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cs.MAcs.AIcs.LG Andrea Iannoli, Ivan Zyrianoff, Angelo Trotta et al. · Oct 1, 2026

Unmanned aerial vehicle swarms operating with independent edge-deployed language models face a dual challenge: reasoning context degrades as interaction histories grow, and indiscriminate information sharing wastes limited bandwidth. This paper proposes a distributed architecture in which each UAV maintains structured atomic notes in bounded core, local, and peer-specific memory queues, coupled with a deterministic Interest-Aware Gossip Engine that forwards messages based on semantic novelty and recency. The work matters because it targets the practical gap between centralized LLM coordination, which introduces bottlenecks and single points of failure, and fully decentralized control, which risks context degradation and communication collapse.

Unmanned aerial vehicle (UAV) swarms increasingly rely on language-model agents to provide adaptive mission-level reasoning in uncertain environments. Fully distributed control, in which each UAV hosts an independent Small Language Model (SLM), removes reliance on a centralized coordinator but introduces an information-management problem: long-running interaction histories can degrade the reasoning context, while indiscriminate information dissemination increases communication and inference overhead. We address these challenges with a distributed UAV-agent architecture that enables continuous local SLM control through an event-driven reason-act-observe lifecycle. Runtime knowledge is represented as structured atomic notes and organized into core, local, and peer-specific memory. A deterministic interest-aware gossip engine selectively disseminates these notes according to recipient-specific semantic novelty and recency. We evaluate the architecture using ten UAVs in a simulated search-and-rescue mission. Our approach completes all experimental runs, whereas unrestricted flooding messages completes only 70-85\%, and delegating forwarding decisions to the SLM prevents mission completion in every run. Compared with unrestricted flooding, our approach approximately halves inference-token consumption, reduces transmitted data, and achieves lower survivor-count error.
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cs.LG Wentao Yue, Tianyou Lai, Hongji Li et al. · Oct 1, 2026

Federated learning on edge devices must simultaneously handle varying resource budgets and domain-shifted local data. FedSAP frames this coupled challenge as a structured pruning problem where channels are assigned to Global, Private, or Dropped states. By inferring pseudo-domains from shallow gradient similarity and allocating layer-wise budgets adaptively, the method improves global mean accuracy under aggressive heterogeneous compression.

Federated learning (FL) on heterogeneous edge devices must jointly accommodate unequal resource budgets and domain-shifted local data. Existing resource-adaptive methods decide how much of a model each client trains but not where retained capacity should reside or how it should be shared, whereas federated domain-generalization methods usually assume a shared full architecture. Uniform compression can therefore discard high-utility channels, and a single aggregation path can mix transferable features with domain-sensitive updates. We propose FedSAP, a domain-aware heterogeneous FL framework that casts structured pruning as budget-constrained tri-state channel allocation. FedSAP converts each keep ratio into non-uniform layer budgets, assigns stable channels to a Global pool, useful domain-sensitive channels to pseudo-domain-specific Private pools, and low-utility channels to a Dropped state. This partition lets broadly useful features benefit from cross-client pooling while isolating domain-sensitive updates from incompatible clients. Domain-Guided Assignment infers pseudo-domains from shallow-gradient similarity, while Type-Matched Aggregation restricts each channel to its intended sharing scope. Across three random seeds, FedSAP reaches 76.00% and 72.67% mean global accuracy on Digits and Office-Caltech, exceeding the strongest baseline by 1.70 and 4.92 percentage points while supporting client pruning ratios of up to 80% across heterogeneous clients.
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cs.LG Sahel Torkamani, Henry Gouk, Rik Sarkar · Oct 1, 2026

Explaining why neural networks generalize and how training unfolds remains a central challenge in deep learning. This paper introduces Magnitude Potential (MP), a point-set coverage measure from metric space theory, and defines the MP ratio $\mathcal{R}^t_{X,X_c}(z)$ as the within-class potential divided by the full-dataset potential at the logit layer. The authors argue this single geometric score predicts per-sample memorization, detects decision-boundary phase transitions, and foreshadows grokking without requiring model retraining or architectural assumptions.

Explaining generalization and training dynamics in neural networks remains a challenge, and various approaches have been developed to study different aspects of these phenomena. In this paper, we introduce the idea of {\em magnitude potential} -- a quantity based on the theory of metric magnitude -- that reflects how well an arbitrary point is represented by a given set. We find that this basic quantity can be applied to examine various features in neural generalization. The ratio between the magnitude potential with respect to a class and with respect to the entire data, computed at the logit layer, is informative of the representation of the point. In experiments, these ratios for individual training points are found to be correlated with the Feldman memorization scores. Magnitude potential ratios aggregated across points detect structural changes in the decision boundaries and provide a geometric indicator of grokking in modular arithmetic. Although the magnitude potential ratio and neural collapse are both closely associated with intra-class and inter-class geometric structure, the magnitude potential ratio remains informative even when neural collapse is explicitly suppressed.
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cs.LGstat.ML Vladimir R. Kostic, Karim Lounici, H\'el\`ene Halconruy et al. · Oct 1, 2026

LITL addresses the problem of recovering target Langevin dynamics when only biased or static source samples are available, complemented by black-box evaluative feedback. The core idea is to learn the dominant spectral subspace of the target infinitesimal generator and its projected drift via importance-weighted Dirichlet representation learning, explicitly avoiding target trajectories, gradients, or retraining. This matters for molecular dynamics, auditing generative models, and post-hoc steering of learned representations under distribution shift.

Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-dimensional structure, evolving on slow timescales. However, target trajectories, used to identify and interpret such dynamics, are often inaccessible: only biased or static samples that explore the underlying manifold are available. We introduce Langevin-Informed Transfer Learning (LITL), a framework for recovering target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift through Dirichlet representation learning, enabling kinetic reconstruction in spectral form and slow-manifold gradient field estimation. We further introduce a spherical variant well suited to steering normalized latent representations commonly used in learning systems toward desired objectives. We establish finite-sample guarantees for eigenvalue, eigenfunction, and projected drift estimation in Sobolev norms, thereby ensuring generalization of these quantities and their first-order derivatives. Empirically, LITL recovers physical transition timescales from biased molecular simulations, builds kinetic structure from static samples of generative models, reconstructs spherical symmetries of physical systems, and enables post-hoc latent steering of trained neural networks under black-box feedback. Together, these results position spectral operator learning as a practical framework for recovering stochastic dynamics under distribution shift and unlock applications across machine learning and the physical sciences.
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cs.LGcs.AIcs.SD Constance Douwes, Paul Magron, Romain Serizel · Oct 1, 2026

Deep learning audio research hides a massive energy footprint behind the final training run. This paper develops a methodology to estimate the full development-phase cost of audio DL projects by mining job logs from the Grid5000 shared computing platform. By tracing thousands of individual jobs across four representative projects, the authors show that prototyping, debugging, and hyper-parameter search can consume $3 imes$ to $256 imes$ more energy than training the reported best models, calling for systematic lifecycle reporting.

The environmental impact of deep learning has attracted increasing attention over the past decade. Existing studies mainly focus on the energy and carbon emissions of model training and inference, while the whole development phase is often overlooked. Yet, architecture prototyping and intensive experiments are conducted during this stage, which is highly energy-demanding. In this article, we propose a methodology to estimate these costs, based on activity logs from the Grid5000 shared computing platform used by the LORIA laboratory. As a case-study, we focus on audio projects developed in the Multispeech research team. We evaluate the overall energy cost of four projects, and we compare them to those of training the reported models. Our results show that the energy required for the development phase is 3 to 256 times greater than that required to train the best-performing model alone. These results advocate for a more systematic reporting of energy consumption across the entire life cycle of deep learning-based audio projects.
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cs.CVcs.AIcs.LG Yuzhou Wang, Emile Anand, Ijay Narang · Oct 1, 2026

Hob-VL introduces a diagnostic benchmark for visually grounded Boolean reasoning, asking vision-language models to evaluate ten-literal Boolean combinations over images and to identify objects satisfying Boolean descriptions. The core idea is to pair each expression with a mechanically verified De Morgan equivalent and to test both symbolic and natural-language presentations, isolating compositional reasoning from surface memorization. It matters because real-world visual queries—warehouse checks, agricultural monitoring, medical imaging—depend on reliably combining multiple visual facts under logical constraints.

Reliable visual reasoning requires composing multiple visual observations and returning consistent answers to logically equivalent questions. We introduce Hob-VL, a benchmark for visually grounded Boolean reasoning. Hob-VL comprises two tasks: (1) evaluating whether a Boolean rule holds in an image, and (2) identifying the (unique) object satisfying a Boolean description. Hob-VL contains 6,000 human-verified balanced Yes/No questions, each defined by a Boolean combination of ten visual statements, across 1,000 generated scenes and 46 diverse labeled photographs, along with 1,000 object-identification questions over the same photographs. Our question families are deliberately constructed to challenge reasoning through misleading local cues and nested logical operations, and include symbolic and structured natural-language presentations. Across eight model configurations with thinking disabled or minimized, Boolean accuracy ranges from 48.52% to 50.57%, while the identification accuracy reaches at most 43.0%. A thinking-enabled GLM configuration achieves uneven gains while retaining substantial errors and inconsistencies. Hob-VL exposes these failures through executable reference answers and matched evaluations.
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cs.LGcs.AI Guy Amit · Oct 1, 2026

Decision models that score a variable-sized set of candidate actions from a serialized sequence are vulnerable to permutation sensitivity because standard causal attention lets later candidates attend to earlier ones and uses absolute positions. The paper proposes candidate-independent block-causal attention (CI), which blocks cross-candidate information flow and resets per-candidate positions so that each candidate is scored based only on the shared prefix and its own tokens. This matters for System 1 components inside generative systems, where runtime-dependent candidate order should not become a latent feature; the authors show that CI cuts flip rates by an order of magnitude across three backbones while preserving competitive accuracy.

Decision models often score a variable-sized set of candidate actions encoded in a single sequence. This setting is increasingly relevant for System 1 components inside generative systems, where candidates may be proposed or ordered differently across runs. Standard causal cross-encoding is expressive, but it can make a candidate's score depend on serialization order rather than on the underlying decision problem. We introduce candidate-independent block-causal attention, which preserves causal computation within the shared context and each candidate while blocking cross-candidate information flow and resetting candidate positions. We compare this architecture with standard causal attention and complementary invariant baselines across Gemma 3 1B, Qwen3 1.7B, and Qwen3 4B backbones. Candidate-independent attention consistently reduces permutation sensitivity while retaining competitive decision quality; ablations indicate that candidate isolation is the primary source of the effect, with position resetting completing the intended symmetry. A larger Qwen3-4B study further examines the behavior of the proposed architecture with substantially more training data. Code is available at the \href{https://github.com/guyAmit/ci-decision-models}{\textcolor{blue}{project repository}}, and the \href{https://huggingface.co/Guy-Amit/qwen3-4b-ci-decision-4096-poc}{\textcolor{blue}{Qwen3-4B model artifact}} is available on Hugging Face.
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cs.LG Yaniv Oren, Viliam Vadocz, Wiktor Zabka et al. · Oct 1, 2026

Iterative policy improvement is central to practical RL, but approximate value estimates make greedification unreliable. This paper defines optimal policy improvement restricted to a state subset as solving an induced MDP, and derives $\mathcal{I}_{\text{opt}}$, a novel greedification operator that formulates approximate evaluation as probabilistic decision-making under uncertainty. It weights advantages by action-dependent uncertainty, generalizes popular regularized operators, and improves aggregate performance across model-based and model-free, discrete and continuous, and online and offline settings.

Practical Reinforcement Learning (RL) algorithms learn to solve Markov Decision Processes (MDPs) through iterative policy improvement in the presence of approximate evaluation. We study policy improvement from first principles, defining optimal policy improvement as producing the best policy attainable in a single update under specified constraints. We show that optimal improvement restricted to a set of states is equivalent to solving an induced MDP, characterizing planning with an explicit or implicit model as a path towards optimal policy improvement. Because practical methods commonly solve such induced problems through iterative improvement in the form of greedification, we take steps towards optimal greedification under the central practical constraint of approximate evaluation. We formulate greedification under this constraint as probabilistic decision-making under uncertainty and derive a novel operator that is optimal with respect to the resulting objective. Empirically, the operator and its practical gradient-based approximations improve aggregate performance across GumbelAlphaZero, SAC, ReBRAC and Generalized Policy Iteration, in experiments spanning discrete and continuous actions, model-based and model-free, online and offline RL.
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cs.LGcs.AI Alessandro Micheli, Andrea Zerio, Samir Bhatt · Oct 1, 2026

This paper extends one-step generative modeling to finite discrete spaces by replacing Euclidean drift with a discrete Wasserstein gradient flow. Using Maas geometry on a reversible Markov kernel, it defines a relative-KL flow that is realized at the particle level by Markov jumps and amortized into a neural generator. The result is a theoretically grounded analogue of continuous drifting that preserves one-step inference. The work is validated only on a small controlled torus, leaving real-world scalability as open future work.

We introduce a new framework for one-step generative modelling on finite state spaces. To extend drifting beyond continuous domains, we use discrete Wasserstein geometry to define a target-relative KL gradient flow over the transitions of a reversible Markov kernel. We realize this probability flow at the particle level through Markov jumps and amortize the resulting transport updates into a latent-conditioned generator, so that the iterative dynamics are required only during training while inference remains one-step. In a controlled setting where the underlying distributions and transport dynamics can be computed exactly, we verify KL dissipation, consistency between the particle dynamics and the probability flow, and the predicted numerical scaling. We further show that a finite-capacity neural generator can track these exact transport targets while retaining one-step generation. These results validate the basic construction and provide a foundation for scaling Discrete Drifting to structured discrete data.
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cs.CLcs.LGcs.SD Yuxiang Wang, Kunyu Feng, Yuancheng Wang et al. · Oct 1, 2026

AURAL tackles the tension between reasoning quality and low latency in speech language models by replacing explicit chain-of-thought with adaptive latent reasoning. Instead of generating slow text intermediates, the model predicts chunks of continuous latent states drawn from a Gaussian mixture, cutting time to the first token by more than 11x while largely matching explicit CoT accuracy across two backbones. The work also constructs AuralReason-683K, a bilingual corpus of 683K utterances with concise reasoning traces used to initialize latent training.

Model intelligence and fast response jointly shape the quality of interaction with speech language models, yet remain difficult to achieve together. Explicit chain-of-thought (CoT) improves reasoning and audio understanding, but generating intermediate reasoning tokens delays responses. Describing fine-grained acoustic cues further lengthens CoT and increases latency. Latent reasoning can reduce this overhead, yet existing methods often trail CoT and remain limited by single-path supervision and reasoning budgets that do not adapt to problem difficulty. We introduce AURAL, which models a distribution over multiple plausible reasoning continuations in latent space and jointly predicts chunks of future states to reduce sequential forward passes and reasoning latency. To provide initial supervision for latent reasoning, we construct AuralReason-683K: 683K bilingual speech utterances (about 1,000 hours) with concise CoT for emotion recognition, empathetic dialogue, and general reasoning. AURAL-RL then explores beyond these traces, rewarding concise reasoning that yields high-quality answers and adapting reasoning effort to each problem. Across two backbones, AURAL-RL achieves performance comparable to CoT-RL, with larger gains over the respective supervised checkpoints on most metrics. Analysis further shows that harder questions elicit more latent reasoning steps. On Qwen2.5-Omni, it reduces time to the first answer token by 11.8x, from 1.22 to 0.10 s, versus 0.05 s for direct answering.
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cs.LG Minho Jeong, Dooho Lee, Jinmo Lee et al. · Oct 1, 2026

Tabular foundation models (TFMs) achieve strong zero-shot performance through in-context learning, but repeatedly encoding the labeled context at inference time is expensive. This paper studies how to distill TFMs into lightweight, dataset-specific students. It systematically examines two design choices—how to construct teacher supervision (full-context versus out-of-fold, mixed with labels or not) and whether cheap synthetic queries improve distillation—and derives a simple recipe that yields median inference speedups of $3.0\times$–$21.6\times$ while recovering roughly two-thirds of the teacher's accuracy advantage over a standard supervised student.

Tabular foundation models (TFMs) achieve strong predictive performance through in-context learning, yet repeatedly conditioning on labeled data makes inference expensive. Knowledge distillation can reduce this cost by transferring their predictive ability to lightweight, dataset-specific students. However, the dependence of TFM predictions on both a labeled context and a query introduces two design questions: how to construct teacher supervision and whether expanding query coverage improves distillation. We examine these questions across two TFMs and both neural and tree-based students, and derive an effective distillation recipe. The recipe uses the full labeled training set as teacher context and trains students solely on teacher predictions for observed and synthetic queries. On TabArena, the resulting students outperform their supervised trained tuned-and-ensembled counterparts by 57-98 Elo points. Applied unchanged to TALENT, the same recipe improves matched default students on 236-258 of 300 datasets and reduces median primary error by 4.0-6.4%. The distilled students also achieve median inference speedups of 3.0-21.6 times over their teachers, offering a practical trade-off between predictive performance and repeated inference cost. Code is available at https://github.com/nums-ai/TFM_Distillation .
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math.OCcs.LGcs.SY Yashdeep Chaudhary, Roberto Armellin, Harry Holt · Oct 1, 2026

This paper tackles deterministic multi-impulse interplanetary rendezvous by embedding classical astrodynamics inside a reinforcement-learning policy. The proposed Reachability Analysis-Informed RL (RARL) framework maps bounded velocity perturbations into a local ellipsoidal waypoint set via the first-order position-from-velocity sensitivity matrix; the policy selects a waypoint, and a Lambert solver reconstructs the dynamically consistent impulsive arc. The core contribution is a physically structured action interface that supports both near-optimal nominal transfers and policy reuse across a family of dispersed departure states.

Reinforcement learning offers the prospect of a reusable sequential decision-making mechanism for spacecraft trajectory design, motivating policy interfaces that connect learned decisions to the underlying maneuver geometry. This paper develops Reachability Analysis-Informed Reinforcement Learning (RARL) for deterministic multi-impulse interplanetary transfers, placing intermediate waypoint selection at the center of the learned decision process. Local first-order reachability maps bounded velocity perturbations into an ellipsoidal set of next-node positions, within which the policy selects its waypoint. Lambert reconstruction then determines the corresponding maneuver to reach this selected waypoint along a dynamically consistent ballistic arc, coupling learned transfer-geometry selection with classical astrodynamics. A terminal two-impulse reconstruction completes the rendezvous, supported by a linear maneuver-demand assessment used for reward shaping. Numerical studies characterize this interface on a two-body Earth-Mars benchmark. Across three independent training runs, RARL achieves a mean maneuver cost of 10.23 km/s, 1.72% above a validated local sequential convex programming reference. Training over dispersed initial states extends policy reuse across a departure family with fixed target state and transfer duration. Each of the three independently trained multi-state policies completes all 10,000 held-out Monte Carlo departures without impulse-cap violations, compared with a mean feasibility rate of 6.49% for single-state policies. This broader sampled feasibility is accompanied by a 0.61% increase in mean nominal maneuver cost, without further training across departures. These results demonstrate that a reachability-informed decision interface supports benchmark-quality trajectory construction and policy reuse across dispersed departure conditions.
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cond-mat.stat-mechcond-mat.mtrl-scics.LG Mengyi Chen, Peichen Zhong, Zihan Zhang et al. · Oct 1, 2026

Bridging quantum-mechanical accuracy with mesoscopic length and time scales remains a grand challenge in materials modeling. This paper develops an ab initio phase-field framework that derives the mesoscopic evolution equation from molecular dynamics via Mori–Zwanzig projection, leaving only the free energy and mobility to be learned by neural networks from short machine-learning-interatomic-potential trajectories. The result is a data-efficient approach that propagates ab initio accuracy to scales far beyond direct atomistic simulation, demonstrated here on iron–boron melts and hydrogen–helium mixtures under planetary conditions.

Simulating microstructure evolution requires quantum-mechanical accuracy and mesoscopic reach in length and time scales, a combination that no current method achieves. Classical phase-field models provide this reach, but their accuracy is limited by phenomenological free energies and mobilities. Here we develop a framework for learning ab initio phase-field models, where the mesoscopic equation is not postulated but derived from a Mori-Zwanzig projection of molecular dynamics onto species-density fields under explicit assumptions. The nonlocal free energy and mobility left unspecified by this equation are parametrized by neural networks and learned from short molecular dynamics trajectories generated with machine-learning interatomic potentials of ab initio accuracy. We demonstrate the framework on an iron-boron melt and on hydrogen-helium mixtures under planetary conditions. For iron-boron, the model shows that the melt at the FeB$_4$ composition is spinodally unstable at ambient pressure but stabilized at 10 GPa, offering a thermodynamic rationale for why FeB$_4$ has been synthesized only under high pressure. For hydrogen-helium, the model predicts the immiscibility boundary and captures droplet nucleation and growth in helium-rain simulations of a column corresponding to 2.2 million atoms, far beyond the scale of atomistic modeling at comparable accuracy. Trained across compositions and conditions, such models could provide a mesoscopic counterpart to ab initio molecular dynamics.
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cs.LGcs.AI Samuele Bortolotti, Weixin Chen, Han Zhao et al. · Oct 1, 2026

Neuro-symbolic predictors require hand-crafted logical constraints, which limits adoption by practitioners without formal-methods expertise. This paper asks whether LLMs can translate natural language into propositional constraints that plug into NeSy predictors, and introduces auto-nesy-bench—an 18-task benchmark that measures both formalization fidelity and downstream accuracy. The core finding is that frontier LLMs can generate formulas approaching expert quality, and when the formulas are syntactically valid they often preserve downstream predictor performance, suggesting a plausible path toward making reliable NeSy AI more accessible.

Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified constraints, making them particularly suitable for high-stakes applications where compliance with domain knowledge is essential. A key bottleneck in this paradigm is the acquisition of symbolic constraints: encoding domain knowledge into logical formulas remains a manual and expert-intensive process. In this work, we investigate the extent to which auto-formalization via LLMs can systematically translate textual knowledge into symbolic knowledge that can be plugged into NeSy predictors. To this end, we introduce auto-nesy-bench, a new benchmark for evaluating constraint formalization and its impact on downstream accuracy of NeSy predictors. Through an extensive evaluation across several domains, we find that LLMs can formalize constraints to a meaningful extent, generating formulas that are often similar to those provided by human experts. Moreover, when the generated formulas are syntactically valid, they can lead to high-quality downstream predictions. The code and benchmark are available at https://unitn-sml.github.io/auto-nesy-bench/.
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cs.CLcs.AIcs.LG Nagham Omar, Mahmoud Jabarin, Maya Rozenshtein et al. · Oct 1, 2026

Most LLM benchmarks treat generalization as aggregate accuracy on fixed prompts, which can hide per-example fragility when the same user intent is rephrased. This paper reframes generalization as behavioral stability across semantically equivalent input variations and proposes SAGO, a per-prompt, multi-axis framework that tracks changes in generation consistency, internal activations, confidence/uncertainty, and response mirroring. By evaluating eleven open- and closed-source models across six datasets and three variation families, the authors show that instability is heterogeneous, axis-specific, and not resolved by scale, challenging the assumption that high benchmark scores imply reliable generalization.

Generalization in large language models (LLMs) is the ability to produce consistent and semantically stable outputs when the same input is expressed in different ways. Existing work typically evaluates generalization through aggregate accuracy on a single prompt format, task, or set of variations, which conflates robustness with overall benchmark performance. In this work, we show generalization evaluation at the level of individual examples, across multiple input variants, and across different aspects of model behavior, focusing on variability rather than reducing performance to a score that can be improved through narrow training or other ways that obfuscate generalization evaluation. Following this view, we introduce the Stability-Aware Generalization Objective (SAGO), a framework that measures how much model behavior changes for the same input under different variations and benchmarks, capturing variability across several dimensions including generation consistency, internal activations, confidence, and response mirroring. We show that many commonly used models exhibit statistically significant and consistent generalization instability: no model generalizes uniformly, behavioral axes capture independent failure modes, and cross-dataset variation can reverse model rankings.
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cs.LGmath.OC Alessandro Betti, Marco Gori, Stefano Melacci et al. · Oct 1, 2026

Standard gradient flow never reaches zero risk in finite time, while naive finite-time modifications drive the weights to the optimum with infinite speed. This paper formulates and solves a regularized least-time problem for the dissipation schedule $u(e)$ that controls the risk clock via $\dot{e}=-u(e)$. By minimizing $\int_0^{e_0}(\frac{\lambda}{2}|u'|^2+1/u)de$ subject to $u(0)=0$, the authors prove the optimal schedule is a cycloid and that it lands with the universal cusp $u^*(e)\sim c e^{2/3}$, placing the dynamics in the finite-time Hölder regime with vanishing weight speed.

Prescribing the speed of gradient flow on the risk itself, by the dynamics $\dot w=-u(E(w))\nabla E(w)/\abs{\nabla E(w)}^{2}$, makes the risk $e(t)=E(w(t))$ obey $\dot e=-u(e)$ exactly, whatever the landscape~$E$; the time needed to reach zero risk from $e_0$ is $\int_0^{e_0}\dd e/u(e)$. Minimizing this time alone is ill posed, and we study the regularized problem $\inf\{\int_0^{e_0}(\tfrac\lambda2\abs{u'}^{2}+1/u)\,\dd e:\ u\in H^{1}(0,e_0),\ u\ge0,\ u(0)=0\}$, $\lambda>0$. We prove that the minimizer exists, is unique, and is a linearly scaled cycloid, and we show that the optimal rate behaves like $u^{*}(e)\sim(9/(2\lambda))^{1/3}e^{2/3}$ near zero risk: the exponent $2/3$ is the one found in \cite{betti2026holder} by a power-law ansatz, and it lies in the H\"older window $(\tfrac12,1)$ where the arrival is in finite time with vanishing weight speed. The proof follows the classical route: existence by the direct method, uniqueness by strict convexity, positivity of the minimizer away from the origin, and the explicit integration of the Euler-Lagrange equation.
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cs.LG Yuchen Li, Mingyu Du, Zongqi Fan et al. · Oct 1, 2026

Train–validation separation is the widening empirical gap between training and held-out accuracy during fine-tuning of pretrained models. This paper proposes a dynamic structural explanation: optimization progressively shifts from broadly reusable shared features that transfer well toward narrower, example-specific residual patterns that fit training data but generalize poorly. The authors formalize this intuition with a local mixture model and introduce fixed training-probe measurements of normalized absolute gradient-allocation dispersion, $D_{\mathrm{den},t}$, to observe this internal evolution without using validation data. Empirical tests span a controlled ResMLP hierarchy simulation, a 90-run NLP cohort across three backbones, and a 40-epoch ResNet-18 vision study.

Train-validation separation is the evolving difference between performance on observed training examples and a finite held-out validation set. We propose a dynamic structural account of how this gap develops during adaptation of pretrained models: continued fitting can shift update demand from broadly reusable support toward narrower support with weaker held-out transfer. A conditional local model links this shift to increasing heterogeneity in gradient allocation and train-validation separation. Fixed training probes make this structural evolution observable without validation examples entering the readouts; held-out performance is used separately to evaluate its relation to the gap. In a constructed hierarchy implemented with a residual multilayer perceptron (ResMLP), increasing the target share of example-private features from $p=.3$ to $.5$ to $.7$, while preserving the relative mixture $1{:}2{:}3{:}4$ among the four shared feature levels, increases the final mean accuracy gap from $.185$ to $.331$ to $.527$ across five runs per condition. Masked-input losses measured separately on training and validation examples expose the corresponding transfer asymmetry. The natural language processing (NLP) analysis uses 10-epoch runs of RoBERTa, DeBERTa, and Qwen on six datasets (90 runs): the training-probe-weighted within-class and overall dispersion readouts each have positive raw and smoothed level correlations with the accuracy gap in all 90 runs. Raw changes paired at approximately one-epoch intervals remain positively associated in 86/90 and 87/90 runs, respectively. A 40-epoch ResNet-18 study tests both readouts on three vision datasets. Together, controlled simulation, NLP, and vision support the dynamic structural account across settings, with real-model evidence testing its observable predictions under the specified monitors.
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cs.LG Arash Lagzian, Paniz Halvachi, Junming Zhang et al. · Oct 1, 2026

Muon trains hidden matrices with a spectral-norm steepest-descent update but falls back to AdamW for embeddings, output heads, and auxiliary parameters. This paper focuses on the tied vocabulary table—one tensor aliased between sparse token lookup and dense softmax classification—and proposes AF-Muon, an AdamW-free Muon variant that assigns a finite-cap clipped-row linear-minimization oracle to the tied table, an RMS-normalized update to one-dimensional parameters, and the standard spectral update to hidden matrices. By eliminating all second-moment state, AF-Muon cuts optimizer-state memory by roughly 20% and improves mean validation loss across nine tied-token settings spanning text, image, and protein modeling.

Muon improves large-scale training by applying a spectral-norm steepest-descent update to matrix parameters, but practical models also contain parameter blocks that do not fit dense-matrix geometry. One important case is the tied vocabulary table, which appears in language models and other token generators and can receive multiple structurally different gradient sources, from sparse input lookups to dense output-classifier updates. In the reference recipe these blocks are handed to an auxiliary AdamW optimizer, which restores second-moment state and updates the aliased table as a generic tensor. We propose AF-Muon, an AdamW-free extension of Muon that keeps the Muon matrix update for hidden weight matrices while using a support-aware finite-cap linear minimization oracle for tied vocabulary tables and an RMS-normalized update for one-dimensional auxiliary parameters. AF-Muon therefore trains every parameter class with a single first-moment buffer and no second-moment state, saving around 20% optimizer-state memory relative to Hybrid Muon in our benchmark. Across nine tied-token settings - decoder-only language models from 124M to 1B parameters, a fully shared T5-style encoder-decoder, and ImageGPT-style image-token, protein, and sparse-MoE variants, spanning text, image, and protein-sequence data - AF-Muon improves mean validation loss and perplexity over both Hybrid Muon and a SCION-style Sign endpoint. Long-horizon runs and hyperparameter sensitivity studies confirm the gain is robust, and identical-momentum diagnostics attribute it to the finite cap, which preserves more within-row magnitude than Sign while bounding the coordinate concentration of row-RMS. These results identify tied vocabulary tables as a distinct optimizer geometry and yield a robust AdamW-free Muon variant across models, modalities, and architectures, with about 1% step-time overhead in matched training.
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cs.LG Charmaine Barker, Daniel Bethell, Simos Gerasimou · Oct 1, 2026

CLEAR proposes a lightweight, task-agnostic post-hoc recalibrator for evidential deep learning that improves OOD and adversarial robustness without retraining the base predictor. Using held-out calibration data, it models group-conditioned latent geometry and measures conflict among perturbed latent views to detect unsupported evidence, selectively down-weighting overconfident predictions while preserving the original prediction. The method achieves strong gains across classification, regression, and object detection, though it trades off some in-distribution calibration and coverage for improved shift detection.

Reliable uncertainty quantification is essential for deploying deep learning models in high-stakes settings, where out-of-distribution and adversarial inputs can induce confident but unreliable predictions. Evidential Deep Learning provides efficient uncertainty estimates in a single forward pass, but can still assign high evidential strength to inputs that are poorly supported by the learned representation, such as adversarial inputs. We introduce CLEAR, a lightweight, task-agnostic post-hoc method that improves evidential robustness without retraining or altering the base prediction. Using held-out calibration data, CLEAR characterises the group-conditioned geometry of the model's latent space. At inference, it efficiently generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group. High latent conflict indicates unsupported evidence, which CLEAR uses to selectively reduce evidential strength while retaining evidence for latent-consistent inputs. On ImageNet$\rightarrow$CUB, CLEAR improves OOD and adversarial AUROC by $+8.29$ and $+5.01$ while running 17.4$\times$ faster than competing post-hoc methods while preserving predictive performance across classification, regression, and object detection benchmarks.
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physics.chem-phcond-mat.softcs.LG Weilong Chen, Nuno Costa, Julija Zavadlav · Oct 1, 2026

SupraTITO tackles the costly problem of predicting how peptide sequences drive supramolecular self-assembly. It learns transferable implicit transfer operators conditioned on sequence, topology, and periodic boundary geometry to generatively propagate many-molecule configurations over long physical lags. Evaluated on 400 coarse-grained dipeptide systems, it generalizes to held-out sequences and unseen concentrations while preserving molecular integrity through recursive rollouts. The work extends generative molecular dynamics from single-molecule conformations to collective periodic assembly.

Peptide sequence governs both the structures formed through supramolecular assembly and the dynamics by which they emerge, but predicting either requires resolving slow collective processes among many interacting molecules. Molecular dynamics (MD) provides microscopic insight into these processes, yet the long timescales of assembly and the vast peptide sequence space make systematic exploration computationally demanding. We introduce SupraTITO, a transferable generative molecular dynamics (GenMD) framework for supramolecular systems, demonstrated through peptide self-assembly. SupraTITO learns transferable implicit transfer operators (TITO) conditioned on peptide sequence, molecular topology, and periodic geometry, allowing configurations to be propagated over physical intervals much longer than an MD integration step. On a comprehensive dipeptide benchmark, SupraTITO generalizes to held-out sequences and reproduces sequence-dependent structures and dynamics while maintaining molecular integrity over long rollouts. Compared with direct ensemble prediction trained on the same trajectory data, SupraTITO more accurately reproduces assembly structures while also resolving their temporal evolution. The learned dynamics generalize across peptide concentrations, including dilute conditions not represented during training. These results extend transferable GenMD to collective dynamics in periodic supramolecular systems and provide a foundation for modeling related processes beyond peptide assembly.