MorphBPE consistently reduces cross-entropy loss, accelerates convergence, and improves morphological alignment scores. Fully compatible with existing LLM pipelines, MorphBPE requires minimal modifications for integration. The MorphBPE codebase and tokenizer playground will be available at: https://github.com/llm-lab-org/MorphBPE and https://tokenizer.llm-lab.org

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

Large Language Models (LLMs) are increasingly deployed in scenarios demanding ultra-long context reasoning, such as agentic workflows and deep research understanding. However, long-context inference is constrained by the KV cache, a transient memory structure that grows linearly with sequence length and batch size, quickly dominating GPU memory usage. Existing memory reduction techniques, including eviction and quantization, often rely on static heuristics and suffer from degraded quality under tight budgets. In this paper, we propose ARKV, a lightweight and adaptive framework that dynamically allocates precision levels to cached tokens based on per-layer attention dynamics and token-level importance. During a short prefill phase, ARKV estimates the original quantization (OQ) ratio of each layer by computing statistical scores such as attention entropy, variance and kurtosis. During decoding, tokens are assigned to one of three states, Original (full precision), Quantization (low precision), or Eviction, according to a fast heavy-hitter scoring strategy. Our experiments on LLaMA3 and Qwen3 models across diverse long- and short-context tasks demonstrate that ARKV preserves ~97% of baseline accuracy on long-context benchmarks while reducing KV memory usage by 4x, with minimal throughput loss. On short-context tasks, ARKV matches full-precision baselines; on GSM8K math reasoning, it significantly outperforms uniform quantization. These results highlight the practical viability of ARKV for scalable LLM deployment, offering fine-grained, data-driven memory control without retraining or architectural modifications. The source code and artifacts can be found in: https://github.com/Large-scale-Sustainable-Computing-LSC/ARKV

Large language models (LLMs) frequently achieve impressive scores on standardized benchmarks, yet accuracy alone offers a limited view of their capabilities. Evaluating open-source LLMs through leaderboards faces persistent issues like data contamination, narrow task scope, and weak alignment with real-world reliability. Benchmark-based evaluations such as MMLU PRO, BBH, or IFEval primarily capture what a model outputs on fixed test sets, not how it processes information, calibrates uncertainty, or structures internal knowledge. In this article, we advocate for a shift from benchmark-centric evaluation toward a complementary, state-centered intrinsic assessment of LLMs. To this end, we introduce Latent Performance Profiling (LPP) -- a framework that derives task-agnostic diagnostics from hidden activations and output distributions. LPP defines a set of scalar metrics on a model's latent representations and dynamics, revealing scale-independent traits that enable interpretable comparisons and uncover hidden vulnerabilities. Unlike static accuracy scores, LPP provides stable, architecture-sensitive signatures across models of similar size. With extensive empirical analyses across eight LLMs, spanning a size range of 0.5B-14B, we demonstrate that models with similar benchmark scores can exhibit contrasting latent profiles, such as differences in entropy or adaptability. Guided by these insights, we design synthetic probes for uncertainty and symbolic reasoning that align with intrinsic metrics while decoupling from leaderboard bias. We recommend that reporting LPP alongside benchmarks provides a deeper, interpretable understanding of model behavior, enabling more reliable model selection, safety assessment, and evaluation beyond surface-level accuracy.

Machine learning classifiers for bearing fault detection produce scalar confidence scores that conflate confident errors with genuinely ambiguous predictions, and the conventional truth/falsity pair (F = 1 - T) is algebraically redundant by construction. We operationalize a refined neutrosophic decomposition of a Random Forest + XGBoost + Logistic Regression ensemble into four indicators -- T-hat (top-class evidence), F-hat (best-competitor evidence), predictive entropy I1-hat, and decision disagreement I2-hat -- evaluated on two bearing benchmarks (CWRU and JNU, 600-1000 rpm) under a leave-one-condition-out protocol. On CWRU, after correcting a file-to-class mapping error, the ensemble reaches 100.00 percent accuracy on three of four held-out loads (92.27 percent on the fourth), leaving too few errors for uncertainty analysis. On JNU, holding out 1000 rpm, accuracy collapses to 40.64 percent, below a majority-class baseline; Logistic Regression (57.91 percent) generalizes far better than the tree ensembles. I1-hat shows a robust association with error beyond T-hat/F-hat, while I2-hat contributes little; standalone Logistic Regression confidence outperforms the full decomposition, a boundary condition we report honestly. Two further results extend this: fusing a time-domain and a frequency-domain model of the same signal and scoring their Jensen-Shannon divergence beats that model own entropy (AURC 0.29 vs. 0.36 on the standard split; 0.54 vs. 0.73 under a harder single-condition reproduction), the only indicator moving correctly under a CWRU-versus-JNU distributional-shift contrast; and, on CWRU alone, literature-verified bearing fault frequencies, correctly demodulated via the envelope spectrum, separate most fault classes almost perfectly (99.57 percent) using three interpretable features. Code, logs, and figures are released for independent verification.

When training large language models with reinforcement learning, terminal rewards provide little guidance about which steps matter. Common methods for assigning step credit overlook that work built on uncorrected mistakes is wasted while independent work remains valid. With only a final success/failure reward, every step in a failed episode has zero total future reward, even when it made progress. We propose Dependency-Aware Reward Shaping (DARS), which represents task progress as predicates linked by prerequisite relations and assigns step-level credit over the dependency graph. An annotator marks which predicates each step verifies, invalidates, or repairs. Verified predicates are discounted according to graph distance from the nearest broken prerequisite, while independent predicates are unaffected. Repairs update these weights based on any errors that remain; invalidated predicates need re-verification to regain credit. A fixed potential converts these annotations into signed per-step rewards. A common reward and annotation interface allows DARS to integrate with a range of reasoning and agentic training methods, such as GiGPO and ARPO/AEPO, without changing their rollout strategies or optimizers. Across five task families and models from 1.5B to 8B, DARS improves success by up to 10 points over GiGPO trained with the same budget and harness (ALFWorld), raises the WebShop task score and Search-R1 QA accuracy, complements AEPO's entropy-based training on AIME24/25 with a Python interpreter, and exceeds OmniOPD in controlled tool-free reasoning comparisons at 1.7B and 4B. Ablations show that step-level credit, dependency attenuation, and graph topology each contribute. On ALFWorld, a distilled 8B annotator matches the API annotator, enabling DARS to run efficiently without a frontier judge. Code is available at https://github.com/JianhuiWei7/DARS.

In this paper, we uncover a systematic bias in the evaluation paradigm of adopting large language models~(LLMs), e.g., GPT-4, as a referee to score and compare the quality of responses generated by candidate models. We find that the quality ranking of candidate responses can be easily hacked by simply altering their order of appearance in the context. This manipulation allows us to skew the evaluation result, making one model appear considerably superior to the other, e.g., Vicuna-13B could beat ChatGPT on 66 over 80 tested queries with ChatGPT as an evaluator. To address this issue, we propose a calibration framework with three simple yet effective strategies: 1) Multiple Evidence Calibration, which requires the evaluator model to generate multiple evaluation evidence before assigning ratings; 2) Balanced Position Calibration, which aggregates results across various orders to determine the final score; 3) Human-in-the-Loop Calibration, which introduces a balanced position diversity entropy to measure the difficulty of each example and seeks human assistance when needed. We also manually annotate the "win/tie/lose" outcomes of responses from ChatGPT and Vicuna-13B in the Vicuna Benchmark's question prompt, and extensive experiments demonstrate that our approach successfully mitigates evaluation bias, resulting in closer alignment with human judgments. We release our code and human annotation at https://github.com/i-Eval/FairEval to facilitate future research.

Monitoring complex assembly processes is critical for maintaining productivity and ensuring compliance with assembly standards. However, variability in human actions and subjective task preferences complicate accurate task anticipation and guidance. To address these challenges, we introduce the Multi-Modal Transformer Fusion and Recurrent Units (MMTFRU) Network for egocentric activity anticipation, utilizing multimodal fusion to improve prediction accuracy. Integrated with the Operator Action Monitoring Unit (OAMU), the system provides proactive operator guidance, preventing deviations in the assembly process. OAMU employs two strategies: (1) Top-5 MMTF-RU predictions, combined with a reference graph and an action dictionary, for next-step recommendations; and (2) Top-1 MMTF-RU predictions, integrated with a reference graph, for detecting sequence deviations and predicting anomaly scores via an entropy-informed confidence mechanism. We also introduce Time-Weighted Sequence Accuracy (TWSA) to evaluate operator efficiency and ensure timely task completion. Our approach is validated on the industrial Meccano dataset and the largescale EPIC-Kitchens-55 dataset, demonstrating its effectiveness in dynamic environments.

For RL algorithms, appropriate entropy control is crucial to their effectiveness. To control the policy entropy, a commonly used method is entropy regularization, which is adopted in various popular RL algorithms including PPO, SAC and A3C. Although entropy regularization proves effective in robotic and games RL conventionally, studies found that it gives weak to no gains in LLM-RL training. In this work, we study the issues of entropy bonus in LLM-RL setting. Specifically, we first argue that the conventional entropy regularization suffers from the LLM's extremely large response space and the sparsity of the optimal outputs. As a remedy, we propose AEnt, an entropy control method that utilizes a new clamped entropy bonus with an automatically adjusted coefficient. The clamped entropy is evaluated with the re-normalized policy defined on certain smaller token space, which encourages exploration within a more compact response set. In addition, the algorithm automatically adjusts entropy coefficient according to the clamped entropy value, effectively controlling the entropy-induced bias while leveraging the entropy's benefits. AEnt is tested in math-reasoning tasks under different base models and datasets, and it is observed that AEnt outperforms the baselines consistently across multiple benchmarks.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Multi-agent systems (MAS) have emerged as a prominent paradigm for leveraging large language models (LLMs) to tackle complex tasks. However, the mechanisms governing the effectiveness of MAS built upon publicly available LLMs, specifically the underlying rationales for their success or failure, remain largely unexplored. In this paper, we revisit MAS through the perspective of entropy, considering both intra- and inter-agent dynamics by investigating entropy transitions during problem-solving across various topologies, six reasoning benchmarks, and two agentic tasks. By analyzing 245 features spanning token-, agent-, and round-level entropy, we counterintuitively find that a single agent outperforms MAS in approximately 43.3\% of cases, and that entropy dynamics are largely determined during the first round of interaction. Furthermore, we provide three key observations: 1) Certainty Preference: peak entropy directly harms and stable entropy directly benefits MAS correctness; 2) Base Entropy: base models with lower entropy during problem-solving causally drive MAS performance; and 3) Task Awareness: entropy dynamics of MAS play varying roles across different tasks. Building on these insights, we introduce a simple yet effective algorithm, the Entropy Judger, to select solutions from MAS's pass@k results, leading to consistent accuracy improvements across all MAS configurations and tasks. Our source code is available at https://github.com/AgenticFinLab/multiagent-entropy{this https URL}.

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution. This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution. Our code is available at: https://github.com/iNLP-Lab/PEAR.

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5\%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20\% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.

Uncertainty estimation is crucial for evaluating Large Language Models (LLMs), particularly in high-stakes domains where incorrect answers result in significant consequences. Numerous approaches consider this problem, while focusing on a specific type of uncertainty, ignoring others. We investigate what estimates, specifically token-wise entropy and model-as-judge (MASJ), would work for multiple-choice question-answering tasks for different question topics. Our experiments consider three LLMs: Phi-4, Mistral, and Qwen of different sizes from 1.5B to 72B and 14 topics. While MASJ performs similarly to a random error predictor, the response entropy predicts model error in knowledge-dependent domains and serves as an effective indicator of question difficulty: for biology ROC AUC is 0.73. This correlation vanishes for the reasoning-dependent domain: for math questions ROC-AUC is 0.55. More principally, we found out that the entropy measure required a reasoning amount. Thus, data-uncertainty related entropy should be integrated within uncertainty estimates frameworks, while MASJ requires refinement. Moreover, existing MMLU-Pro samples are biased, and should balance required amount of reasoning for different subdomains to provide a more fair assessment of LLMs performance.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, an all-round framework is presented which relies on a feedforward neural network, the selection of physically-meaningful features and, when applicable, joint-learning. Next to being faster in terms of training time, this approach is shown to outperform current graph-network models on small datasets. In particular, the vibrational entropy at 305 K of crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint-learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps understanding the underlying physics.

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific operational constraints. In this paper, we present a new machine learning approach to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm for non-convex settings to efficiently recover its optimal solution. We improve our algorithm with specialized techniques to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our approach can fit risk scores in a way that scales linearly in the number of samples, provides a certificate of optimality, and obeys real-world constraints without parameter tuning or post-processing. We benchmark the performance benefits of this approach through an extensive set of numerical experiments, comparing to risk scores built using heuristic approaches. We also discuss its practical benefits through a real-world application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital.

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Strictly proper scoring rules identify the true conditional class distribution at population level, but their curvature can alter optimization and finite-sample behavior. We study three multiclass objectives: a class-aware quadratic Bregman score (CAPM), a strongly convex generator with constrained log-cosh ridges (HPG), and an HPG objective with an annealed probability-margin penalty (APMS). CAPM is treated as a structured instance of established quadratic scoring-rule theory. We derive conditional-regret, curvature, range, and logit-gradient bounds for CAPM and HPG, and prove exact penalty-range and conditional-target displacement bounds for APMS. Controlled five-seed experiments use Digits, Wisconsin breast cancer, and synthetic confusion and long-tail problems under clean labels, symmetric and pair-flip corruption, class imbalance, calibration evaluation, input corruption, and first-order adversarial perturbations. The candidates are close to cross-entropy on clean data and show descriptive gains in some noisy-label cells, but the five-seed comparisons are interpreted descriptively rather than as significance evidence. The selected noisy-label baselines perform better on Digits with 40% symmetric label noise, and explicit prior-adjustment methods perform better in the 30:1 synthetic long-tail experiment. Ablations do not show a consistent benefit from the candidate-specific graph, ridge, or margin components. The mathematical analysis establishes the stated properties, and the experiments delimit the empirical evidence; together they do not support a claim of general superiority.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.

The development of large language models (LLMs) has achieved superior performance in a range of downstream tasks, including LLM-based retrieval-augmented generation (RAG). The quality of generated content heavily relies on the usefulness of the retrieved information and the capacity of LLMs' internal information processing mechanism to incorporate it in answer generation. It is generally assumed that the retrieved information is relevant to the question. However, the retrieved information may have a variable degree of relevance and usefulness, depending on the question and the document collection. It is important to take into account the relevance of the retrieved information in answer generation. In this paper, we propose OpenDecoder, a new approach that leverages explicit evaluation of the retrieved information as quality indicator features for generation. We aim to build a RAG model that is more robust to varying levels of noisy context. Three types of explicit evaluation information are considered: relevance score, ranking score, and QPP (query performance prediction) score. The experimental results on five benchmark datasets demonstrate the effectiveness and better robustness of OpenDecoder by outperforming various baseline methods. Importantly, this paradigm is flexible to be integrated with the post-training of LLMs for any purposes and incorporated with any type of external indicators.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

Domain-specific large language models (LLMs), typically developed by fine-tuning a pre-trained general-purpose LLM on specialized datasets, represent a significant advancement in applied AI. A common strategy in LLM fine-tuning is curriculum learning, which pre-orders training samples based on metrics like difficulty to improve learning efficiency compared to a random sampling strategy. However, most existing methods for LLM fine-tuning rely on a static curriculum, designed prior to training, which lacks adaptability to the model's evolving needs during fine-tuning. To address this, we propose EDCO, a novel framework based on two key concepts: inference entropy and dynamic curriculum orchestration. Inspired by recent findings that maintaining high answer entropy benefits long-term reasoning gains, EDCO prioritizes samples with high inference entropy in a continuously adapted curriculum. EDCO integrates three core components: an efficient entropy estimator that uses prefix tokens to approximate full-sequence entropy, an entropy-based curriculum generator that selects data points with the highest inference entropy, and an LLM trainer that optimizes the model on the selected curriculum. Comprehensive experiments in communication, medicine and law domains, EDCO outperforms traditional curriculum strategies for fine-tuning Qwen3-4B and Llama3.2-3B models under supervised and reinforcement learning settings. Furthermore, the proposed efficient entropy estimation reduces computational time by 83.5% while maintaining high accuracy.

Reinforcement learning (RL) has enabled machine learning models to achieve significant advances in many fields. Most recently, RL has empowered frontier language models to solve challenging math, science, and coding problems. However, central to any RL algorithm is the reward function, and reward engineering is a notoriously difficult problem in any domain. In this paper, we propose RENT: Reinforcement Learning via Entropy Minimization -- a fully unsupervised RL method that requires no external reward or ground-truth answers, and instead uses the model's entropy of its underlying distribution as an intrinsic reward. We find that by reinforcing the chains of thought that yield high model confidence on its generated answers, the model improves its reasoning ability. In our experiments, we showcase these improvements on an extensive suite of commonly-used reasoning benchmarks, including GSM8K, MATH500, AMC, AIME, and GPQA, and models of varying sizes from the Qwen, Mistral, and Llama families. The generality of our unsupervised learning method lends itself to applicability in a wide range of domains where external supervision is unavailable.

Estimating the performance difficulty of a musical score is crucial in music education for adequately designing the learning curriculum of the students. Although the Music Information Retrieval community has recently shown interest in this task, existing approaches mainly use machine-readable scores, leaving the broader case of sheet music images unaddressed. Based on previous works involving sheet music images, we use a mid-level representation, bootleg score, describing notehead positions relative to staff lines coupled with a transformer model. This architecture is adapted to our task by introducing an encoding scheme that reduces the encoded sequence length to one-eighth of the original size. In terms of evaluation, we consider five datasets -- more than 7500 scores with up to 9 difficulty levels -- , two of them particularly compiled for this work. The results obtained when pretraining the scheme on the IMSLP corpus and fine-tuning it on the considered datasets prove the proposal's validity, achieving the best-performing model with a balanced accuracy of 40.34\% and a mean square error of 1.33. Finally, we provide access to our code, data, and models for transparency and reproducibility.

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

A standard way to evaluate the abilities of LLM involves presenting a multiple-choice question and selecting the option with the highest logit as the model's predicted answer. However, such a format for evaluating LLMs has limitations, since even if the model knows the correct answer, it may struggle to select the corresponding letter simply due to difficulties in following this rigid format. To address this, we introduce new scores that better capture and reveal model's underlying knowledge: the Query-Key Score (QK-score), derived from the interaction between query and key representations in attention heads, and the Attention Score, based on attention weights. These scores are extracted from specific select-and-copy heads, which show consistent performance across popular Multi-Choice Question Answering (MCQA) datasets. Based on these scores, our method improves knowledge extraction, yielding up to 16\% gain for LLaMA2-7B and up to 10\% for larger models on popular MCQA benchmarks. At the same time, the accuracy on a simple synthetic dataset, where the model explicitly knows the right answer, increases by almost 60\%, achieving nearly perfect accuracy, therefore demonstrating the method's efficiency in mitigating MCQA format limitations. To support our claims, we conduct experiments on models ranging from 7 billion to 70 billion parameters in both zero- and few-shot setups.

Entropy-based pruning has been proposed as an effective method for compressing Chain-of-Thought (CoT) reasoning with negligible accuracy loss. We test the robustness of low- and high-entropy CoT step selection methods across various models and reasoning tasks, showing that entropy offers no advantage over random pruning in any evaluated setting. Moving from sentences to tokens, we then show that retaining low-entropy tokens seems effective only on mathematical benchmarks. We find this is due to the inherently low-entropy nature of numeric tokens, which also convey semantic content in such problems. Finally, we demonstrate that patching a subset of a few CoT tokens with their original activations recovers near-perfect full-trace performance, providing causal evidence that task information is not concentrated in a small set of CoT tokens identifiable by heuristics, but rather distributed across the full reasoning chain.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

In this paper we show that reporting a single performance score is insufficient to compare non-deterministic approaches. We demonstrate for common sequence tagging tasks that the seed value for the random number generator can result in statistically significant (p < 10^-4) differences for state-of-the-art systems. For two recent systems for NER, we observe an absolute difference of one percentage point F1-score depending on the selected seed value, making these systems perceived either as state-of-the-art or mediocre. Instead of publishing and reporting single performance scores, we propose to compare score distributions based on multiple executions. Based on the evaluation of 50.000 LSTM-networks for five sequence tagging tasks, we present network architectures that produce both superior performance as well as are more stable with respect to the remaining hyperparameters.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Large Language Models are prompting us to view more NLP tasks from a generative perspective. At the same time, they offer a new way of accessing information, mainly through the RAG framework. While there have been notable improvements for the autoregressive models, overcoming hallucination in the generated answers remains a continuous problem. A standard solution is to use commercial LLMs, such as GPT4, to evaluate these algorithms. However, such frameworks are expensive and not very transparent. Therefore, we propose a study which demonstrates the interest of open-weight models for evaluating RAG hallucination. We develop a lightweight approach using smaller, quantized LLMs to provide an accessible and interpretable metric that gives continuous scores for the generated answer with respect to their correctness and faithfulness. This score allows us to question decisions' reliability and explore thresholds to develop a new AUC metric as an alternative to correlation with human judgment.

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

RL training of multi-turn LLM agents is inherently unstable, and reasoning quality directly determines task performance. Entropy is widely used to track reasoning stability. However, entropy only measures diversity within the same input, and cannot tell whether reasoning actually responds to different inputs. In RAGEN-2, we find that even with stable entropy, models can rely on fixed templates that look diverse but are input-agnostic. We call this template collapse, a failure mode invisible to entropy and all existing metrics. To diagnose this failure, we decompose reasoning quality into within-input diversity (Entropy) and cross-input distinguishability (Mutual Information, MI), and introduce a family of mutual information proxies for online diagnosis. Across diverse tasks, mutual information correlates with final performance much more strongly than entropy, making it a more reliable proxy for reasoning quality. We further explain template collapse with a signal-to-noise ratio (SNR) mechanism. Low reward variance weakens task gradients, letting regularization terms dominate and erase cross-input reasoning differences. To address this, we propose SNR-Aware Filtering to select high-signal prompts per iteration using reward variance as a lightweight proxy. Across planning, math reasoning, web navigation, and code execution, the method consistently improves both input dependence and task performance.

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

We trained 13,440 large language models and found that entropy minimization requires only a single unlabeled data and 10 steps optimization to achieve performance improvements comparable to or even greater than those obtained using thousands of data and carefully designed rewards in rule-based reinforcement learning. This striking result may prompt a rethinking of post-training paradigms for large language models. Our code is avaliable at https://github.com/zitian-gao/one-shot-em.

As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an entropy-based pruning strategy to enhance efficiency while maintaining performance. Empirical analysis reveals that the entropy of hidden representations decreases in the early blocks but progressively increases across most subsequent blocks. This trend suggests that entropy serves as a more effective measure of information richness within computation blocks. Unlike cosine similarity, which primarily captures geometric relationships, entropy directly quantifies uncertainty and information content, making it a more reliable criterion for pruning. Extensive experiments demonstrate that our entropy-based pruning approach surpasses cosine similarity-based methods in reducing model size while preserving accuracy, offering a promising direction for efficient model deployment.