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Temperature scaling is the dominant post-hoc calibration method in modern deep learning. Its theoretical justification rests on an assumption that is rarely stated explicitly: that ground-truth labels are one-hot and deterministic. In practice, labels are frequently soft, crowd-sourced, or genuinely distributional, reflecting real disagreement among human annotators rather than annotation noise. We study whether temperature scaling retains its calibration properties when this assumption is violated, and whether any resulting degradation depends on model scale. Using CIFAR-10H and ChaosNLI, two publicly available datasets with human-annotated soft label distributions, we evaluate three model scales per modality under both hard one-hot and soft distributional label targets. Across all nine configurations we find a positive soft-label calibration gap: temperature scaling calibrated on hard labels consistently underperforms an oracle calibrated directly on soft labels, with Brier Score gaps ranging from 0.002 to 0.134. The gap grows monotonically with model scale in the vision domain and on the SNLI-derived split of ChaosNLI, and is substantially larger in the language domain (mean gap 0.079) than in vision (mean gap 0.003). A scale-ordering reversal on the MNLI-derived split remains after matched-domain training; we treat it as inconclusive for the scale hypothesis and attribute it primarily to near-chance accuracy on that split. As a second post-hoc baseline, multiclass isotonic regression yields the same qualitative conclusion: positive soft-label gaps in all nine configurations, and larger gaps in language than in vision. These findings suggest that calibration protocols built on majority-vote labels systematically misstate model reliability wherever label ambiguity is structural, with direct consequences for deployment in safety-critical settings.

Microscaling is a critical technique for preserving the quality of Large Language Models (LLMs) quantized to ultra-low precision formats. Intuitively, finer block sizes should yield lower quantization error; however, a paradox recently identified by Fasoli et al. (2026) demonstrates that standard abs-max scaling can actually result in degraded model quality as block sizes shrink. In this work, we investigate the underlying mechanics of this phenomenon. We demonstrate that this degradation is not an inherent limitation of finer granularity, but is primarily driven by how elements in smaller blocks statistically cluster closer to their local block maximum, interacting poorly with the coarse subnormal E4M3 values used as scaling factors. Specifically, we show that i) preventing the scaling factor from underflowing to zero mitigates errors caused by extreme underflow, ii) targeted algorithmic interventions like the 4-over-6 methodology that give more flexibility to the choice of scaling factor resolve the paradox for larger values, and iii) a brute-force search establishes an optimal baseline, confirming that the theoretical Mean Squared Error (MSE) strictly improves with finer block sizes. Ultimately, our findings highlight a critical insight for hardware-software co-design: the block-size paradox is partially an artifact of naive scale selection. While using hierarchical scaling factors or wider formats like UE5M3 interchangeably resolves much of the quality loss, we found the 4-over-6 scale selection heuristic can even further improve quality, especially for very small block sizes. Consequently, maximizing the performance of next-generation ML accelerators will require treating silicon format specifications and software scaling algorithms as tightly coupled design choices.

Modern image generation and editing systems can produce photorealistic, prompt-aligned images, but still often render familiar objects at implausible relative sizes. To measure this failure mode, we introduce GenScale, a benchmark and evaluation protocol for real-world relative object scale in image generation and editing. GenScale contains 900 image-level entries and 1,643 pairwise anchor-target scale relations across common-object generation, human-product generation with metric dimensions, and scale correction from failed generations. We further design a human-calibrated ordinal judge for scalable pairwise scale evaluation. Last but not the least, we introduce Rescale, a model-agnostic post-processing agent for localized scale correction without modifying the source generator. Experiments reveal that state-of-the-art image generators and editors cannot reliably observe relative scale yet, while Rescale consistently improves scale plausibility across generated and edited images. Together, GenScale establishes relative object scale as a distinct, measurable, and actionable capability for image generation systems.

Pathological diagnosis is inherently multi-scale, requiring the integration of global tissue architecture at low magnification with cellular morphology at higher magnification. However, existing pathology benchmarks and vision-language models (VLMs) are still largely developed under single-scale settings, limiting their ability to learn clinically meaningful multi-magnification reasoning. Moreover, naively constructed visual question answering (VQA) tasks may be susceptible to text-only or superficial visual shortcuts, leading to unreliable assessments of visual understanding. To address these limitations, we introduce a benchmark and training framework for shortcut-resistant cross-scale pathology reasoning. We design an Adversarial Text-only Screening strategy for semantic reasoning questions and a Structure-controlled Distractor Sampling strategy for visual grounding questions, encouraging models to rely on cross-scale visual evidence. Based on this pipeline, we construct PathScale-VQA, a high-quality cross-scale pathology VQA benchmark with 10,373 multiple-choice questions grounded in 1,368 diagnostic paths across multiple magnification levels. Building on the semantic reasoning set, PathScale-R1 is optimized through Difficulty-driven Reasoning Distillation supervised fine-tuning followed by reinforcement learning with a Scale-aware Reasoning Structure reward, which encourages the use of evidence across magnifications. Extensive experiments demonstrate state-of-the-art performance of PathScale-R1 on cross-scale reasoning tasks and effective transfer to conventional single-scale pathology VQA. Our code is available at https://github.com/iMVR-PL/PathScale-R1.

A central challenge in image-goal UAV navigation under Global Navigation Satellite System (GNSS) denial is estimating metric distance and heading between current and goal views. Dense pairwise geometry models capture relative scene structure, but without a calibrated metric scale, they cannot directly provide reliable distance estimates for navigation. Although global scale calibration corrects the dominant scale bias, the remaining errors vary systematically with distance. In this paper, Range-Aware Scale Recovery (RASR) is proposed, which complements global scale calibration with range-aware residual correction. RASR encodes pairwise geometry extracted by a frozen Matching And Stereo 3D Reconstruction (MASt3R) backbone as a compact descriptor and separates the scale-recovery core from task-specific command calibration. On the official online evaluation of the UAVs in Multimedia 2026 PairUAV challenge, RASR achieved a total error of 0.003189, achieving a lower total error than global scale calibration alone. The results demonstrate that range-aware residual correction improves metric distance estimation beyond global scale calibration. Code and materials are available at https://github.com/lht-research/rasr-pairuav.

Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width $W$, the optimal frequency scales as $1/W$. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.

Existing deep learning methods perform well in medical image classification but struggle with multi-scale morphology and limited annotations due to fixed sampling and data-hungry training. Existing approaches address these challenges in isolation: DCN-based models provide adaptive sampling but lack explicit multi-scale attention fusion and label-efficient regularisation; multi-scale architectures typically rely on static fusion; and semi-supervised methods target label scarcity without jointly modelling adaptive cross-scale representations. We propose MSA-DCNN, a scale-consistent deformable attention learning framework that introduces adaptive multi-scale sampling, within-scale saliency refinement, learned cross-scale fusion, and auxiliary self-distillation within a unified optimisation scheme, with potential to generalise to structurally heterogeneous anatomy. We evaluate on three public benchmarks and an external hold-out set for leukaemia. MSA-DCNN demonstrates competitive and often better performance against ViT baselines, CNN baselines, and a MICCAI semi-supervised baseline under distribution shift and label scarcity in accuracy, F1, and AUC (binary), while using fewer parameters. Ablations confirm complementary component contributions, supporting MSA-DCNN as a practical foundation for data-efficient medical image classification.

Enterprise AI aims to move toward continuous event monitoring, detection, and action across specialist agents, yet existing multi-agent systems largely assume discrete request-response workflows and remain underexplored at enterprise scale. We evaluate DAG Plan and Execute and ReAct across 208 production-derived enterprise scenarios spanning Persona (<10 agents), Department (20-80), and Enterprise (200) scales, and introduce a Task Manager for continuous operation via priority inference, related-event merging, and preemption. Results show that scale, not task complexity, dominates orchestration performance: both architectures perform well at small scale but degrade at enterprise scale as agent discovery noise becomes the primary bottleneck, with simple tasks degrading more sharply than complex ones. DAG Plan and Execute offers higher precision and structured parallelization at smaller scales, but its higher overhead worsens at enterprise scale; ReAct is more robust by handling failures incrementally. The Task Manager reduces high-priority queue latency by 14-75% and improves related-event correctness by over 20 percentage points at enterprise scale.

The scale of speech anti-spoofing datasets has grown exponentially over the past decade, driven by the assumption that larger data leads to better performance. However, it remains unclear whether indiscriminate scaling commensurately improves model generalization. This study challenges the "scale-first" paradigm by decoupling the impacts of training data scale versus diversity. Through experiments on representative datasets, we report two key findings: (1) Larger is not always better. Expanding data scale excessively under fixed generation methods yields negligible returns and may even degrade cross-domain generalization due to overfitting.(2) Diversity outweighs scale. A smaller composite training set featuring diverse attacks significantly outperforms larger-scale datasets with limited diversity in cross-dataset evaluations. We conclude that future dataset construction should prioritize the diversity of generation methods over scale to effectively enhance model generalization.

Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables distance-aware scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors. Code is available at https://github.com/cheonwoolee/SiGMA.

City-scale 3D surface reconstruction from multiview images for downstream 3D simulation, poses highly challenging problems due to the scale and complexity of urban scenes. Existing city-scale 3D reconstruction methods based on NeRF, Gaussian Splatting etc. often fail to recover 3D meshes ready for simulation due to incomplete/missing geometry and irregular, noisy surfaces. Scaling existing small-scale 3D reconstruction methods to arbitrarily large urban scenes is highly infeasible due to their computational complexity. We present City-Mesh3R, a scalable framework for reconstructing watertight surface meshes directly from large unordered image collections. Unlike recent methods which use global sparse SfM point-cloud initialization followed by a distributed 3D dense reconstruction of large-scale scenes, our method follows an end-to-end images-to-mesh 3D reconstruction approach using a divide-and-conquer strategy. The sparse city map is reconstructed via topological image clustering, cluster-wise independent sparse SfM and map merging, without need for exhaustive image feature matching. Then this map is partitioned spatially to perform geometry-aware camera selection, followed by dense surface reconstruction and surface refinement using curvature-aware adaptive vertex density remeshing. These partition meshes are then stitched together to produce the global mesh of the city. The proposed end-to-end framework is evaluated on city-scale reconstruction datasets. As demonstrated by our qualitative and quantitative results, our proposed method yields high-fidelity watertight 3D meshes with regular geometry, capturing fine surface details, and is suitable for scaling to arbitrarily large scenes owing to the end-to-end processing in a distributed setting.

Modern GANs often introduce adversarial supervision on intermediate generator outputs and interpret the resulting multi-stage synthesis as coarse-to-fine hierarchical generation. In this work, we challenge this interpretation. We argue that standard scale-wise adversarial supervision does not construct a proper coarse-to-fine hierarchy: each intermediate image is independently pushed toward the real distribution at its own resolution, but this scale-wise realism does not ensure that outputs across stages represent the identical generated sample. Moreover, the scale-specific image produced at each stage is not used as an explicit refinement target for the subsequent stage. Therefore, its adversarial loss can improve a scale-specific output without constraining later stages to preserve the same sample trajectory, allowing them to move toward a different sample rather than refine the previous output. We refer to this problem as a cross-scale trajectory misalignment problem. To resolve it, we propose CAT, a Cross-scale Aligned Transformer for multi-scale adversarial generation. CAT keeps the discriminator scale-wise, so each intermediate output is evaluated at its own resolution, while adding a simple generator-side consistency regularization that aligns intermediate outputs with the final output. On class-conditional ImageNet-256, CAT-H/2 achieves an FID-50K of 1.56 with one-step inference after only 60 training epochs, outperforming strong one-step GAN and diffusion/flow baselines.

NVFP4 has recently emerged as an efficient 4-bit microscaling format for large language models (LLMs), offering superior numerical fidelity with native hardware support. However, existing methods often yield suboptimal performance due to inflexible scale selection and the coupled treatment of quantization and dequantization scales. To address these issues, we propose Scale Optimization for Accurate Reconstruction (SOAR), a novel post-training quantization framework that improves the accuracy of NVFP4 quantization. At its core, SOAR features Closed-form Joint Scale Optimization (CJSO), which jointly optimizes global and block-wise scales via analytical solutions derived from reconstruction error minimization. Furthermore, it incorporates Decoupled Scale Search (DSS). DSS decouples the high-precision quantization scale from its constrained dequantization counterpart, and performs discrete search to mitigate precision loss from scale quantization. Extensive experiments across multiple LLMs show that our method consistently outperforms existing NVFP4 quantization baselines, achieving superior accuracy under the same memory footprint with no additional hardware overhead. The code and models will be available at https://github.com/steven-bao1/SOAR.

Metric questions about video require vision-language models to use supplied real-world references to convert visual measurements into physical units. Yet we find that current models use this scale information only partially. When every world-space quantity in a prompt is rescaled by a common factor, the video remains equally valid and the correct answer changes by exactly that factor, but model predictions move only part of the way and accuracy remains concentrated near the familiar scale of the depicted objects. Across eight vision-language models, this under-response persists over four orders of magnitude. The same models recover the correct closed-form scaling laws when the identical physics is asked in a scale-free form, indicating that the main deficit lies in metric grounding rather than physical mechanism knowledge. We use this exact scaling relation as supervision without requiring metric annotations. Under a common rescaling of the supplied world-space quantities, the correct metric answer must change by the same factor. EquiSD exploits this constraint by projecting a model's own prediction onto the scale-equivariant family and fine-tuning the model on the resulting targets. It requires no ground-truth answers and only one model query per training video. On held-out simulated videos, EquiSD increases a 3B model's median response slope from 0.66 to 0.94 and improves mean relative accuracy by 9.2 points across scales. The learned relation generalizes to unseen world scales and transfers without adaptation to real QuantiPhy videos, where accuracy increases by 6.4 points. These results show that an exact physical symmetry can provide label-free supervision for improving metric grounding in vision-language models.

Existing theories derive neural scaling from data geometry or a specified data-model spectrum, but systems trained on the same data can scale differently when architecture or optimization changes the representations they can efficiently reach. We introduce Coupled Scaling, a task-conditioned framework in which finite-budget scaling depends on the relation between task structure and the geometry accessible to an architecture-optimization system. In a solvable mode-truncation model, loss separates into target energy outside architectural support and an unresolved supported tail. For an arbitrary priority order, the residual lies between the best-N supported tail and the tail beyond the largest completed high-value prefix. If the cumulative-tail and coverage log-rates are $γ_{A,T}$ and $ρ_{A,O,T}$, the residual exponent lies in $[ρ_{A,O,T}γ_{A,T},γ_{A,T}]$. Under bounded off-prefix gain, the completed prefix is rate-determining and $α_{A,O,T}=ρ_{A,O,T}γ_{A,T}$; for $a_{A,T,j}\asymp j^{-b_{A,T}}$, this gives $α_{A,O,T}=ρ_{A,O,T}(b_{A,T}-1)$. A fixed-kernel specialization derives the training-time exponent from the near-zero tail of a task-weighted spectral measure defined independently of the loss fit. The framework separates architectural support from finite-budget acquisition and motivates two tests: static task-relevant geometry should track loss at a common budget, while multiscale geometry should track coupling-specific exponent ordering, including reversal across contrasting tasks. An audit of released emergence trajectories identifies the controls needed for a direct factorial test that measures geometry separately from the scaling fit.

Looped language models turn hidden states into runtime state: each state is decoded for prediction and fed back into future computation. This creates a basic supervision question: which state variables does cross-entropy actually control? We show that dense per-loop cross-entropy controls the variables exposed by the readout, not every variable active in the recurrent transition. Hidden-state scale gives a concrete failure mode. Scale-invariant readouts such as RMSNorm and LayerNorm hide radial scale from the immediate cross-entropy loss, while pre-norm residual recurrence continues to carry and update that same scale. Thus per-loop loss can make early exits usable without controlling recurrent scale. In 44M and 129M looped transformers without inter-loop normalization, per-loop cross-entropy through RMSNorm readouts still drives final hidden-state norms into the thousands or tens of thousands. Scale-visible readouts and explicit norm penalties keep norms in the tens, and scale-removing recurrence is the complementary architectural fix. The resulting design rule is simple: dense supervision trains exits; recurrent scale control requires either making scale visible to a loss or removing it from the loop. Consistent with this rule, scale-controlled variants achieve lower perplexity at matched inference-depth operating points in our variable-depth benchmarks.

Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce $\textbf{SKILD}$, a $\textbf{S}$cale-invariant $\textbf{K}$-Space $\textbf{I}$mage $\textbf{L}$earning $\textbf{D}$iffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: $\textit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}$. Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2\times$--$8\times$ super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.

Rigid-body interpenetration frequently occurs in procedurally assembled and generated scenes and must be removed before downstream applications such as physical simulation. We present S4R (Scaling for Rigid-Body Interpenetration Resolution), a scale-continuation method for static interpenetration repair. S4R first uniformly shrinks each body about a fixed reference center to a small initial scale, at which the layout is penetration-free, and then restores full scale through a sequence of minimum-norm convex contact quadratic programs (QPs) that target the linearized separation margin during continuation. Resolution thereby replaces one deep correction with a sequence of shallow-contact subproblems. A conservative scale-event bound and frozen-witness gap predictions cut the number of exact mesh queries; the continuation then ends with a full-scale evaluator check and bounded tail refinement. We evaluate S4R on Kubric, HY3D-Bench, and Thingi10K using a shared mesh-level evaluator and a unified per-scene timing protocol. In the main comparisons on all three benchmarks, up to N=5000 bodies, S4R reaches zero reported penetration with displacement that stays small and nearly independent of scene size, and at the lowest wall time within each hardware tier among the compared methods. A GPU implementation extends these results to large-scale scenes. Our code and data can be found on our project page: https://frank-zy-dou.github.io/projects/S4R/index.html.

The growing ability of large language models and vision language models to jointly interpret and reason over images and text is reshaping medical agents, moving them from task specific predictors toward autonomous systems that perceive, reason, plan, remember, and act in clinical environments. This work departs from the capability first perspective of existing literature and instead begins from clinical deployment, asking what tasks, contamination resistant benchmarks, and interactive training environments are required before medical agents can be trusted in practice. Medical agents are formalized as sequential decision making systems under partial observability, together with a three level autonomy taxonomy spanning assisted, cooperative, and fully autonomous operation. The field is organized along a unified scaling spine consisting of framework scaling, capability scaling, and environment scaling. Within this framework, clinical environment scaling, the integration of tools, data, and clinical gyms, is identified as the most actionable yet underexplored direction for agents operating in PACS, EHR, and FHIR ecosystems. Clinical self evolution, where agents improve through interaction with their environments rather than parameter scaling alone, is further positioned as a key research frontier, drawing insights from self improving agents, agent gyms, and test time compute scaling. Applications across radiology, pathology, ophthalmology, and hospital workflows are examined together with deployment challenges including hallucination, cascading failures, and fairness. By consolidating more than 300 references, with particular emphasis on advances from 2025 to 2026, this work provides a roadmap toward trustworthy, self improving medical imaging systems for real clinical practice.

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.

Scaling laws describe how learning performance varies with model size, data size, and compute. While recent theoretical work has established scaling laws for sketched linear regression, much less is understood for contrastive representation learning. In this paper, we study a sketched linear model for contrastive learning under a paired Gaussian latent-variable setup. The learner observes only sketched views of two correlated variables and trains a bilinear contrastive score by full-batch empirical gradient descent. We analyze a Gaussian-negative quadratic contrastive surrogate under aligned power-law spectra and a contrastive source condition, where we derive a risk decomposition into irreducible risk, approximation error, GD bias, GD variance, and a cross term. The cross term is controlled by the bias and variance and therefore does not affect the upper-bound scaling. Our main theorem gives an explicit scaling law with respect to sketch dimension $M$, sample size $N$, and effective optimization horizon $L_{\mathrm{eff}}γ$. Compared with standard linear-regression scaling laws, the contrastive setting must learn interactions between two views, and this changes how optimization and finite-sample noise scale with model size, data, and training time. This provides a first theoretical step toward understanding scaling behavior in contrastive learning and gives guidance for balancing model size, data, and optimization compute.

In this paper, a novel test-time scaling law for physical artificial intelligence (AI) agents is introduced. This scaling law enables physical AI agents to reason with their world models to generalize in unforeseen scenarios at test time. The derived scaling law is grounded in the first principle of active inference, which equips agents with the general objective to survive in the real world, under which their specific task objectives are subsumed. Active inference achieves this by providing the reasoning to resolve prediction errors that arise when the agent encounters unforeseen situations outside its training distribution, enabling generalization in non-stationary environments. The proposed scaling law captures this by dynamically updating the agent's policy with this reasoning at test time. This policy update is modeled as a soft Bayesian inference process in which beliefs about the policy are updated using the reasoning that reduces expected prediction errors under allowable policies as a likelihood. The resulting posterior policy admits a biological interpretation, recovering the scaling mechanism that engages the brain's basal ganglia and prefrontal cortex at test time. To solve this analytically intractable problem, a variational inference solution minimizing free energy bounds is developed. This solution extends to enable learning beyond training by reinforcing new instances, resolved at test time, in both the policy and world model. Unlike existing scaling laws constrained by model size and training data, the derived solution scales with the continuous real-world experience of a physical AI agent. Simulation results on an autonomous driving task demonstrate that the proposed solution outperforms model-free Q-learning and model-based Bayesian reinforcement learning, achieving robust generalization to unforeseen scenarios while improving inference efficiency by over 36%.

Large Language Models (LLMs) demonstrate remarkable potential in dynamic graph reasoning, but suffer from a scaling bottleneck: current models can only handle graphs with tens of nodes, constrained by exponential reasoning overhead and finite context windows. While multi-agent systems (MAS) offer collective reasoning and topology-aware orchestration, capabilities naturally suited for graph-structured tasks, their application to dynamic graphs remains unexplored. This paper presents Scaling LLM Reasoning on Dynamic Graphs via Adaptive Spatio-Temporal Multi-Agent Collaboration (AdaSTORM), a framework that reformulates large-scale dynamic graph reasoning into two stages: (i) Adaptive Partitioning, partitioning large-scale dynamic graphs into subregions that match the model's reasoning capacity while minimizing inference cost; and (ii) Collaborative Reasoning, aligning graph partition topologies with a spatio-temporal decoupled multi-agent architecture. AdaSTORM is the first multi-agent framework tailored for dynamic graph reasoning. Extensive experiments show that AdaSTORM successfully breaks through the scaling bottleneck, scaling reasoning to thousand-node graphs with over 90% accuracy across several large-scale dynamic graph settings without external tools, significantly outperforms seven competitive baselines. Furthermore, it achieves state-of-the-art accuracy on existing benchmarks and generalizes robustly to real-world datasets. The source code is available at: https://github.com/irisorchid107/AdaSTORM/.

The scaling exponent $α$ in neural scaling laws $L(N) \propto N^{-α}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $α$ depends systematically on the optimizer. In controlled random-feature regression experiments -- the canonical theoretical framework for neural scaling -- we measure $α$ across five optimizer variants and six spectral conditions. Preconditioned optimizers consistently yield steeper scaling (larger $α$), with the $α$-shift increasing across most of the tested spectral range, peaking near $s = 1.5$, and remaining large at $s = 2.0$. At $s \approx 1.0$ (characteristic of natural language), the full natural gradient achieves $α\approx 0.31$ versus $α\approx 0.12$ for gradient descent -- a $2.6\times$ larger fitted exponent that, within the random-feature model, compounds with each model-size doubling. Whether and how this exponent shift transfers to large-scale LLM training -- where recent evidence suggests the advantage may attenuate with scale -- remains an important open question. Our results imply that scaling-law forecasts should account for optimizer choice, and we provide a spectral diagnostic predicting when advanced optimizers will pay off.

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Scaling laws have made language-model performance predictable from model size, data, and compute, but they typically treat the optimizer as a fixed training detail. We show that this assumption misses a fundamental axis of representation scaling: how effectively the optimizer converts added FFN width into utilized spectral capacity. Using eigenspectra of feed-forward network representations, measured through soft and hard spectral-ranks, we find that \emph{the same Transformer architecture realizes markedly different spectral scaling laws when trained with different optimizers}. Holding architecture and width schedule fixed, AdamW exhibits weak hard-rank scaling ($β$=0.44) on rare-token (TAIL) representations where learning is known to be hardest, whereas Muon achieves linear scaling ($β$=1.02) in the same regimes, a $2.3\times$ increase in the scaling exponent. This difference is not reducible to validation loss: AdamW configurations can match low-rank Dion variants in perplexity, under extended training, while exhibiting sharply different spectral geometry, demonstrating that matched loss does not imply matched representation structure. Hard--soft rank asymmetry further reveals that optimizers differ not only in how much capacity is realized, but also in how that capacity is structured across eigenmodes. To disentangle optimizer effects from architectural ones, we compare against architectural interventions (e.g., attention rank and positional encoding), and find that optimizer-induced spectral shifts often exceed the architectural effects. These results suggest optimization as a first-class axis of representation scaling, motivating optimizer--architecture co-design.

Model scaling has demonstrated remarkable success through large-scale training on diverse datasets. It remains an open question whether the same paradigm would apply to autonomous driving perception systems due to unique challenges, such as fusing heterogeneous sensor data and the need for sophisticated 3D spatial understanding. To bridge this gap, we present a comprehensive study on systematically analyzing the impact of scale on these systems. We develop our STELLAR model based on Sparse Window Transformer, by extending the input modalities to include LiDAR, radar, camera, and map prior. We train the model on a large-scale dataset of 50 million driving examples with up to 500 million parameters. Our large-scale experiments reveal empirical scaling trends that connect model performance to model size, data, and compute. The resulting model establishes a new state-of-the-art on the Waymo Open Dataset challenge, outperforming prior arts by a large margin. Our work demonstrates that large-scale training is a highly promising path for advancing the capabilities of perception models for autonomous driving.

Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in general norm geometries and develop three complementary algorithms. For smooth non-convex objectives, we introduce Distance-Adaptive Muon, whose trust-region radius is set from the radius explored by the trajectory, and prove a stationarity guarantee under a bounded-trajectory assumption. We then turn to star-convex objectives, a tractable model of the favorable global geometry often used to reason about the empirical loss landscapes of deep neural networks, where objective-gap guarantees are possible. In this setting, we first introduce Scale-Calibrated Muon, which keeps Muon's exponential moving average but sets the step length from a local descent certificate computed from the current gradient and momentum. For this method, we prove a last-iterate O(1/T) objective-gap bound under a bounded initial sublevel-set assumption, where the corresponding radius parameter appears only in the analysis and not in the algorithm. Finally, we develop Distance-Free Muon, a recentered trust-region method that uses a scalar distance certificate and a majorized one-dimensional search to select the trust-region radius without requiring the unknown distance from the initialization to a global minimizer. Experiments on Transformer language modeling (GPT-124M/WikiText-103) and image classification (ViT-Tiny/CIFAR-100) show that the proposed adaptive scaling rules reduce sensitivity to manual scale tuning and match or improve tuned fixed-scale Muon baselines under the tested budgets.

Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are hardest to obtain: fitting one for a new model task pair demands expensive sweeps that typically exhaust the very compute budget the law is meant to economize. This paper poses the research question of how to develop generalizable scaling laws: laws fit once on a well-resourced source domain and reliably transported to new domains where running a full sweep is infeasible, which requires a fundamental understanding of when and why scaling properties change. We address this by identifying the right invariants: scaling laws are preserved under bijective (information-preserving) transformations of the data and modified in predictable, information-theoretically grounded ways under non-bijective transformations that lower its information resolution $ρ$: a single axis along which a law fit in one domain can be transported to another. We validate this across language, vision, and speech, and demonstrate two cross-domain applications: predicting scaling for language models trained on electronic health records from laws fit on general text, and predicting time-series classification scaling under varying levels of noise injection, recovering the data-scaling exponents to within $3\%$ error.

Legged robots operate across a wide range of physical scales, but how their designs should be adapted as size changes remains unclear. Here, we tackle this question in two ways. First, we survey existing legged robots to provide a broad context for the key scaling variables, robot mass m and leg length L. We find the surprising result that bipedal robot mass generally scales with the length squared, L^2, rather than the isometric prediction L^3. Then, to reduce the variance in design choices, we focus on a pair of previously developed bipeds that share the same quasi-passive morphology but differ by a factor of six in leg length, use different feet and controllers, and achieve different relative speeds. We reconstruct both robots in a common 3-D simulation environment and scale each design over leg lengths from 0.02 to 1.2 meters under both mass models (mass is proportional to L^2 and is proportional to L^). The controlled comparison shows that velocity follows dynamic similarity, velocity is proportional to L^{1/2}, across designs and mass models, while the torque needed to sustain walking follows that tau is proportional to mL. Consequently, torque scales approximately with L^3 when m is proportional to L^2 and L^4 when mass is proportional to L^3. A 3-D foot-shape sweep further shows that foot dimensions that permit walking scale approximately linearly with leg length, but the speed-maximizing shape and the mechanism by which each robot moves do not transfer by scaling alone. Overall, the results provide practical insights for rescaling legged systems that leverage natural body dynamics.