Daily Papers

The rapid evolution of large language models necessitates robust machine-generated text detection. Existing paradigms typically follow two isolated tracks. Training-free methods rely on global statistical scalars such as perplexity, while training-based methods utilize semantic hidden states. Both approaches exhibit fundamental vulnerabilities in adversarial scenarios. Global scalars act as lossy compressions that obscure local probabilistic burstiness in interleaved texts, whereas pure semantic models overfit to specific fingerprints and remain susceptible to spoofing. To expose these flaws, we introduce MOSAIC, a comprehensive adversarial benchmark comprising 16000 samples across a full-granularity attack spectrum. To address these challenges, we propose NeuroStat, an end-to-end framework bridging the statistical and semantic gap. NeuroStat captures uncompressed token-level probabilistic logits alongside deep semantic hidden states from a single causal language model backbone. We fuse these heterogeneous signals through Macro-State Residual Modulation, which adaptively calibrates local convolutional features using global uncertainty indicators. Orthogonal and contrastive losses further ensure the learning of complementary representations. Extensive experiments demonstrate that NeuroStat maintains exceptional robustness on MOSAIC compared to the severe degradation of state-of-the-art methods, establishing a new standard for adversarial text detection. Code and the MOSAIC benchmark are available at https://github.com/TencentBAC/NeuroStat.

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

Self-supervised monocular depth estimators can be trained or fine-tuned on new scenes using only images and no ground-truth depth data, achieving good accuracy. However, these estimators suffer from the inherent ambiguity of the depth scale, significantly limiting their applicability. In this work, we present a method for transferring the depth-scale from existing source datasets collected with ground-truth depths to depth estimators that are trained using self-supervision on a newly collected target dataset consisting of images only, solving a significant limiting factor. We show that self-supervision based on projective geometry results in predicted depths that are linearly correlated with their ground-truth depths. Moreover, the linearity of this relationship also holds when jointly training on images from two different (real or synthetic) source and target domains. We utilize this observed property and model the relationship between the ground-truth and the predicted up-to-scale depths of images from the source domain using a single global scalar. Then, we scale the predicted up-to-scale depths of images from the target domain using the estimated global scaling factor, performing depth-scale transfer between the two domains. This suggested method was evaluated on the target KITTI and DDAD datasets, while using other real or synthetic source datasets, that have a larger field-of-view, other image style or structural content. Our approach achieves competitive accuracy on KITTI, even without using the specially tailored vKITTI or vKITTI2 datasets, and higher accuracy on DDAD, when using both real or synthetic source datasets.

Despite remarkable progress, video generation models often produce highly similar outputs when repeatedly sampled from the same prompt, limiting their usefulness for creative exploration. Existing diversity evaluations primarily rely on global scalar metrics, which obscure where diversity collapses in the spatiotemporal space of videos. We introduce DiVid, a dimension-level diagnostic framework that decomposes video generation diversity into six interpretable dimensions: Semantic, Style, Subject, Scene, Motion, and Camera. Each dimension is measured through a reproducible computer-vision pipeline and analyzed alongside quality and instruction faithfulness to examine potential trade-offs. Systematic evaluation of representative video generation models reveals that diversity is highly dimension-specific: models with strong global diversity scores still collapse on specific factors, particularly Motion and Camera. These rankings persist after filtering unfaithful generations, indicating genuine capability differences rather than off-prompt outputs. Beyond measurement, controlled prompt interventions identify two fundamental bottlenecks: default mode convergence, where models fall back to dominant patterns under open-ended prompts; and realization gaps, where models fail to faithfully realize diverse, explicitly requested alternatives, particularly for temporal factors. The larger faithfulness losses for temporal factors highlight the difficulty of controlling motion and camera variation through text alone. DiVid thus shifts the study of diversity from measuring whether it exists to diagnosing where and why it collapses, and provides actionable directions for dimension-aware training objectives and control signals. The framework will be released to facilitate future research on diverse and controllable video generation.

Long-horizon video editing agents receive final-product feedback only after many interdependent decisions. Yet editing quality is subjective, admits multiple valid solutions, and is not meaningfully calibrated across heterogeneous requests, making a global scalar objective both ambiguous and temporally uninformative. Our key observation is that fixing the request, materials, and production constraints converts this subjective objective into an ordinal comparison among directly comparable alternatives. We introduce Group-Relative Preference Backpropagation (GRPB), which transforms same-task rankings into zero-sum advantages and redistributes them as bounded credit over semantic editing segments. A lagged allocator and guarded transmission prevent current judgments or unreliable estimates from directly shaping the same rollout group. We manually construct a project-disjoint, horizon-stratified suite of realistic editing tasks for training and controlled evaluation. Across matched baselines, credit interventions, external benchmarking, and blinded human evaluation, GRPB improves both editing behavior and rendered products. The resulting 9B Crayotter model surpasses several proprietary systems on AgenticVBench, supporting task-local preference reduction as a practical approach to learning from subjective, delayed outcomes. Code and all supporting materials are publicly available at https://github.com/idwts/Crayotter.

We investigate the effectiveness of adaptive zeroth-order (ZO) optimization for memory-constrained fine-tuning of large language models (LLMs). Contrary to prior claims, we show that adaptive ZO methods such as ZO-Adam offer no convergence advantage over well-tuned ZO-SGD, while incurring significant memory overhead. Our analysis reveals that in high dimensions, ZO gradients lack coordinate-wise heterogeneity, rendering adaptive mechanisms memory inefficient. Leveraging this insight, we propose MEAZO, a memory-efficient adaptive ZO optimizer that tracks only a single scalar for global step size adaptation. We support our method with theoretical convergence guarantees under standard assumptions. Experiments across multiple LLM families and tasks demonstrate that MEAZO matches ZO-Adam's performance with the memory footprint of ZO-SGD. Additional experiments on synthetic quadratic problems and LLM fine-tuning further demonstrate MEAZO's enhanced robustness to step size choices, particularly in grouped or block-structured optimization settings.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS_4) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means. Furthermore, the Legendre transformation gives rise to pairs of dual quasi-arithmetic averages via the convex duality. We study the invariance and equivariance properties under affine transformations of quasi-arithmetic averages via the lens of dually flat spaces of information geometry. We show how these quasi-arithmetic averages are used to express points on dual geodesics and sided barycenters in the dual affine coordinate systems. We then consider quasi-arithmetic mixtures and describe several parametric and non-parametric statistical models which are closed under the quasi-arithmetic mixture operation.

We introduce the Ignition Index (I), a validated scalar metric that operationalizes Global Workspace Theory's (GWT) all-or-none ignition prediction in transformer language models. The metric fits a four-parameter sigmoid to per-layer linear probe accuracy as a function of input signal strength, extracting steepness parameter beta-hat: high values indicate abrupt, ignition-like transitions; low values indicate graded build-up. Across 11 models spanning five architecture families, shuffled-label controls demonstrate 9.6-fold selectivity for genuine linguistic structure over spurious probe capacity (p < 0.001, Mann-Whitney U-test). We find: (1) Feedforward transformers exceed SSMs by 89% in aggregate beta-hat (p < 1e-13, Cohen's d = 0.52), with Mamba exhibiting near-linear profiles consistent with absent global broadcast. (2) Huginn-3.5B exhibits 2.12-fold higher ignition along its iteration axis than its depth axis, demonstrating that recurrent architectures manifest workspace-like transitions along the recurrence dimension. (3) Pythia-410M shows a PELT-detected phase transition at training step 256 (+67%), preceding induction-head formation. (4) Hypotheses linking ignition to model scale and signal strength were not confirmed, suggesting transformer architectures may saturate available ignition mechanisms. The Ignition Index provides the first validated quantitative bridge between GWT's dynamical predictions and mechanistic interpretability, with 9.6-fold measurement selectivity and architecture-level discriminability not previously characterized in the scaling literature. Code: https://github.com/saman-rahbar/ignition-index

Camera-controlled video models are rapidly advancing toward long generation horizons and complex camera control. A key failure mode is 3D inconsistency: as the camera moves, objects lose permanence and scene structures shift. Existing post-training techniques, which assign a single scalar reward to the entire generation, are poorly suited to correcting these inconsistencies over long horizons. We introduce LoGo, which blends global and spatially localized rewards for camera-controlled video models. The local reward provides fine-grained credit assignment, which substantially improves 3D consistency, while the global reward preserves camera following and video quality. Across three base models, LoGo shows a clear advantage on DL3DV and TrajectoryBench, a new benchmark for long-horizon, complex-camera-control generation that current evaluations lack. LoGo effectively reduces local object shifts, artifacts, and global scene changes, illustrating the importance of credit assignment in post-training video models. Project website: https://ziqi-ma.github.io/logo-website/

We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ''internal mode''. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical ϕ^4 model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the ϕ^4 model.

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is challenging because it remains nonlinear and nonconvex. Existing exact deterministic approaches become increasingly difficult to scale as the number of training data points grows, leading to approximation-based methods that improve tractability by optimizing a modified (inexact) objective. In this work, we propose PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound. At each node, kernel terms that are locally important are replaced by a sign-aware piecewise-linear relaxation in an appropriate scalar distance variable, while the remaining terms are bounded analytically in closed form. We show this hybrid approach yields a valid lower bound for the posterior mean, while limiting the size of the branch-and-bound subproblems. We establish validity of the node lower bounds and varepsilon-global convergence of the resulting algorithm. Computational results on synthetic benchmarks and real-world application problems show that PALM-Mean improves scalability relative to representative general-purpose deterministic global solvers, particularly as the number of training data points increases.

The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite stream, and name three resource walls: a Shannon wall barring any o(Nb)-state architecture, a horizon wall barring any fixed window, and a circuit wall barring fixed-depth attention-only composition (conditional on TC0 != NC1). Under an explicit separability assumption a hybrid crosses all three by paying each wall's price, so capability is strictly super-additive under composition. We separate what we prove from what we conjecture: the access-completeness principle rests on information-theoretic lower bounds and pre-registered experiments, while the field-level convergence trend is an economics-motivated conjecture. We report the first pre-registered small-scale tests under criteria frozen before the data: the predicted scissors gap is measured (exact-retrieval error 0.994 vs. 0.000 once a 64-scalar state gains one global-attention layer), the state-tracking bifurcation lands at the registered boundary, and a conjunction witness shows an irreducibly two-channel solution; one prediction failed with its direction reversed and is reported as such. Representational convergence is given freely by scale; capability convergence must be purchased by access structure.

As language models (LMs) become more capable, it is increasingly important to align them with human preferences. However, the dominant paradigm for training Preference Models (PMs) for that purpose suffers from fundamental limitations, such as lack of transparency and scalability, along with susceptibility to overfitting the preference dataset. We propose Compositional Preference Models (CPMs), a novel PM framework that decomposes one global preference assessment into several interpretable features, obtains scalar scores for these features from a prompted LM, and aggregates these scores using a logistic regression classifier. Through these simple steps, CPMs allow to control which properties of the preference data are used to train the preference model and to build it based on features that are believed to underlie the human preference judgment. Our experiments show that CPMs not only improve generalization and are more robust to overoptimization than standard PMs, but also that best-of-n samples obtained using CPMs tend to be preferred over samples obtained using conventional PMs. Overall, our approach demonstrates the benefits of endowing PMs with priors about which features determine human preferences while relying on LM capabilities to extract those features in a scalable and robust way.

We study a persistent failure mode in multi-objective alignment for large language models (LLMs): training improves performance on only a subset of objectives while causing others to degrade. We formalize this phenomenon as cross-objective interference and conduct the first systematic study across classic scalarization algorithms, showing that interference is pervasive and exhibits strong model dependence. To explain this phenomenon, we derive a local covariance law showing that an objective improves at first order when its reward exhibits positive covariance with the scalarized score. We extend this analysis to clipped surrogate objectives used in modern alignment, demonstrating that the covariance law remains valid under mild conditions despite clipping. Building on this analysis, we propose Covariance Targeted Weight Adaptation (CTWA), a plug-and-play method that maintains positive covariance between objective rewards and the training signal to effectively mitigate cross-objective interference. Finally, we complement these local improvement conditions with a global convergence analysis under the Polyak--Łojasiewicz condition, establishing when non-convex scalarized optimization achieves global convergence and how cross-objective interference depends on specific model geometric properties.

We study the accuracy of Gauss-Newton curvature in ridge-regularized nonlinear least squares. Under local regularity and persistence of level-set curvature magnitude along an exact-fit section, we prove uniform coexistence of two curvature regimes. Global minimizers exist, and every global minimizer has relative Hessian error below (1+sqrt2)/8, while the same low-cost set contains a point with an indefinite Hessian and relative error at least 15/8. One positive ridge cap works for all independent center and label perturbations in fixed neighborhoods and every positive ridge weight up to the cap. These neighborhoods do not shrink as the ridge weight tends to zero. A pointwise certificate based on the current prediction level set controls the normal, mixed, and tangent parts of the Hessian correction. We prove a sharp relative-error bound over the stated pointwise class when the prediction map and ridge vary. Analytic examples describe the roles of output alignment, curvature orientation, and persistence. A separate structural result gives full Jacobian row rank throughout low-cost sets and exact interpolation near a rank-deficient reference.

Controllable image synthesis, which enables fine-grained control over generated outputs, has emerged as a key focus in visual generative modeling. However, controllable generation remains challenging for Visual Autoregressive (VAR) models due to their hierarchical, next-scale prediction style. Existing VAR-based methods often suffer from inefficient control encoding and disruptive injection mechanisms that compromise both fidelity and efficiency. In this work, we present SCALAR, a controllable generation method based on VAR, incorporating a novel Scale-wise Conditional Decoding mechanism. SCALAR leverages a pretrained image encoder to extract semantic control signal encodings, which are projected into scale-specific representations and injected into the corresponding layers of the VAR backbone. This design provides persistent and structurally aligned guidance throughout the generation process. Building on SCALAR, we develop SCALAR-Uni, a unified extension that aligns multiple control modalities into a shared latent space, supporting flexible multi-conditional guidance in a single model. Extensive experiments show that SCALAR achieves superior generation quality and control precision across various tasks.

We develop a theory of pseudo-differential operators associated with the gyrator transform on modulation spaces. The gyrator transform is a two-dimensional linear canonical transform which can be viewed as a rotation in the time-frequency plane and is closely related to the fractional Fourier transform. Motivated by the global structure of the gyrator kernel, we work with Shubin global symbol classes on R^4. We first recall basic properties of modulation spaces and establish continuity and invertibility of the gyrator transform on these spaces, using its representation as a metaplectic operator. Then we introduce pseudo-differential operators defined via the gyrator transform and a Shubin symbol, and we prove boundedness results on modulation spaces and on gyrator-based modulation-Sobolev spaces. Our work extends and generalises earlier results of Mahato, Arya and Prasad on Schwartz and Sobolev spaces MahatoGyrator to the more flexible framework of modulation spaces.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling A(phi) and chameleon/Vainshtein screening, we map cosmological responses {mu(z,k),Sigma(z,k)} inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials Phi_N. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with |gamma-1|simfewtimes 10^{-6}, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization {V(phi),A(phi)}. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters gamma,beta; and dot G/G) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, |gamma-1|lesssim (2-5)times 10^{-6} (Ka-/X-band or optical Shapiro), eta_{EEP}sim (1--10)times 10^{-17} (drag-free AIS), |dot G/G|sim(3-5)times10^{-15},yr^{-1} (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and (3-10)times improved ULDM-coupling reach from clocks. For a conformal benchmark, mu_{ lin,0}=0.10 implies chisimeq mu_{lin,0/2} and a Sun thin shell Delta R/Rlesssim (1/3chi)|gamma-1|/2=2.4times 10^{-3} at |gamma-1|=5times 10^{-6}; Vainshtein screening at 1 AU yields |gamma-1|lesssim 10^{-11}, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling F=1 βϕ^{2}/4+γβ^{2}ϕ^{4}+O(ϕ^{6}) that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in β, changes sign at β=1.1156, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to γ. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as γ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Asymptotic Safety provides a promising framework for the quantization of Scalar-Tensor theories as non-perturbatively renormalizable quantum field theories. Over the past years, growing evidence has accumulated for the existence of non-trivial renormalization group fixed points in a variety of Scalar-Tensor models. In this work, we investigate the robustness of these fixed points under significant modifications of the computational setup. In particular, we employ a gauge condition that explicitly depends on the dynamical scalar field, going beyond a mere gauge-parameter deformation of the standard linear covariant gauges commonly used in the literature. Exploring different field parameterizations, we identify fixed points belonging to the Gaussian Matter class in four spacetime dimensions that are consistent with previous studies. The real part of the critical exponents associated with the scalar-field mass and the non-minimal scalar-curvature coupling turn out to have very small absolute value. We provide a comprehensive exploration of how the anomalous dimension of the scalar field and field parameterization impact those critical exponents showing that fixed-point candidates with two or four relevant directions emerge.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs). Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the "single-column approximation" which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

Pruning neural networks has become popular in the last decade when it was shown that a large number of weights can be safely removed from modern neural networks without compromising accuracy. Numerous pruning methods have been proposed since then, each claiming to be better than the previous. Many state-of-the-art (SOTA) techniques today rely on complex pruning methodologies utilizing importance scores, getting feedback through back-propagation or having heuristics-based pruning rules amongst others. In this work, we question whether this pattern of introducing complexity is really necessary to achieve better pruning results. We benchmark these SOTA techniques against a naive pruning baseline, namely, Global Magnitude Pruning (Global MP). Global MP ranks weights in order of their magnitudes and prunes the smallest ones. Hence, in its vanilla form, it is one of the simplest pruning techniques. Surprisingly, we find that vanilla Global MP outperforms all the other SOTA techniques and achieves a new SOTA result. It also achieves promising performance on FLOPs sparsification, which we find is enhanced, when pruning is conducted in a gradual fashion. We also find that Global MP is generalizable across tasks, datasets, and models with superior performance. Moreover, a common issue that many pruning algorithms run into at high sparsity rates, namely, layer-collapse, can be easily fixed in Global MP by setting a minimum threshold of weights to be retained in each layer. Lastly, unlike many other SOTA techniques, Global MP does not require any additional algorithm specific hyper-parameters and is very straightforward to tune and implement. We showcase our findings on various models (WRN-28-8, ResNet-32, ResNet-50, MobileNet-V1 and FastGRNN) and multiple datasets (CIFAR-10, ImageNet and HAR-2). Code is available at https://github.com/manasgupta-1/GlobalMP.

We study scalaron quasinormal modes and quasi-bound states of Schwarzschild black holes directly within the Bondi-Sachs formulation of metric f(R) gravity, combining frequency-domain analyses with characteristic time evolution. Starting from the linearised characteristic equations, we obtain the massive scalar master equation and show that the tensor master equation takes the same form as in general relativity. For the analytic models considered here, the linear scalar spectra depend on the f(R) theory only through the dimensionless combination μM. We compute both quasinormal and quasi-bound spectral branches using Leaver's continued-fraction method and compare them with independent literature benchmarks. To complement the frequency domain analysis, we evolve the scalaron perturbation equations using a fourth order convergent characteristic scheme. Applying matrix-pencil stability scans to the resulting waveforms, we independently recover fundamental quasinormal frequencies consistent with the continued-fraction results within the measured extraction-stability scales. Finally, for a selected finite-mass case, we demonstrate the extraction of both oscillation frequencies and damping rates of the fundamental quasinormal mode and quasi-bound state from separate time windows of the same waveform at one extraction radius, without imposing either spectral branch at the finite outer boundary.

We prove strong ill-posedness for the two-dimensional incompressible Euler equation in the endpoint velocity space W^{3,1}_σ(mathbb R^2). Given any compactly supported smooth divergence-free background and any δ>0, we construct a single compactly supported divergence-free datum within δ of the background in W^{3,1}. The perturbation can be localized inside any prescribed nonempty open neighborhood of the background support while remaining disjoint from that support. The associated unique global finite-energy solution u satisfies {rm curl} uin C([0,infty);W^{2,1}(mathbb R^2)), but \[ \operatorname*{ess\,sup}_{0<t<T}\|u(t)\|_{W^{3,1}}=\infty \qquadfor every T>0. \] The proof combines localized hyperbolic insertion, the Bonami--Poornima nonmultiplier mechanism, and many-packet dilution. Moment cancellation and positive material separation control the nonlocal Biot--Savart interactions, allowing a nested construction inside one fixed compact region. Without the compact-support requirement on the limiting datum, a complementary far-field argument yields a dense G_δ set of data whose solutions leave W^{3,1} at every positive rational time and on a residual set of times, with unbounded essential supremum on every nonempty open time interval.

In a low-energy effective field theory (EFT), scaling logarithmic terms arise from the renormalization of higher-dimensional couplings that absorb divergences generated by loop integrals with lower-order vertices. Consequently, leading logarithms (LLs) are generated entirely by the leading-order Lagrangian, rendering them universal low-energy predictions. Adapting techniques developed for chiral perturbation theory, we analyze the series of LLs in the EFT of general relativity. As a concrete application, we compute LL corrections to the scalar pole mass up to three-loop order and demonstrate that they can be determined recursively to arbitrary loop order. To confirm the physical validity of our results, we carry out the calculation using a general gauge-fixing parameter and explicitly verify its complete cancellation in the physical observable.

We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in metric f(R) gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary + or times tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy R+αR^2-2Λ model with α,Λ>0. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with f'>0 and 1+w>0; hence no nonzero vector harmonic survives on that branch. The familiar coasting R^3 example evades this sign obstruction only because it lies on an f'<0 branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.

In the 3-3-1 model with right-handed neutrinos, three triplets of scalars engender the correct sequence of symmetry breaking, SU(3)_C times SU(3)_L times U(1)_X rightarrow SU(3)_C times SU(2)_L times U(1)_Y rightarrow SU(3)_C times U(1)_{EM}, generating mass for all fermions, except neutrinos. Tiny neutrino masses may be achieved by adding one sextet of scalars to the original scalar content. As consequence, it emerges a very complex scalar sector, involving terms that violate lepton number explicitly, too. The main obstacle to the development of the phenomenology of such scenario is the knowledge of its spectrum of scalars since, now, there are 15 massive scalar particles on it. The proposal of this work is to do an exhaustive analysis of such scalar sector with lepton number being explicitly violated at low, electroweak and high energy scales by means of trilinear terms in the potential. The first case can be addressed analytically and, as a nice result, we have observed that the scalar content of such case is split into two categories: One belonging to the 331 energy scale and the other belonging to the EWSB energy scale, with the last recovering the well known THDM+triplet. For the other cases, the scalar sector can be addressed only numerically. Hence, we proposed a very general approach for the numerical study of the potential, avoiding simplifications that can make us reach conclusions without foundation. We show that, in the case of lepton number being explicitly violated at electroweak scale, it is possible to recover the same physics of the THDM+triplet, as the previous case. Among all the possibilities, we call the attention to one special case which generates the 3HDM+triplet scenario. For the last case, when lepton number is violated at high energy scale, the sextet become very massive and decouples from the original scalar content of the 3-3-1 model.

Cosmological first-order phase transitions can generate curvature perturbations through inhomogeneous quantum tunneling, as studied previously on superhorizon scales. In this work, we for the first time conduct three-dimensional lattice simulations that incorporate scalar metric perturbations and radiation perturbations, covering a range from bubble wall scales to super-horizon scales. We obtain the precise scalar perturbation power spectrum and the probability density function of energy density perturbations. Furthermore, we simulate the gravitational-wave energy spectra generated by each source during the first-order phase transition, including the scalar field itself, scalar metric perturbations, and the energy density and velocity perturbations of radiation. For gravitational waves, the contribution from other sources can exceed 1/3 of that from the scalar field at superhorizon scales. Additionally, we compare the effects of different values of the transition strength and rate on the results. This paper provides more accurate numerical results for research aimed at detecting or constraining first-order phase transitions via gravitational waves and curvature perturbations.

According to a scalar theory of gravity with a preferred frame, electromagnetism in the presence of a gravitational field implies that there is an additional energy tensor, which might contribute to dark matter. The expression of this tensor is determined by a mere scalar p, that depends on the EM field and (for a weak field) on the Newtonian gravitational field. We briefly recall why this tensor arises and how the EM field in a galaxy can be calculated. The data fields that enter the PDE for the scalar field p oscillate very quickly in space and time, as does the EM field. This prevents integration of that PDE at the relevant galactic scale. Therefore, a homogenization of that PDE has to be operated. We discuss in some detail three possible ways of applying the homogenization theory to that PDE: time, space, or spacetime homogenization. The second and third ways may lead to feasible, albeit heavy calculations.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.

Recent measurements from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) have placed the strictest constraints on the primordial scalar perturbation spectrum, reporting a spectral index of n_ssim0.967-0.98 at 95% confidence level. This result indicates a stronger scale invariance of the scalar perturbation than earlier estimates, posing challenges for numerous inflation models. In this work, we propose a novel inflationary scenario based on Weyl scale-invariant gravity, where the quadratic curvature establishes the scale invariance of the scalar spectrum, while the higher-order extensions imprint the observed slight deviation. Specifically, the exponential curvature extensions are introduced to suppress the mass divergence of the inflaton. We find such scenario naturally yields leading-order predictions of n_ssimeq1-3/(2N)sim0.97-0.975 or n_ssimeq1-5/(3N)sim0.967-0.972 for various models, in excellent agreement with the ACT/SPT constraints. This result builds a concrete bridge between theoretical and observational scale invariance, implying an enduring cosmic echo of the primordial symmetry.

For every integer Nge4, we construct a fixed smooth, non-locally-conformally-flat metric on the n-dimensional unit sphere S^n for which the constant Q_{2N}-curvature equation admits an L^infty-unbounded sequence of positive solutions. The construction applies for nge2N+20 when N=4,5, nge2N+19 when 6le Nle8, nge2N+18 when 9le Nle17, and nge2N+17 when Nge18. For each L in N cup {0}, the metric can be chosen arbitrarily close to the round metric in the C^L norm. Together with the known cases N=1,2,3, this establishes noncompactness at every order, with dimension bounds that we expect to be optimal. We derive an explicit formula for the fixed-volume Hessian of total Q_{2N}-curvature in transverse-traceless (TT) directions at closed Einstein metrics satisfying Ric=(n-1)g. Building on Juhl's formulas, we identify this Hessian, for every NinN and n>2N, as a degree-N polynomial in the Lichnerowicz Laplacian. For the metric perturbations generated by algebraic Weyl tensors in the construction, the quadratic reduced energy with fixed bubble center is a positive multiple of this Hessian restricted to a four-dimensional TT space. Differentiation with respect to the bubble scale then yields a finite matrix whose exact sign analysis establishes the required indefiniteness in the stated dimension ranges. After continuation to real n, this matrix changes from negative definite to indefinite at n_N=2N+a_*+c_*N^{-1}+O(N^{-2}) as Ntoinfty, with a_*approx16.201871 and c_*approx13.512880, explaining the eventual bound nge2N+17.

Continuous physical fields represent a large fraction of data under scientific investigation. Their multiscale structures are central to discovery, yet useful coordinates are not known in advance. Standard self-supervised methods define context and targets in fixed image coordinates, posing a predictive task misaligned with fields organized across a continuous scale hierarchy. We introduce ScaleAware-JEPA, a framework that constructs dense, label-free latent coordinates for continuous scalar fields. Constrained Diffusion Decomposition (CDD) separates each field into pixel-registered scale components and provides the scale coordinates that define the masking geometry. The resulting JEPA objective predicts hidden structure with a context footprint tied to the diffusion scale of each component rather than to an arbitrary patch size. Across MHD turbulence, interstellar molecular gas and urban nighttime-light structure, the learned geometry maps back to coherent morphology, forming dense structural atlases without labels or predefined segmentation rules. By tying latent prediction to the scale hierarchy of a field, ScaleAware-JEPA constructs latent coordinates through which complex physical patterns can be inspected before their relevant structures have been prescribed. Code is available at https://github.com/gxli/SA-JEPA.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for this system given bounded initial data. In particular, this shows that the model does not allow for thermal blow-up. If the initial temperature and fuel density also satisfy certain integrability conditions, the L^2-norms of these global solutions are uniformly bounded in time. Additionally, I use a bootstrap argument to show that small initial temperatures give rise to solutions that decay to zero as time goes to infinity, proving the existence of initial states that do not develop into travelling combustion waves.

Residual connections are the de facto mechanism for training deep neural networks stably. Geodesic Normalization (GeoNorm) recasts them on a Riemannian manifold, orthogonalizing each layer output against the current hidden state and applying the resulting update through the Riemannian exponential map. Every hidden state thus keeps a constant ell_{2}-norm, confining the residual stream to a hypersphere. The exponential map, however, is only one member of a broad family of retraction maps. We show that on the hypersphere this entire family collapses to a single scalar design choice. What distinguishes one retraction from another is only how the magnitude of an update is converted into a rotation angle within the plane spanned by the hidden state and the update. This view places Euclidean residual connections and GeoNorm in one framework. Instantiating it with the metric projection retraction and the Cayley retraction yields Proj-SpheretNorm and Cay-SpheretNorm, which are exactly norm-preserving yet require only algebraic operations. Both prove to be members of a one-parameter family of angular retractions, p-SpheretNorm, whose rotation angle saturates rather than growing without bound. The two methods above are recovered exactly at p = 1 and p = 2, while the identity map and GeoNorm arise only as limits at either end. On nanoGPT, all three methods outperform existing lightweight deep connection schemes, and the best validation loss is attained at finite p, indicating that the exponential map is not the preferred retraction for spherical residual streams but merely one end of a spectrum.

The production of W^{pm}H, ZH, W^+W^-, and W^pm Z pairs probes non-Standard-Model interactions of quarks, gauge bosons, and the Higgs boson. New effects can be parameterized in terms of an effective field theory (EFT) where the Lagrangian is expanded in terms of higher-dimension operators suppressed by increasing powers of a high scale Λ. We examine the importance of including next-to-leading-order QCD corrections in global fits to the coefficients of the EFT. The numerical implications on the fits due to different approaches to enforcing the validity of the EFT are quantified. We pay particular attention to the dependence of the fits on the expansion in 1/Λ^2 since the differences between results calculated at {O}(1/Λ^2) and {O}(1/Λ^4) may give insight into the possible significance of dimension-8 effects.

A recent trend among generalizable novel view synthesis methods is to learn a rendering operator acting over single camera rays. This approach is promising because it removes the need for explicit volumetric rendering, but it effectively treats target images as collections of independent pixels. Here, we propose to learn a global rendering operator acting over all camera rays jointly. We show that the right representation to enable such rendering is a 5-dimensional plane sweep volume consisting of the projection of the input images on a set of planes facing the target camera. Based on this understanding, we introduce our Convolutional Global Latent Renderer (ConvGLR), an efficient convolutional architecture that performs the rendering operation globally in a low-resolution latent space. Experiments on various datasets under sparse and generalizable setups show that our approach consistently outperforms existing methods by significant margins.

Recent results from Type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO), in combination with cosmic microwave background (CMB) measurements, have focused renewed attention on dark energy models with a time-varying equation-of-state parameter, w(z). In this paper, we describe the simplest, physically motivated models of evolving dark energy that are consistent with the recent data, a broad subclass of the so-called thawing scalar field models that we dub w_ϕCDM. We provide a quasi-universal, quasi-one-parameter functional fit to the scalar-field w_ϕ(z) that captures the behavior of these models more informatively than the standard w_0w_a phenomenological parametrization; their behavior is completely described by the current value of the equation-of-state parameter, w_0=w(z=0). Combining current data from BAO (DESI Data Release 2), the CMB (Planck and ACT), large-scale structure (DES Year-3 3times2pt), SNe Ia (DES-SN5YR), and strong lensing (TDCOSMO + SLACS), for w_ϕCDM we obtain w_0=-0.904_{-0.033}^{+0.034}, 2.9σ discrepant from the Λ cold dark matter (ΛCDM) model. The Bayesian evidence ratio substantially favors this w_ϕCDM model over ΛCDM. The data combination that yields the strongest discrepancy with ΛCDM is BAO+SNe Ia, for which w_0=-0.837^{+0.044}_{-0.045}, 3.6σ discrepant from ΛCDM and with a Bayesian evidence ratio strongly in favor. We find that the so-called S_8 tension between the CMB and large-scale structure is slightly reduced in these models, while the Hubble tension is slightly increased. We forecast constraints on these models from near-future surveys (DESI-extension and the Vera C. Rubin Observatory LSST), showing that the current best-fit w_ϕCDM model will be distinguishable from ΛCDM at over 9σ.

Multi-site neuroimaging analysis is fundamentally confounded by scanner-induced covariate shifts, where the marginal distribution of voxel intensities P(x) varies non-linearly across acquisition protocols while the conditional anatomy P(y|x) remains constant. This is particularly detrimental to radiomic reproducibility, where acquisition variance often exceeds biological pathology variance. Existing statistical harmonization methods (e.g., ComBat) operate in feature space, precluding spatial downstream tasks, while standard deep learning approaches are theoretically bounded by local effective receptive fields (ERF), failing to model the global intensity correlations characteristic of field-strength bias. We propose SA-CycleGAN-2.5D, a domain adaptation framework motivated by the HΔH-divergence bound of Ben-David et al., integrating three architectural innovations: (1) A 2.5D tri-planar manifold injection preserving through-plane gradients nabla_z at O(HW) complexity; (2) A U-ResNet generator with dense voxel-to-voxel self-attention, surpassing the O(L) receptive field limit of CNNs to model global scanner field biases; and (3) A spectrally-normalized discriminator constraining the Lipschitz constant (K_D le 1) for stable adversarial optimization. Evaluated on 654 glioma patients across two institutional domains (BraTS and UPenn-GBM), our method reduces Maximum Mean Discrepancy (MMD) by 99.1% (1.729 to 0.015) and degrades domain classifier accuracy to near-chance (59.7%). Ablation confirms that global attention is statistically essential (Cohen's d = 1.32, p < 0.001) for the harder heterogeneous-to-homogeneous translation direction. By bridging 2D efficiency and 3D consistency, our framework yields voxel-level harmonized images that preserve tumor pathophysiology, enabling reproducible multi-center radiomic analysis.

We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity ρ^β, and pressure ρ^γ. For every β>1 and γ>1, we construct global finite-energy renormalized weak solutions from strictly positive bounded W^{1,q} densities, q>2, and arbitrary H^1 velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the β-power density potential yields weak--strong uniqueness against positive H^2 strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when γ>max{5-2β,β+1}. Writing m=intρ_0, the density perturbation is bounded in the scaled norm m^{(γ-3)/2}|ρ_0-m|_{H^2}, while the fixed H^2 velocity and magnetic norms need not be small. For sufficiently large m, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum 7/3, with the endpoint excluded. For β>2 the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on β. The strong theorem has no upper restriction on γ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to γ=3.

In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar geometries.We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging. Such uncertainties are obtained for free by considering the Jacobians of two-view refinements. Moreover, we explore integrating a variant of the MAGSAC loss into the rotation averaging problem, instead of using classical robust losses employed in current frameworks. The proposed method leads to results superior to baselines, in terms of accuracy, on large-scale public benchmarks. The code is public. https://github.com/zhangganlin/GlobalSfMpy

The efficient spatial allocation of primitives serves as the foundation of 3D Gaussian Splatting, as it directly dictates the synergy between representation compactness, reconstruction speed, and rendering fidelity. Previous solutions, whether based on iterative optimization or feed-forward inference, suffer from significant trade-offs between these goals, mainly due to the reliance on local, heuristic-driven allocation strategies that lack global scene awareness. Specifically, current feed-forward methods are largely pixel-aligned or voxel-aligned. By unprojecting pixels into dense, view-aligned primitives, they bake redundancy into the 3D asset. As more input views are added, the representation size increases and global consistency becomes fragile. To this end, we introduce GlobalSplat, a framework built on the principle of align first, decode later. Our approach learns a compact, global, latent scene representation that encodes multi-view input and resolves cross-view correspondences before decoding any explicit 3D geometry. Crucially, this formulation enables compact, globally consistent reconstructions without relying on pretrained pixel-prediction backbones or reusing latent features from dense baselines. Utilizing a coarse-to-fine training curriculum that gradually increases decoded capacity, GlobalSplat natively prevents representation bloat. On RealEstate10K and ACID, our model achieves competitive novel-view synthesis performance while utilizing as few as 16K Gaussians, significantly less than required by dense pipelines, obtaining a light 4MB footprint. Further, GlobalSplat enables significantly faster inference than the baselines, operating under 78 milliseconds in a single forward pass. Project page is available at https://r-itk.github.io/globalsplat/

The search for life beyond Earth will depend on detecting faint signatures in the atmospheres of potentially habitable exoplanets. Interpreting those signatures requires understanding the host planet's climate: the same molecule may signal life on one planet and abiotic chemistry on another. Global climate models (GCMs) provide this understanding, but individual runs can require up to millions of core-hours and substantial domain expert time. Machine-learning emulators could remove this bottleneck, but progress has been limited by the absence of a curated, multi-model exoclimate dataset. We introduce ThousandWorlds, an ML-ready benchmark for exoclimate emulation and for the broader regime of low-data, multi-simulator, parameter-to-field regression. The dataset contains approximately 1800 simulations from five GCMs, mapping eight planet parameters to 3D atmospheric fields including temperature, humidity, winds, clouds, and radiation. Three nested subsets define progressively harder challenges: single-simulator regression, multi-simulator regression with complete observations, and multi-simulator regression with structured missingness. We propose two evaluation protocols: one for ranking methods, and one that measures performance relative to the disagreement between GCMs themselves. We evaluate seven baselines spanning simple methods, deep learning, and Gaussian processes. GP-based methods perform best, suggesting that ThousandWorlds exposes a regime where off-the-shelf deep learning does not yet succeed. Data: https://doi.org/10.57967/hf/8695. Code: https://github.com/edstevenson/ThousandWorlds.

Embodied AI requires agents that perceive, act, and anticipate how actions reshape future world states. World models serve as internal simulators that capture environment dynamics, enabling forward and counterfactual rollouts to support perception, prediction, and decision making. This survey presents a unified framework for world models in embodied AI. Specifically, we formalize the problem setting and learning objectives, and propose a three-axis taxonomy encompassing: (1) Functionality, Decision-Coupled vs. General-Purpose; (2) Temporal Modeling, Sequential Simulation and Inference vs. Global Difference Prediction; (3) Spatial Representation, Global Latent Vector, Token Feature Sequence, Spatial Latent Grid, and Decomposed Rendering Representation. We systematize data resources and metrics across robotics, autonomous driving, and general video settings, covering pixel prediction quality, state-level understanding, and task performance. Furthermore, we offer a quantitative comparison of state-of-the-art models and distill key open challenges, including the scarcity of unified datasets and the need for evaluation metrics that assess physical consistency over pixel fidelity, the trade-off between model performance and the computational efficiency required for real-time control, and the core modeling difficulty of achieving long-horizon temporal consistency while mitigating error accumulation. Finally, we maintain a curated bibliography at https://github.com/Li-Zn-H/AwesomeWorldModels.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

We develop a novel systematic method for constructing exact, static, and asymptotically flat black-hole solutions in shift-symmetric and Z_2-symmetric beyond Horndeski theories. In contrast to previous studies, our approach does not rely on the restrictive reciprocal condition g_{tt}g_{rr}=-1, allowing for more general geometries characterized by two independent metric functions. The resulting solution space contains two qualitatively distinct types of hair originating from different branches of the theory. One branch is characterized by khronometric hair, while the other by genuine scalar hair. In both, the scalar profile defines a nontrivial preferred foliation, but the shift-symmetry Noether current and the associated propagating degree of freedom are trivial for the former and nonvanishing for the latter. Focusing mainly on the second branch, we derive several distinct families of exact black-hole solutions. In general, these solutions are singular and exhibit primary scalar hair associated with an independent scalar charge. Nevertheless, we demonstrate that they can be regularized to yield regular black-hole or solitonic configurations, for which the scalar hair becomes secondary. We further investigate the stability properties of these solutions under linear perturbations by analyzing the axial sector and the monopole (ell=0) mode of the even-parity sector. For representative solutions with scalar hair, the perturbative analysis provides evidence for linear stability under the modes considered.

In this paper, we establish a quantitative finite-time approximation of scattering fields for nonlinear Alfvén waves in three-dimensional ideal incompressible magnetohydrodynamics near a strong constant magnetic background. Using the global weighted estimates, we prove that truncating the scattering profiles at time T introduces an error in both the L^infty norm and the H^{N_*+1} norm of order $ Obigl(varepsilon^2(R+T)^{-δ}bigr), where \varepsilon\in (0,1) measures the size of the initial perturbation, R\ge100 is the scale parameter in the weighted energy, δ\in(0,2/3) is the exponent related to weights, and N_*+1$ is the Sobolev regularity order assumed for the initial data. The pointwise estimate follows from the decay of the nonlocal pressure along nonlinear characteristics, while the Sobolev estimate combines higher-order weighted pressure bounds with estimates for derivatives of the characteristic flows. Numerical experiments measure pointwise and Sobolev pressure-integral tails to verify the quadratic dependence of the initial perturbation amplitude.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Functional brain network (FBN) modeling often relies on local pairwise interactions, whose limitation in capturing high-order dependencies is theoretically analyzed in this paper. Meanwhile, the computational burden and heuristic nature of current hypergraph modeling approaches hinder end-to-end learning of FBN structures directly from data distributions. To address this, we propose to extract high-order FBN structures under global constraints, and implement this as a Global Constraints oriented Multi-resolution (GCM) FBN structure learning framework. It incorporates 4 types of global constraint (signal synchronization, subject identity, expected edge numbers, and data labels) to enable learning FBN structures for 4 distinct levels (sample/subject/group/project) of modeling resolution. Experimental results demonstrate that GCM achieves up to a 30.6% improvement in relative accuracy and a 96.3% reduction in computational time across 5 datasets and 2 task settings, compared to 9 baselines and 10 state-of-the-art methods. Extensive experiments validate the contributions of individual components and highlight the interpretability of GCM. This work offers a novel perspective on FBN structure learning and provides a foundation for interdisciplinary applications in cognitive neuroscience. Code is publicly available on https://github.com/lzhan94swu/GCM.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

Kilometer-scale modeling of global atmosphere dynamics enables fine-grained weather forecasting and decreases the risk of disastrous weather and climate activity. Therefore, building a kilometer-scale global forecast model is a persistent pursuit in the meteorology domain. Active international efforts have been made in past decades to improve the spatial resolution of numerical weather models. Nonetheless, developing the higher resolution numerical model remains a long-standing challenge due to the substantial consumption of computational resources. Recent advances in data-driven global weather forecasting models utilize reanalysis data for model training and have demonstrated comparable or even higher forecasting skills than numerical models. However, they are all limited by the resolution of reanalysis data and incapable of generating higher-resolution forecasts. This work presents FengWu-GHR, the first data-driven global weather forecasting model running at the 0.09^{circ} horizontal resolution. FengWu-GHR introduces a novel approach that opens the door for operating ML-based high-resolution forecasts by inheriting prior knowledge from a pretrained low-resolution model. The hindcast of weather prediction in 2022 indicates that FengWu-GHR is superior to the IFS-HRES. Furthermore, evaluations on station observations and case studies of extreme events support the competitive operational forecasting skill of FengWu-GHR at the high resolution.

Scalar fields are ubiquitous in theories of high-energy physics. In the context of cosmic inflation, this suggests the existence of spectator fields, which provide a subdominant source of energy density. We show that spectator fields boost the inflationary production of primordial black holes, with single-field ultra-slow roll evolution supplanted by a phase of evolution along the spectator direction, and primordial perturbations amplified by the resulting multifield dynamics. This generic mechanism is largely free from the severe fine-tuning that afflicts single-field inflationary PBH models.

Accurate ocean forecasting is crucial in different areas ranging from science to decision making. Recent advancements in data-driven models have shown significant promise, particularly in weather forecasting community, but yet no data-driven approaches have matched the accuracy and the scalability of traditional global ocean forecasting systems that rely on physics-driven numerical models and can be very computationally expensive, depending on their spatial resolution or complexity. Here, we introduce GLONET, a global ocean neural network-based forecasting system, developed by Mercator Ocean International. GLONET is trained on the global Mercator Ocean physical reanalysis GLORYS12 to integrate physics-based principles through neural operators and networks, which dynamically capture local-global interactions within a unified, scalable framework, ensuring high small-scale accuracy and efficient dynamics. GLONET's performance is assessed and benchmarked against two other forecasting systems: the global Mercator Ocean analysis and forecasting 1/12 high-resolution physical system GLO12 and a recent neural-based system also trained from GLORYS12. A series of comprehensive validation metrics is proposed, specifically tailored for neural network-based ocean forecasting systems, which extend beyond traditional point-wise error assessments that can introduce bias towards neural networks optimized primarily to minimize such metrics. The preliminary evaluation of GLONET shows promising results, for temperature, sea surface height, salinity and ocean currents. GLONET's experimental daily forecast are accessible through the European Digital Twin Ocean platform EDITO.

Deep learning models are known to exhibit a strong texture bias, while human tends to rely heavily on global shape structure for object recognition. The current benchmark for evaluating a model's global shape bias is a set of style-transferred images with the assumption that resistance to the attack of style transfer is related to the development of global structure sensitivity in the model. In this work, we show that networks trained with style-transfer images indeed learn to ignore style, but its shape bias arises primarily from local detail. We provide a Disrupted Structure Testbench (DiST) as a direct measurement of global structure sensitivity. Our test includes 2400 original images from ImageNet-1K, each of which is accompanied by two images with the global shapes of the original image disrupted while preserving its texture via the texture synthesis program. We found that black{(1) models that performed well on the previous cue-conflict dataset do not fare well in the proposed DiST; (2) the supervised trained Vision Transformer (ViT) lose its global spatial information from positional embedding, leading to no significant advantages over Convolutional Neural Networks (CNNs) on DiST. While self-supervised learning methods, especially mask autoencoder significantly improves the global structure sensitivity of ViT. (3) Improving the global structure sensitivity is orthogonal to resistance to style-transfer, indicating that the relationship between global shape structure and local texture detail is not an either/or relationship. Training with DiST images and style-transferred images are complementary, and can be combined to train network together to enhance the global shape sensitivity and robustness of local features.} Our code will be hosted in github: https://github.com/leelabcnbc/DiST

In the quantum inverse scattering method, the sine-Gordon model is solved on a lattice, and its continuum and infinite-volume limits become uniform only after the length of the box is rescaled. We show that this rescaling, supplemented by an on-shell condition, defines a renormalization scheme. The whole dependence on the cut-off is absorbed into a factor Z_L multiplying the length of the box, with an exponent fixed by the scaling dimension of the vertex operator; neither the field nor the coupling β is renormalized, no subtraction scale is introduced, and the mass parameter receives a finite renormalization, fixed by requiring that the lightest breather has the mass of the boson in the linearized theory. The soliton and breather masses follow from the eigenvalues of the monodromy operator as functions of parameters that do not run, and reduce to the classical and semiclassical results as βrightarrow0. In particular, the mass ratios are produced directly from the regularized construction, while the relation between the lattice parameters and the physical scale is absorbed into Z_L and never needs to be computed. The scheme is a reparameterization of the theory which makes explicit the interplay between integrability and renormalization. We compare it with Coleman's normal ordering and with conformal perturbation theory, and we argue that it extends to ultralocal integrable theories with a massive spectrum, possibly including asymptotically free models that admit an ultralocal lattice regularization.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable operator learning approach with reduced memory requirement and better generalization, called multi-grid tensorized neural operator (MG-TFNO). MG-TFNO scales to large resolutions by leveraging local and global structures of full-scale, real-world phenomena, through a decomposition of both the input domain and the operator's parameter space. Our contributions are threefold: i) we enable parallelization over input samples with a novel multi-grid-based domain decomposition, ii) we represent the parameters of the model in a high-order latent subspace of the Fourier domain, through a global tensor factorization, resulting in an extreme reduction in the number of parameters and improved generalization, and iii) we propose architectural improvements to the backbone FNO. Our approach can be used in any operator learning setting. We demonstrate superior performance on the turbulent Navier-Stokes equations where we achieve less than half the error with over 150x compression. The tensorization combined with the domain decomposition, yields over 150x reduction in the number of parameters and 7x reduction in the domain size without losses in accuracy, while slightly enabling parallelism.

Within the context of a Chern-Simons running-vacuum-model (RVM) cosmology, one expects an early-matter dominated (eMD) reheating period after RVM inflation driven by the axion field. Treating thus in this work Chern-Simons RVM cosmology as an effective f(R) gravity theory characterized by logarithmic corrections of the spacetime curvature, we study the gravitational-wave (GW) signal induced by the nearly-scale invariant inflationary adiabatic curvature perturbations during the transition from the eMD era driven by the axion to the late radiation-dominated era. Remarkably, by accounting for the extra GW scalaron polarization present within f(R) gravity theories, we find regions in the parameter space of the theory where one is met with a distinctive induced GW signal with a universal f^6 high-frequency scaling compared to the f^7 scaling present in general relativity (GR). Interestingly enough, for axion masses m_a higher than 1 GeV and axion gauge couplings f_a above 10^{-3} Planck mass, one can produce induced GW spectra within the sensitivity bands of future GW observatories such as the Einstein Telescope (ET), the Laser Interferometer Space Antenna (LISA), the Big Bang Observer (BBO) and the Square Kilometer Arrays (SKA).

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension Delta (Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in different dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4+epsilon dimensions. As an example of the second type we consider the U(N)times U(M) model in 4-epsilon dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.

Recent advances in multimodal foundation models, exemplified by GPT-6 Astra, raise the prospect of general-purpose embodied reasoning and planning. Using Internet videos for embodied pretraining calls for reliable physical-scale annotations. Yet visual geometry foundation models often recover scene structure and camera motion without reliable metric scale. We show that uncertain size priors of familiar objects can jointly constrain a reconstruction's shared scale. Building on this insight, we present UniMetric, a universal and training-free metric scale recovery framework for geometry foundation models, without additional sensors or task-specific metric supervision. Specifically, Metric Prior Acquisition elicits object height intervals from a vision-language model. Semantic-Geometric Alignment measures reconstructed object heights along the estimated support-surface normal in each frame and converts the priors into scale intervals. Global Scale Recovery reconciles these intervals through a convex objective, yielding a jointly feasible scale when they overlap and a unique compromise otherwise. The estimated sequence-level scale is applied uniformly to reconstructed points and camera translations. Controlled experiments with real VLM priors show that combining observations improves scale accuracy with exact relative object heights. To evaluate metric accuracy on GFM reconstructions without ground-truth scale alignment, we introduce MetricBench, covering twelve embodied, driving, and roadside subsets with sensor-derived ground truth. Across nine geometry foundation models, UniMetric reduces mean depth Abs Rel, reconstruction Chamfer distance, and trajectory error by 54.2%, 83.8%, and 65.6%, respectively, improving every model on all three tasks at the suite level. We release the UniMetric code and MetricBench data.

We investigate scalar induced gravitational waves (SIGWs) at third-order during a matter-dominated (MD) era. We classify the sources into four parts---built from three first-order scalars, and from a first-order scalar times the second-order tensor, vector, and scalar perturbations---and obtain all four kernel functions analytically in closed form. Unlike their radiation-dominated counterparts, the MD kernel functions grow secularly, translating into a rapid growth of the spectrum, Ω^{(3)}_{GW}propto x^{6} versus Ω^{(2)}_{GW}propto x^{2} at xequiv kηgg1. We derive the third-order power spectrum as a five-fold integral for a general primordial spectrum, and evaluate it numerically for a monochromatic one, where all contributions from the second-order vector source vanish identically. As an application, we consider the early MD era driven by primordial black holes (PBHs) before their evaporation. Requiring that the induced gravitational waves do not backreact on the cosmological perturbations, intdln k, Ω^{tot}_{GW}<1 then bounds the initial PBH abundance as Ω_{PBH,f}lesssim4.6times10^{-7}, (m_{PBH}/10^{7},g)^{-0.48}, about three orders of magnitude stronger than the second-order-only bound. Our results indicate that higher-order SIGWs inevitably become nonperturbative during a sufficiently long MD era, with important implications for scenarios involving an early matter domination.

Despite increasing progress in development of methods for generating visual counterfactual explanations, especially with the recent rise of Denoising Diffusion Probabilistic Models, previous works consider them as an entirely local technique. In this work, we take the first step at globalizing them. Specifically, we discover that the latent space of Diffusion Autoencoders encodes the inference process of a given classifier in the form of global directions. We propose a novel proxy-based approach that discovers two types of these directions with the use of only single image in an entirely black-box manner. Precisely, g-directions allow for flipping the decision of a given classifier on an entire dataset of images, while h-directions further increase the diversity of explanations. We refer to them in general as Global Counterfactual Directions (GCDs). Moreover, we show that GCDs can be naturally combined with Latent Integrated Gradients resulting in a new black-box attribution method, while simultaneously enhancing the understanding of counterfactual explanations. We validate our approach on existing benchmarks and show that it generalizes to real-world use-cases.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

We study the Yamabe--Escobar equation prescribing positive constant scalar curvature and minimal boundary. The compactness conjecture asks whether being conformally equivalent to the round hemisphere is the only obstruction for its set of positive solutions to be compact. In this paper we show that this is true for dimensions 3leq nleq 14. We show that this dimensional threshold n_*=14 is sharp by constructing in ngeq 15 nonumbilic and non-locally-conformally-flat examples of metrics in the hemisphere for which a noncompact sequence of solutions exists. We do the same for the special classes of locally conformally flat metrics, n_*^{LCF}=18, and the metrics with umbilic boundary, n_*^{umb} =20. In all three settings we also prove that the Weyl--umbilicity vanishing conjecture holds for 4leq nleq n_* and construct counterexamples in n>n_* by perturbing the noncompactness examples. To the best of the author's knowledge, these are the first locally conformally flat noncompactness constructions for the positive-scalar-curvature, minimal-boundary case of the Yamabe--Escobar equation, outside the conformal class of the round hemisphere.

The observed cosmological constant may originate as the minimum value U_{min} of a scalar field potential, where the scalar field is frozen due to a large mass. If this vacuum is metastable, it may decay to a true vacuum either at present or in the future. Assuming its decay rate Gamma is comparable to the Hubble expansion rate H_0, we estimate the scale of true vacuum bubbles and analyze their evolution. We find that their initial formation scale is sub-millimeter and their tension causes rapid collapse if m gtrsim 1.7 cdot 10^{-3}, eV. For smaller masses, the bubbles expand at the speed of light. We extend our analysis to scalar-tensor theories with non-minimal coupling, finding that the nucleation scale of gravitational constant bubbles remains consistent with the sub-millimeter regime of General Relativity. The critical mass scale remains around 10^{-3},eV. A theoretical estimate at redshift z_{obs} sim 0.01 suggests an observable bubble radius of sim 50 Mpc, implying a gravitational transition triggered sim 300 Myr ago, with a present-day size approaching 100 Mpc. Additionally, we explore mass ranges (m < 10^{-3},eV) and non-minimal coupling xi ranges (10^{-8},eV^{2-n} - 10^{-1},eV^{2-n}) that lead to a variation Delta G/G_N within the 1%-7% range. We assume non-minimal coupling of the form F(phi)=1/kappa - xi phi^n, with kappa=8pi G_N and 2 leq n leq 9. Finally, we review various local physics or/and transition based proposed solutions to the Hubble tension, including ultra-late-time transitional models (z sim 0.01), screened fifth-force mechanisms, and the Lambda_{rm s}CDM model, which features a transition at z sim 2. We discuss observational hints supporting these scenarios and the theoretical challenges they face.

Many dynamical processes unfold on the sphere but the default scientific machine learning architectures are Euclidean. Applying these architectures on a regular lat-lon grid causes problems: Cartesian convolutions become distorted at high latitude; 2D FFTs in Fourier neural operators incorrectly assume double periodicity; Cartesian positional encodings in ViTs distort spherical geodesic distances. Recent work moves towards natively spherical primitives, including spherical convolutions (e.g., DeepSphere or DISCO), Spherical Fourier Neural Operators (SFNOs), and geodesic attention. Here we propose Dandelion, a spherical version of Flower, a warp-based neural PDE solver. Layers of Dandelion predict a tangent-plane displacement and transport features along great circles. We obtain a U-Net-like structure by implementing hierarchical pooling entirely in the spherical-harmonic domain. There are thus no convolutions: spatial mixing is achieved only through spherical coordinate changes, or warps. To compare Dandelion with existing spherical architectures, we release an evolving benchmark suite of challenging, natively-spherical PDE datasets including a modified Galewsky jet, anomalous chained turbulence, Cahn-Hilliard decomposition, spherical Riemann shocks, Held-Suarez dry atmospheric transport and global ocean dynamics. This new benchmark fills the gap in existing spherical datasets which are either too small and stylized, or much too large (ERA5) for model iteration. Dandelion is best or second-best on every dataset, and the gap to non-warp baselines widens with resolution: at 256times 512, Dandelion and Flower2D occupy the top two slots in both single-step prediction and rollout.

Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning has attracted considerable interest as a biologically plausible alternative to backpropagation. Nevertheless, its exclusive reliance on local information, without consideration of global task objectives, fundamentally limits its scalability. Inspired by the biological synergy between neuromodulators and local plasticity, we introduce a novel model-agnostic Global-guided Hebbian Learning (GHL) framework, which seamlessly integrates local and global information to scale up across diverse networks and tasks. In specific, the local component employs Oja's rule with competitive learning to ensure stable and effective local updates. Meanwhile, the global component introduces a sign-based signal that guides the direction of local Hebbian plasticity updates. Extensive experiments demonstrate that our method consistently outperforms existing Hebbian approaches. Notably, on large-scale network and complex datasets like ImageNet, our framework achieves the competitive results and significantly narrows the gap with standard backpropagation.

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of \(2\to2\) scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons \((TTT)\) and Abelian gauge currents \((TJJ)\), through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated \(4\)-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

The global topology of the Universe is a longstanding open question. In this work, we examine the statistical signatures of a positively curved universe with a Friedmann--Lemaitre--Robertson--Walker metric and the topology of a lens space L(p,q). Since these manifolds are generally statistically anisotropic and inhomogeneous, their cosmic microwave background (CMB) covariance matrices contain non-zero off-diagonal entries that depend on observer location. We compute these full harmonic-space covariance matrices for scalar perturbations for arbitrary lens spaces and observer position. Using the Kullback--Leibler divergence, we assess the distinguishability of these spaces from a simply connected three-sphere with the same curvature. The results show that topological signatures can still be significant in a cosmic-variance-limited regime even when the length, d_{rm NC}, of the shortest loop around the Universe through the observer exceeds the diameter, d_{rm LSS}, of the last-scattering surface by up to 10%. This distinguishability depends on the curvature, the lens space and the observer position mainly through the ratio d_{rm NC}/d_{rm LSS}, which is set not only by the curvature radius but also by p, q and the observer location. Therefore, for any value of the spatial curvature, however small, there are lens spaces and observer positions for which 0.985,d_{rm LSS}<d_{rm NC}<1.1,d_{rm LSS}. Such observers would find no matched circles in the CMB large enough to have been detected to date, yet the topology would remain potentially discoverable through its statistical signatures.

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.

In this paper we study quasinormal modes and absorption cross sections for the (1+3)-dimensional Bardeen black hole surrounded by perfect fluid dark matter. Studies of the massless scalar field is already done in Sun:2023slzl. Hence, in this paper we will focus on the massive scalar field perturbations and massless Dirac field perturbations. To compute the quasinormal modes we use the semi-analytical 3rd-order WKB method, which has been shown to be one of the best approaches when the effective potential is adequate and when n < ell and n < lambda. We have also utilized the P\"oschl-Teller method to compare the valus obtained using the WKB approach. We have computed quasinormal frequencies by varying various parameters of the theory such as the mass of the scalar field mu, dark matter parameter alpha and the magnetic charge g. We have summarized our solutions in tables and figures for clarity. As for the absorption cross section, we used third order WKB approach to compute reflection, transmission coefficients and partial absorption cross sections. Graphs are presented to demonstrate the behavior of the above quantities when the dark matter parameter and mass of the massive scalar field are varied.

World modeling enables intelligence to anticipate consequences, guide interventions, and learn from interaction. Yet predictive models remain domain-specific: can a common learning principle support world modeling across radically different systems? We introduce JEPA-Anything, a domain-agnostic framework based on orthogonal predictive factorization (OPF). Extending joint-embedding predictive architectures, OPF decomposes latent targets into complementary factors, learns them through dedicated pathways, and recombines them within a shared predictive design. We evaluate JEPA-Anything across seven domains: vision, biology, clinical trajectories, control, molecular dynamics, physical fields, and weather. Experiments span representation learning, intervention prediction, out-of-distribution generalization, and long-horizon dynamics, including 10 matched dynamics tasks, forecasting of over 1,000 clinical events, and 100-step molecular rollouts across four systems. Against matched JEPA baselines, JEPA-Anything improves reported metrics on all 10 dynamics tasks and reduces single-intervention prediction error on Interventional Pong by 34.8%. It achieves the lowest one-step and 100-step molecular errors among compared methods in all four systems. Beyond prediction, a factor-nominated biological intervention receives experimental support in cell co-cultures, patient-derived organoids, tumor fragments, and mice; latent orbital modes recover the Keplerian scaling exponent with a fitted slope of -1.4991. These results support a common factorized predictive principle across heterogeneous worlds, connecting world modeling with intervention and experimentally grounded scientific discovery. Code: https://github.com/Gen-Verse/JEPA-Anything

Understanding diffuse Galactic radio emission is interesting both in its own right and for minimizing foreground contamination of cosmological measurements. Cosmic Microwave Background experiments have focused on frequencies > 10 GHz, whereas 21 cm tomography of the high redshift universe will mainly focus on < 0.2 GHz, for which less is currently known about Galactic emission. Motivated by this, we present a global sky model derived from all publicly available total power large-area radio surveys, digitized with optical character recognition when necessary and compiled into a uniform format, as well as the new Villa Elisa data extending the 1.4 GHz map to the entire sky. We quantify statistical and systematic uncertainties in these surveys by comparing them with various global multi-frequency model fits. We find that a principal component based model with only three components can fit the 11 most accurate data sets (at 10, 22, 45 & 408 MHz and 1.4, 2.3, 23, 33, 41, 61, 94 GHz) to an accuracy around 1%-10% depending on frequency and sky region. Both our data compilation and our software returning a predicted all-sky map at any frequency from 10 MHz to 100 GHz are publicly available at http://space.mit.edu/home/angelica/gsm .

Purpose: Simulation of motion in the frequency domain during the MRI acquisition process is an important tool to study the effect of object motion. It is natural in this context to rely on a voxel-to-voxel difference metric between the original image and its motion-simulated version to quantify the alteration. These metrics are very sensitive to any mis-coregistration between the two images. As we observed global displacements of the corrupted image for specific simulated motions, we focused this work on the critical choice of a reference position of the object for the motion simulation that avoids any global displacement. Methods: We used the motion simulation framework and we studied the different proposed solutions. Classically, the position around the k-space center is considered as a reference with two analytical solutions to correct for global image shifts: demeaning the image in the Fourier domain either using the exact position at k-space center or using a weighted average around the center. Results: We demonstrated with motion simulated examples that these analytical solutions did not yield the same results as a direct co-registration method. Indeed, short transitions around the k-space center did not induce any global displacement, in contrast with what both analytical solutions assumed. We also observed a dependence of the global shift to both the motion amplitude and the translation direction. Conclusion: In the absence of a theoretical solution, we concluded that an extra co-registration step after motion simulation was needed in order to compare the simulation with its reference image.

Foundation models for Earth systems have so far been trained primarily on physical climate and weather data, with limited representation of the human systems that both drive and respond to environmental change. The lack of a unified global training resource that combines climate, land, ocean, cryosphere, infrastructure, hazards, and socioeconomic data on a common grid hinders progress toward truly multimodal Earth system foundation models. We present WorldTensor, a harmonised global dataset that aligns hundreds of environmental and socioeconomic variables to a standardised 0.25^circ spatial grid and annual temporal framework. WorldTensor integrates reanalysis products, remote sensing, emissions inventories, land use reconstructions, hydrological observations, infrastructure and hazard datasets, and socioeconomic indicators within a single representation designed for machine learning workflows. To build the dataset, we regridded inputs across heterogeneous native resolutions and projections, rasterised point and vector datasets into spatially meaningful gridded fields, and reconciled temporal coverages ranging from daily observations to sparse multiyear socioeconomic snapshots. All outputs are distributed as NetCDF files with standardised coordinates, variable metadata, and a common CF metadata convention. WorldTensor provides a reproducible resource for training and evaluating foundation models that learn coupled dynamics across environmental and human systems at planetary scale.

In this work, we compute multi-field core and halo properties in wave Dark Matter models. We focus on the case where Dark Matter consists of two light (real) scalars, interacting gravitationally. As in the single-field Ultra Light Dark Matter (ULDM) case, the scalar field behaves as a coherent BEC with a definite ground state (at fixed total mass), often referred to in the literature as a gravitational soliton. We establish an efficient algorithm to find the ground and excited states of such two-field systems. We then use simulations to investigate the gravitational collapse and virialization, starting from different initial conditions, into solitons and surrounding halo. As in the single-field case, a virialized halo forms with a gravitational soliton (ground state) at the center. We find some evidence for an empirical relation between the soliton mass and energy and those of the host halo. We use this to then find a numerical relation between the properties of the two. Finally, we use this to address the issue of alleviating some of the tensions that single-field ULDM has with observational data, in particular, the issue of how a galaxy's core and radius are related. We find that if galaxies of different masses have similar percentages of the two species, then the core-radius scaling tension is not addressed. However, more general possibilities occur if the relative abundance of species in each halo correlates with the total mass of the galaxy. If this is the case, the model predicts several other phenomenological signatures.

To study the onset of scalarization, we investigate linear scalar perturbations around Kerr--Newman black holes in the Einstein-Chern-Simons-Maxwell-scalar theory with quadratic Chern--Simons (CS) coupling γ (hatγ=γ/M^2) and Maxwell coupling η. For this purpose, we employ hyperboloidal Rácz--Tóth evolution and a stationary axisymmetric zero-mode computation. The resulting thresholds are compared with the time-domain response at representative points. For hatγ=0, we find two asymmetric threshold branches in η, while for hatγ=η, the two branches have opposite signs and unequal magnitudes. For unequal CS and Maxwell couplings, the two real threshold branches merge as the spin or CS coupling increases.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

This paper presents the first numerical realization of Suzuki's Weil-Quadratic-Form operator, a candidate for the Hilbert--Pólya program linking spectral positivity to the Riemann Hypothesis (RH). Suzuki's 2026 construction was purely theoretical; here, the operator is instantiated via P1 finite-element discretization and Richardson extrapolation. Key results include: (R1) In the prime-free regime, the spectrum follows a closed Archimedean law A_k(a) = log(1/a) + log(k-2) + B_0 + O(a), with B_0 = log q - 2log 2, confirmed to 30-digit precision. (R2) A Mellin double-pole argument proves the head coefficient B(ν) and shows B_0 depends only on the conductor q, independent of the Archimedean parameter. (R2b) The degree d of an L-function appears directly as the logarithmic slope of the spectrum. (R3) Total spectral intensity follows the prime number theorem, S(a) sim (2a)^3/6. (R4) Nontrivial zeros are not eigenvalues but occur in the explicit-formula error term of the prime symbol. (R5) The best-match line σ^*(a) descends toward the critical line. (R6) Weil's positivity criterion is realized in operator form: bounded residual growth corresponds to all zeros on the line, while an injected off-line zero causes exponential blow-up. (R7) The lowest eigenvalue λ_1(a) is strictly positive, decays superexponentially, and passes smoothly through the first prime threshold. (R8) The characteristic function W(a,0;z) is computed for the first time, with all zeros confirmed real. (R9) Indirect traces of GUE statistics appear in the moment structure, even where direct detection is blocked. The authors emphasize that this work does not prove RH. All results are Archimedean and universal, with significance lying in the faithful numerical realization of classical identities rather than new arithmetic.

This paper presents a new state-of-the-art algorithm for exact 3times3 matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.

Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.

We establish a conditional theory of genuinely non-perturbative global dynamics for the cutoff Boltzmann equation with hard potentials on the three-dimensional torus. We prove that any global mild solution satisfying \[ \sup_{t\ge0}\int_{\mathbb R^3}W(v)\sup_{x\in\mathbb T^3}F(t,x,v)\,dv<\infty, \] for a suitable stretched-exponential weight \(W\), enjoys uniform weighted \(L^\infty\) control, is unique in the dissipative mild class, and converges exponentially to the global Maxwellian. In particular, these conclusions hold for arbitrary-amplitude solutions admitting a uniform stretched-exponential velocity upper bound. The key mechanism is a *tail-to-coercivity principle*: uniform velocity-tail control generates positive lower bounds for the local density and nonlinear collision frequency, without imposing macroscopic coercivity a priori. A double-Duhamel positivity argument also generates a Gaussian lower bound at arbitrarily short positive times, allowing initial data with local vacuum. We establish a polynomially weighted counterpart under an additional spatially uniform lower velocity profile, obtaining analogous weighted \(L^\infty\) bounds, uniqueness, and exponential relaxation. Our results provide a low-regularity alternative to conditional theories requiring smoothness and pointwise macroscopic bounds. They reveal how a single velocity-tail condition controls large-data Boltzmann dynamics and suggest a route toward problems with physical boundary conditions.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments that have a permeable boundary. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. In the limit of large bulk diffusivity an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

Visual AutoRegressive modeling (VAR) has pioneered a coarse-to-fine multi-scale autoregressive generative paradigm, demonstrating strong capabilities in image generation. However, VAR still suffers from inherent deficiencies in multi-scale representation learning. Specifically, lower scales primarily capture global semantics, while higher scales focus on fine-grained details. Employing a shared architecture across scales induces optimization conflicts. Moreover, due to the causal autoregressive process, inaccurate semantics at early scales can propagate and significantly degrade the final output. To address these issues, we introduce a scale-aware token-routed Mixture of Experts (MoE) architecture, allowing scale-adaptive expert selection, thereby facilitating decoupled representation learning across scales. In addition, we enhance semantic modeling at early scales by incorporating external self-supervised features. Unlike naive alignment, we analyse and design a residual feature aggregation scheme tailored to the VAR paradigm. Extensive experiments show that our method significantly improves both training efficiency and generation quality. On the ImageNet 256*256 benchmark, our model achieves a superior FID compared to the dense baseline while requiring only half of the default training epochs and a smaller parameter budget, with a merely marginal increase in training cost. Moreover, the performance gap further widens with larger training epochs.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

Neural Radiance Fields (NeRF) have achieved photorealistic novel views synthesis; however, the requirement of accurate camera poses limits its application. Despite analysis-by-synthesis extensions for jointly learning neural 3D representations and registering camera frames exist, they are susceptible to suboptimal solutions if poorly initialized. We propose L2G-NeRF, a Local-to-Global registration method for bundle-adjusting Neural Radiance Fields: first, a pixel-wise flexible alignment, followed by a frame-wise constrained parametric alignment. Pixel-wise local alignment is learned in an unsupervised way via a deep network which optimizes photometric reconstruction errors. Frame-wise global alignment is performed using differentiable parameter estimation solvers on the pixel-wise correspondences to find a global transformation. Experiments on synthetic and real-world data show that our method outperforms the current state-of-the-art in terms of high-fidelity reconstruction and resolving large camera pose misalignment. Our module is an easy-to-use plugin that can be applied to NeRF variants and other neural field applications. The Code and supplementary materials are available at https://rover-xingyu.github.io/L2G-NeRF/.

We allow the Higgs field Phi to interact with a dilaton field chi of the background spacetime via the coupling chi^2,Phi^daggerPhi. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to chi. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on chi, we present an textit alternative mechanism: the Higgs VEV will be used to construct Planck's constant hbar and speed of light c. Specifically, each open set vicinity of a given point x^* on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of hbar_* and c_* per hbar_*proptochi^{-1/2}(x^*) and c_*proptochi^{1/2}(x^*), causing these ``fundamental constants'' to vary alongside the dynamical field chi. Moreover, in each open set around x^*, the prevailing value chi(x^*) determines the length and time scales for physical processes occurring in this region as lproptochi^{-1}(x^*) and tauproptochi^{-3/2}(x^*). This leads to an textit anisotropic relation tau^{-1}propto l^{-3/2} between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of c along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lema\^itre redshift relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa through a declining speed of light in an expanding Einstein--de Sitter universe, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the H_0 tension without requiring a dynamical dark energy component.

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling such global inputs to km-scale, as a cost-effective machine learning alternative. The model is trained to predict 2km data from a regional weather model over Taiwan, conditioned on a 25km global reanalysis. To address the large resolution ratio, different physics involved at different scales and prediction of channels beyond those in the input data, we employ a two-step approach where a UNet predicts the mean and a corrector diffusion (CorrDiff) model predicts the residual. CorrDiff exhibits encouraging skill in bulk MAE and CRPS scores. The predicted spectra and distributions from CorrDiff faithfully recover important power law relationships in the target data. Case studies of coherent weather phenomena show that CorrDiff can help sharpen wind and temperature gradients that co-locate with intense rainfall in cold front, and can help intensify typhoons and synthesize rain band structures. Calibration of model uncertainty remains challenging. The prospect of unifying methods like CorrDiff with coarser resolution global weather models implies a potential for global-to-regional multi-scale machine learning simulation.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

A major goal of ongoing and future cosmological surveys of the large-scale structure is to measure local type primordial non-Gaussianity in the galaxy power spectrum through the scale-dependent bias. General relativistic effects have been shown to be degenerate with this measurement, therefore requiring a non-Newtonian approach. In this work, we develop a consistent framework to compute integrated effects, including lensing convergence, time delay, and integrated Sachs--Wolfe, along with the local relativistic projection and wide-separation corrections in the multipoles of the power spectrum. We show that, for a Euclid-like Hα-line galaxy survey and a MegaMapper-like Lyman-break galaxy survey, ignoring these effects leads to a bias on the best fit measurement of the amplitude of primordial non-Gaussianity, f_{rm NL}, of around 3,σ and 20 , σ respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of f_{rm NL}. In this work, we show that this degeneracy can be partly mitigated by using a bright-faint multi-tracer analysis, where the observed galaxy sample is subdivided into two separate populations based on luminosity, which provides a 15--20% improvement on the forecasted constraints of local type f_{rm NL}. In addition, we present a novel calculation of the full multi-tracer covariance with the inclusion of wide-separation corrections~-- all of these results are implemented in the Python code CosmoWAP.

Structural pruning enhances hardware-agnostic inference efficiency for large language models (LLMs) yet often fails to maintain comparable performance. Local pruning performs efficient layer-by-layer compression but ignores global topology. Although global pruning aims to identify an optimal sparse model, intuitive methods typically adopt a two-stage paradigm that first evaluates substructure saliency and then applies global pruning, which ignores inter-structure dependencies and fails to achieve end-to-end optimization. To address these limitations, we propose T\'yr-the-Pruner, an efficient end-to-end search-based global structural pruning framework. This framework constructs a supernet by repeatedly applying local pruning across a range of sparsity ratios to each layer in an LLM, with the core goal of determining the optimal sparsity distribution under a target overall sparsity ratio. Concretely, we introduce an effective local pruning and an expectation error accumulation approach to improve supernet construction. Furthermore, we employ an iterative prune-and-search strategy with coarse-to-fine sparsity granularity to ensure efficient search convergence. Experimental results show that T\'yr-the-Pruner achieves state-of-the-art structural pruning, retaining 97% of the dense model's performance while removing a challenging 50% of Llama-3.1-70B's parameters. Code will be available at https://github.com/AMD-AGI/Tyr-the-Pruner.

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data, and on estimating local Hessian matrices of neural network loss landscapes.

Neural operators that accept arbitrary meshes are often treated as geometry-general, but unseen domain topology changes both the invariant and decaying subspaces of a PDE operator. We use Hodge heat flow as a controlled lens on this distinction and introduce TopoBox-3D, where tunnels and cavities vary Betti support while the exact Hodge decomposition separates the harmonic kernel from the positive spectrum. Across six architectures, models that infer topology implicitly suffer excess matched degradation in 37 of 45 model--task topology-OOD cells, yet cases that change harmonic dimension are not more strongly penalized on average. The dominant difficulty is instead spectral: the initial Rayleigh quotient is the most stable predictor of error, and spectral broadening adds information for edge and face cochains. Most strikingly, controlled probes show that explicit incidence and harmonic coordinates do not yield the best kernel-identity accuracy; nevertheless, TNO ranks first in mixed-input nonharmonic accuracy on all six tasks with nontrivial harmonic support. Together, these results establish topology as a distinct generalization axis beyond arbitrary-geometry compatibility and show that its influence extends across the Hodge spectrum rather than remaining confined to the harmonic kernel. More broadly, they suggest that global, low-frequency structural priors may help organize predictions in the faster-decaying complementary component, offering a new perspective on how neural operators may generalize across topology as well as geometry.

We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of 2-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of k-local Hamiltonians, k geq 3, cannot have Lee-Yang radius at least one for all inverse temperatures βgeq 0. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures βgeq 0.

We study the scalar curvature of the Fisher information metric on the microscopic coupling-parameter manifold of lattice spin models at criticality. For a d-dimensional lattice with periodic boundary conditions and n = L^d sites, the Fisher manifold has m = d cdot n dimensions (one per bond), and we find |R(J_c)| sim n^{d_R} with d_R = (dν+ 2η)/(dν+ η), where ν and η are the correlation-length and anomalous-dimension critical exponents. For 2D Ising (ν= 1, η= 1/4), this predicts d_R = 10/9, confirmed by exact transfer-matrix computations (L = 6--9: d_R = 1.1115 pm 0.0002) and multi-seed MCMC through L = 24. For 3D Ising (ν= 0.630, η= 0.0363), the prediction d_R = 1.019 is consistent with MCMC on L^3 tori up to L = 10 (power-law fit: d_R = 1.040). For 2D Potts q = 3 (predicted 33/29 approx 1.138), FFT-MCMC through L = 40 shows d_eff oscillating non-monotonically around sim 1.20, consistent with O(1/(ln L)^2) logarithmic corrections. For q = 4 (predicted 22/19), effective exponents oscillate with strong logarithmic corrections. The Ricci decomposition identity R_3 = -R_1/2, R_4 = -R_2/2 holds to 5--6 digits for all models. This exponent is distinct from Ruppeiner thermodynamic curvature and reflects the collective geometry of the growing Fisher manifold. We provide falsification criteria and predictions for additional universality classes.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Massive activations, residual-stream coordinates with magnitudes far larger than typical activations, are associated with attention sinks in transformers, but how their scale is regulated during training remains incompletely understood. Combining training-trajectory analyses and controlled interventions, we trace their emergence, growth, and consolidation. Sink-carrying channels vary across random seeds but stabilize early within each run. Over longer training, surrounding channels erode and the sink concentrates onto a few redundant carriers. Across ablations, gradient attenuation follows the sink token's collective root-mean-square magnitude rather than any single channel, making collective scale central to understanding their effects. Our central result is that weight decay causally controls the turnover of global activation scale. In controlled continuations, removing decay near the peak allows this scale to keep rising, whereas retaining it produces decline even at constant learning rate. We develop a balance model for the rise and peak of massive-activation magnitude, in which AdamW-preconditioned growth opposes weight decay. Sweeping the decay coefficient λ shifts peak timing approximately log-linearly and yields peak magnitudes scaling approximately as λ^{-1/2}, consistent with this balance. Optimizer measurements further show that preconditioning sustains the large-channel cohort against decay even when raw maintaining forces are too small to do so. Together, these findings connect the observed life cycle to scale-regulating training dynamics and establish weight decay as a training-time lever on activation magnitude.

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Deep neural networks have reached human-level performance on many computer vision tasks. However, the objectives used to train these networks enforce only that similar images are embedded at similar locations in the representation space, and do not directly constrain the global structure of the resulting space. Here, we explore the impact of supervising this global structure by linearly aligning it with human similarity judgments. We find that a naive approach leads to large changes in local representational structure that harm downstream performance. Thus, we propose a novel method that aligns the global structure of representations while preserving their local structure. This global-local transform considerably improves accuracy across a variety of few-shot learning and anomaly detection tasks. Our results indicate that human visual representations are globally organized in a way that facilitates learning from few examples, and incorporating this global structure into neural network representations improves performance on downstream tasks.

Can Transformers predict new syllogisms by composing established ones? More generally, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity, but this does not address the learnability objective. This paper puts forward the notion of 'globality degree' of a target distribution to capture when weak learning is efficiently achievable by regular Transformers, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions, distributions with high globality cannot be learned efficiently. In particular, syllogisms cannot be composed on long chains. Furthermore, we show that (i) an agnostic scratchpad cannot help to break the globality barrier, (ii) an educated scratchpad can help if it breaks the globality at each step, however not all such scratchpads can generalize to out-of-distribution (OOD) samples, (iii) a notion of 'inductive scratchpad', that composes the prior information more efficiently, can both break the globality barrier and improve the OOD generalization. In particular, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the φ^{4} scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the φ^{4} theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the φ^{4} machine learning algorithms and target probability distributions.

Proper evaluations are crucial for better understanding, troubleshooting, interpreting model behaviors and further improving model performance. While using scalar-based error metrics provides a fast way to overview model performance, they are often too abstract to display certain weak spots and lack information regarding important model properties, such as robustness. This not only hinders machine learning models from being more interpretable and gaining trust, but also can be misleading to both model developers and users. Additionally, conventional evaluation procedures often leave researchers unclear about where and how model fails, which complicates model comparisons and further developments. To address these issues, we propose a novel evaluation workflow, named Non-Equivariance Revealed on Orbits (NERO) Evaluation. The goal of NERO evaluation is to turn focus from traditional scalar-based metrics onto evaluating and visualizing models equivariance, closely capturing model robustness, as well as to allow researchers quickly investigating interesting or unexpected model behaviors. NERO evaluation is consist of a task-agnostic interactive interface and a set of visualizations, called NERO plots, which reveals the equivariance property of the model. Case studies on how NERO evaluation can be applied to multiple research areas, including 2D digit recognition, object detection, particle image velocimetry (PIV), and 3D point cloud classification, demonstrate that NERO evaluation can quickly illustrate different model equivariance, and effectively explain model behaviors through interactive visualizations of the model outputs. In addition, we propose consensus, an alternative to ground truths, to be used in NERO evaluation so that model equivariance can still be evaluated with new, unlabeled datasets.

Geospatial Foundation Models (GFMs) have emerged as powerful tools for extracting representations from Earth observation data, but their evaluation remains inconsistent and narrow. Existing works often evaluate on suboptimal downstream datasets and tasks, that are often too easy or too narrow, limiting the usefulness of the evaluations to assess the real-world applicability of GFMs. Additionally, there is a distinct lack of diversity in current evaluation protocols, which fail to account for the multiplicity of image resolutions, sensor types, and temporalities, which further complicates the assessment of GFM performance. In particular, most existing benchmarks are geographically biased towards North America and Europe, questioning the global applicability of GFMs. To overcome these challenges, we introduce PANGAEA, a standardized evaluation protocol that covers a diverse set of datasets, tasks, resolutions, sensor modalities, and temporalities. It establishes a robust and widely applicable benchmark for GFMs. We evaluate the most popular GFMs openly available on this benchmark and analyze their performance across several domains. In particular, we compare these models to supervised baselines (e.g. UNet and vanilla ViT), and assess their effectiveness when faced with limited labeled data. Our findings highlight the limitations of GFMs, under different scenarios, showing that they do not consistently outperform supervised models. PANGAEA is designed to be highly extensible, allowing for the seamless inclusion of new datasets, models, and tasks in future research. By releasing the evaluation code and benchmark, we aim to enable other researchers to replicate our experiments and build upon our work, fostering a more principled evaluation protocol for large pre-trained geospatial models. The code is available at https://github.com/VMarsocci/pangaea-bench.

Gradient descent on a factored model W = UV^top is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not. We trace the difference to the gauge symmetry of the loss, its invariance under (U, V) mapsto (UQ, VQ). Gradient flow's low-rank mechanism is available to an optimizer only if that optimizer is gauge-equivariant, a condition necessary for the transfer but not sufficient for low-rank recovery. Gradient descent, momentum, "shared-scalar" Adam, Muon, and Shampoo satisfy it. Adam, RMSProp, and the other coordinate-wise methods do not. A structure theorem characterizes the memoryless equivariant rules as exactly the Gram-determined left preconditioners, and a transfer theorem carries gradient flow's pathwise properties to common-scalar flows. We then sort nine update rules on underdetermined matrix sensing by recovery error against the planted ground truth. A one-parameter family from coordinate-wise to shared-scalar preconditioning restores the bias monotonically, isolating anisotropy as the cause. A "spectral schedule" reconciles two opposing reports about Muon: equal-rate updates recover exactly low-rank targets but lose their edge as the spectral tail grows. In transformers, Adam separates two gauge-equivalent initializations at the first step, where the equivariant optimizers stay at float precision, and ends with the per-head invariants W_Q^top W_K 56% apart in relative Frobenius distance, a gap no per-head rotation can close. On two hyperspectral datasets at matched training loss, gradient descent cuts held-out error by 43-44% at the lowest sampling density, and at lower effective rank. Basis choice is therefore not a tuning detail but a decision about which interpolant the optimizer selects.

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS. Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines. The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill. This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies.

Global visual geolocation predicts where an image was captured on Earth. Since images vary in how precisely they can be localized, this task inherently involves a significant degree of ambiguity. However, existing approaches are deterministic and overlook this aspect. In this paper, we aim to close the gap between traditional geolocalization and modern generative methods. We propose the first generative geolocation approach based on diffusion and Riemannian flow matching, where the denoising process operates directly on the Earth's surface. Our model achieves state-of-the-art performance on three visual geolocation benchmarks: OpenStreetView-5M, YFCC-100M, and iNat21. In addition, we introduce the task of probabilistic visual geolocation, where the model predicts a probability distribution over all possible locations instead of a single point. We introduce new metrics and baselines for this task, demonstrating the advantages of our diffusion-based approach. Codes and models will be made available.

Kilometer-scale convection shapes precipitation extremes, tropical organization, and cloud feedbacks, but most global atmospheric models approximate these processes at 25-100 km resolution. Global storm-resolving physics models resolve convective systems explicitly, but at a cost -- roughly one MWh per simulated day on exascale supercomputers -- that limits long-duration simulation. We introduce STRATA (Storm-resolving Tile-based autoRegressive Atmosphere Transformer Architecture), the first autoregressive AI emulator for global storm-resolving atmospheric dynamics. STRATA is trained on the highest-resolution atmospheric dataset yet used for global AI emulation: 17 days of SCREAM physics-model output at 4.9-km resolution (~25 million grid cells) sampled every 10 minutes. Our central premise is that on 10-minute timescales atmospheric dynamics are predominantly local, so training on small spatial tiles trades scarce global temporal samples for abundant local spatial samples and enables global rollout via overlapping-tile blending. STRATA combines 3D patch embedding and local 3D neighborhood attention, a novel Stereographic Rotary Position Embedding (StereoRoPE) for grid-invariant encoding, and a pixel-space de-aliasing decoder that suppresses patch-scale rollout artifacts. An iso-FLOP scaling study reveals that km-scale emulation requires ~10x more FLOPs per grid point than coarse-resolution AI weather models, consistent with the higher information density of convective-scale dynamics. Trained on only 17 days of data, STRATA produces stable 24-hour global rollouts with realistic km-scale dynamics across diverse regimes, though large-scale biases develop with lead time. It achieves 48 simulation days per megawatt-hour -- about 50 times better energy efficiency than the SCREAM physics model -- and 741 simulated days per wall-clock day at 512 H100 GPUs. Code and dataset are publicly available.

We study the inverse adjoint problem for a perturbative bosonic outgoing map. Within the polynomial bosonic canonical-commutation-relation (CCR) algebra, we prove a constructive integrability theorem: order-by-order preservation of the CCRs is sufficient to reconstruct recursively a formal self-adjoint generator whose exponential implements the outgoing map by adjoint conjugation. At each order, the Baker--Campbell--Hausdorff contribution determined by previously reconstructed generators is subtracted from the outgoing coefficient, and the remaining homogeneous CCR conditions determine the next generator explicitly. We apply the construction to graviton scattering in the null-surface formulation (NSF), specialized to the flat solution-space sector with Minkowski metric, null generators, affine parameter, and cone measure. The NSF outgoing map preserves the Ashtekar radiative CCRs through (δa_3), corresponding to order (\varepsilon^2). At this order, the scalar CCR sector uniquely selects the symmetric ordering (c=1) for the nontrivial interacting kernel. The associated linear contraction, generated by the same cubic kernel, cancels the double-contraction contribution from ([δa_2,δa_2^\dagger]). The theorem then reconstructs the self-adjoint generators (δT_1) and (δT_2), providing a formal perturbative unitary implementation. The resulting canonical organization also separates the direct (2\to2) contribution into irreducible-loop, one-particle-reducible, and factorized sectors.

We present a new method for measuring the E_G statistic that combines two CMB secondaries -- the kinematic Sunyaev-Zeldovich (kSZ) effect and CMB lensing -- for the first time to probe gravity on linear scales. The E_G statistic is a discriminating tool for modified gravity theories, which leave imprints in lensing observables and peculiar velocities. Existing E_G measurements rely on redshift space distortions (RSD) to infer the velocity field. Here, we employ kSZ velocity-reconstruction instead of RSD, a complementary technique that constrains the largest-scale modes better than the galaxy survey it uses. We construct a novel V_G estimator that involves a ratio between cross-correlations of a galaxy sample with a CMB convergence map and that with a 3D kSZ-reconstructed velocity field. We forecast for current and upcoming CMB maps from the Atacama Cosmology Telescope (ACT) and the Simons Observatory (SO), respectively, in combination with three spectroscopic galaxy samples from the Dark Energy Spectroscopic Instrument (DESI). We find cumulative detection significances in the range S/N sim 20-55, which can robustly test the scale-independent E_G prediction under general relativity (GR) at different effective redshifts of the galaxy samples (zapprox 0.73, 1.33, 1.84). In particular, the SOtimesDESI LRG measurement would be able to distinguish between GR and certain modified gravity models, including Hu-Sawicki f(R) and Chameleon theories, with high confidence. The proposed V_G estimator opens up a new avenue for stress-testing gravity and the LambdaCDM+GR model at the largest observable scales.