Machine Learning
Layer-wise Curriculum Learning for Efficient LLM Compression
Donggeon Lee, Dooyeon Na, Seungmin Oh et al. (+1 more)
In this paper, we introduce layer-wise curriculum learning for efficient LLM compression. The proposed method facilitates the knowledge transfer from the teacher model to the student model, utilizing a curriculum learning approach that begins with easier optimization tasks and progressively tackles harder ones. In order to adopt the layer-wise learning in LLM compression, we partition the whole model into multiple segments consisting of layers, thereby enabling more computationally efficient knowledge transfer for LLMs. Based on our theoretical analysis of cumulative error phenomenon, layer-wise curriculum learning accelerates convergence while stabilizing the knowledge transfer process. In addition, we present a feature caching method with a multi-threading strategy to efficiently address feature misalignment across layers, maximizing GPU utilization. Consequently, our method exhibits advanced model compression performance, as well as high computational efficiency in terms of minimized
memory usage and short training hours. Experiments on multiple
datasets show that the proposed method achieves state-of-the-art performance while reducing GPU
memory usage and training hours by more than 50% on BERT and GPT-2. Moreover, it outperforms the other
pruning methods on LLaMA-family and Qwen models under the same training hours, with a lower GPU
memory footprint.
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All authors Donggeon Lee, Dooyeon Na, Seungmin Oh, Jongbin Ryu
Machine Learning · Cross-listed from cs.SI
Not All Nodes Are Created Equal: Homophily-Aware Stratification for Stable GNN Evaluation
Naga Venkata Sai Jitin Jami, Thomas Altstidl, Sebastian Hoefler et al. (+4 more)
Graph neural networks are widely used for transductive node classification, with accuracy typically measured on randomly drawn train/validation/test splits. Reported accuracy has been shown to shift substantially across different random splits of the same
dataset, making published comparisons between architectures unreliable. The classical remedy in non-graph settings is stratified $k$-fold cross-validation, which ensures each test fold reflects the full class distribution of the
dataset. We argue that class stratification alone is insufficient for graphs: nodes are not isolated but connected, and folds that differ in their distribution of local neighbourhood homophily expose the model to systematically different relational conditions that directly affect message-passing behaviour. The resulting cross-fold variation reflects the homophily composition of each split, inflating reported variance beyond what model behaviour alone would produce. To address this, we propose \hp{}, a
topology-aware stratification procedure that treats node homophily as the primary stratification axis, aligning folds with respect to local relational consistency alongside the class marginal that standard stratification already controls. Stratifying on homophily alone does not guarantee class balance, so \hp{} incorporates class label as a secondary axis, preserving class representativeness as a natural consequence of the procedure. We evaluate \hp{} on a broad
benchmark suite comprising 15 node-classification
datasets spanning the full homophily spectrum and 7 GNN architectures. \hp{} achieves a mean stability rank of 1.49 compared to 2.31 for random $k$-fold, achieving the lowest mean stability rank on 13 of 15
datasets while preserving class balance close to class-stratified splits and substantially better than random. We argue that homophily-aware split construction merits broader adoption for GNN evaluation.
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All authors Naga Venkata Sai Jitin Jami, Thomas Altstidl, Sebastian Hoefler, Jonas Mueller, Dario Zanca, Bjoern Eskofier, Heike Leutheuser
Machine Learning
Generative Query Suggestion via Intent Coverage and Query-Level Credit Assignment
Xinpeng Liu, Lu Ma, Jiayi Qiao et al. (+6 more)
Generative query suggestion aims to enhance user engagement by anticipating user intents and recommending relevant follow-up queries. A central challenge is to generate slates whose individual queries are useful while the slate covers distinct intents. We propose an Intent-Driven Query Suggestion Framework with dual-stage optimization. First, intent-aware diversity modeling constructs intent-aligned supervised fine-tuning (SFT) data and uses an Intent-Aware Diversity Reward to optimize intent coverage. Second, query-level credit assignment routes individual quality signals to the corresponding query
tokens while sharing a slate-level diversity signal across the slate. Experiments on a large-scale production
dataset, including online A/B testing and offline evaluation, show improvements in click-through rate, query quality, and intent coverage.
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All authors Xinpeng Liu, Lu Ma, Jiayi Qiao, Mengyu Zhou, Linglong Li, Xiaofeng Bian, Haonan Chen, Xiaoxi Jiang, Guanjun Jiang
Machine Learning · Cross-listed from cs.AI
Position: It is Time to Virtualize Foundation Models with a Self-evolving Operating System Layer
Suparna Bhattacharya, Tarun Kumar, Cong Xu et al. (+7 more)
AI applications have shifted from single, monolithic foundation models (FM) to compound agentic systems. Yet today's stacks remain fragmented: even as protocols (e.g., MCP, A2A) ease tool/
agent connectivity, each framework embeds an implicit runtime for state,
memory, budgets, and guardrails, making behavior non-portable and governance brittle. It mirrors computing before operating systems, when every program re-implemented basic services. This position paper argues that the field now needs a Foundation Model Operating System (FMOS) – a system layer that virtualizes FM interactions analogous to how virtual machines abstract physical hardware, giving applications the illusion of dedicated, trustworthy FM instances with effectively unbounded capabilities. Internally, the FMOS orchestrates knowledge across
memory tiers, model selection and resource allocation, and verification and policy enforcement. Like the human
brain switching between fast intuition and slow deliberation, the FMOS learns when to intervene and when to let inference proceed directly and continuously adapting its policies based on operational experience.
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All authors Suparna Bhattacharya, Tarun Kumar, Cong Xu, Satish Kumar Mopur, Jiahao Li, Ashish Mishra, Aalap Tripathy, Annmary Justine Koomthanam, Martin Foltin, Ian Foster
Machine Learning · Cross-listed from stat.ML
Federated Soft Clustering via Generalized Total Variation Minimization
Shamsiiat Abdurakhmanova and Alexander Jung
We study
federated soft clustering over
federated learning (FL) networks of devices that each hold a private local
dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.
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Machine Learning · Cross-listed from cs.CL
A Zeroth-Order Paradigm for LLM Preference Alignment
Peter Chen, Xi Chen, Wotao Yin et al. (+1 more)
Direct preference
alignment methods are widely used to align large
language models (LLMs) with human preferences because of their computational and
memory efficiency. However, likelihood displacement motivates alternative ways to extract information from preference pairs with small likelihood margins. In this paper, we propose and analyze Comparison-based Preference Optimization (ComPO), a zeroth-order
alignment method based on comparison oracles. ComPO extracts directional information from these pairs without directly optimizing a differentiable preference loss on them. We establish a convergence guarantee for its basic offline scheme under smoothness, gradient sparsity, and compatibility between the oracle and a latent objective. We further introduce online ComPO, which retains the offline comparison mechanism and uses unlabeled policy generations for reverse-KL control relative to a reference policy. Following the coverage perspective of preference fine-tuning, we establish a performance guarantee for a basic constrained scheme under local coverage and in-distribution pairwise reward accuracy. Experiments on Mistral, Llama, Gemma-2, Qwen3, and Gemma-3 models demonstrate improvements over existing direct
alignment methods, including length-controlled win rates, with pair-level diagnostics providing evidence consistent with mitigating likelihood displacement.
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All authors Peter Chen, Xi Chen, Wotao Yin, Tianyi Lin
Machine Learning
Exponential Hardness of Off-Policy Evaluation under History-Dependent Logging
Pranaya Jajoo
Can a logged
dataset visit every hidden state frequently and still be exponentially uninformative about a target policy's value? We show that it can when the logger depends on history. For every horizon $H \ge 3$, we construct two POMDPs with at most two latent states per stage, three actions, and a common logger with three
memory states. Action coverage, belief coverage, and two behavior-marginal outcome-revealing conditions all have constants independent of $H$. Nevertheless, evaluating a known deterministic target policy to accuracy $1/8$ requires $\Theta((3/2)^H \log(1/\delta))$ logged episodes at confidence $1-\delta$, for $0 < \delta \le 1/4$, even when both candidate models are known. The mechanism is simple: a reset erases the unknown transition that determines the target value. We characterize the resulting statistical experiment exactly and obtain a matching optimal
estimator. A directed two-lane gridworld realizes the construction, and trajectory simulations agree with its finite-sample prediction. The result establishes intractability for the history-dependent-logging, model-based case posed by Zhang and Jiang (2025, arXiv:2503.01134), under their behavior-marginal definition of revealing.
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Machine Learning · Cross-listed from cs.AI
Cognitive Extensions for Dual-Process Language Agents: Memory and Self-Reflection in Interactive Environments
João Meneses dos Santos and Arlindo L. Oliveira
Language agents remain brittle in interactive environments, where success requires long-horizon state tracking, valid action execution, and recovery from failed steps. We extend SwiftSage, a dual-process
agent that combines a fast action proposer with a slower planner, using two modular cognitive extensions: an Adaptive
Memory Module (AMM) for salience-gated episodic storage and trigger-driven
retrieval, and a Self-Reflection Module (SRM) for bounded execution-time validation and corrective intervention. Both modules are implemented as feature-flagged extensions over the same execution substrate, enabling controlled ablations on ScienceWorld. Across four configurations—baseline, baseline+AMM, baseline+SRM, and the full system—the full system achieves the best mean final score (64.62), success rate (43.17%), and successful-step efficiency (19.33 steps), while SRM is the strongest standalone contributor. The results suggest that execution-time control is the dominant bottleneck in this setting, while episodic
memory becomes most useful once the runtime loop is stabilized.
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Machine Learning · Cross-listed from cs.CV
Training-Adaptive Convolutional Sparse Coding via Information Bottleneck for Robust Visual Representation
Meng'en Qin, Yinchen Liu, Mingxuan Cui et al. (+1 more)
Visual signals require compact yet sufficient representations for robust downstream prediction. Convolutional sparse coding (CSC) provides an explicit mechanism for suppressing redundant components while preserving signal content, but its sparsity coefficient is often manually selected during training. We propose a training-adaptive convolutional sparse coding framework for robust visual signal representation. Specifically, we unfold the CSC optimization with the Fast Iterative Shrinkage-Thresholding
Algorithm (FISTA) and treat the sparsity coefficient as a differentiable variable jointly learned with the network parameters. From the information bottleneck perspective, this coefficient controls the trade-off between information retention and compression: the sparsity term promotes compact representations, while the reconstruction term together with task loss preserves task-relevant signal content. We further introduce a label-free post-training strategy that adjusts the compression strength for corrupted inputs with the main network parameters fixed. Experiments on CIFAR and ImageNet demonstrate competitive clean-data recognition and greatly improved robustness under different input perturbations.
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All authors Meng'en Qin, Yinchen Liu, Mingxuan Cui, Youlu Xing
Machine Learning
How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents
Zixi Chen, Akshay Vegesna, Samip Dahal et al. (+1 more)
Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped
transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly $20\times$ less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla
transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the
transformer, which can lead to efficiency gains that increase with scale.
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All authors Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson
Machine Learning · Cross-listed from cs.CL
Monitoring and Discovering Reward Hacking with Internal Representations during LLM Evaluations
Leon Bergen, Usha Bhalla, Andrew Lee et al. (+15 more)
As models scale, reward hacking becomes more frequent, more sophisticated, and more consequential. Does it leave a telltale signature in model representations? This work analyzes how reward hacking is represented internally in frontier open source LLMs, and how those representations can be used to understand and discover the range of hacking behaviors a model displays. In particular, we find that simple difference of means vectors coherently represent reward hacking in Kimi K3, GLM 5.2, and Qwen 3.8 Max across a variety of behaviors in common evaluations. Despite their simplicity, these vectors are both generalizable and interpretable, and we can use them to reliably detect reward hacking. We first evaluate reward hacking in commonly reported
benchmarks like DeepSWE and SWE-bench, finding that models reward hack excessively in these environments; GLM 5.2 hacks in 57.2% of rollouts on DeepSWE and in 73% of rollouts on SWE-bench. Catching these requires monitors; LLM monitors are effective, but expensive detectors. We show that DoM vectors are similarly effective but virtually free, catching 3.1% more hacks in Kimi K3 and 7.9% fewer hacks in GLM 5.2 on DeepSWE at a monitor matched false positive rate. DoM vectors run on the chain-of-thought also predict reward hacks in the model's subsequent actions, meaning we can run them online and catch potential hacks before they occur. Finally, we analyze probe-hits that LLM monitors do not catch and discover other undesirable behaviors, as well as show transfer to finding hacks in non-SWE evaluations. Together, these results provide evidence that simple, white-box methods can be used to scalably study and monitor reward hacking behaviors in frontier open source models
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All authors Leon Bergen, Usha Bhalla, Andrew Lee, Barak Widawsky, Linas Nasvytis, Connor Watts, Siddharth Boppana, Sidharth Baskaran, Dron Hazra, Michael Byun, Atticus Geiger, Owen Lewis, Matthew Kowal, Vasudev Shyam, Thomas Fel, Thomas McGrath, Ekdeep Singh Lubana, Jack Merullo
Machine Learning
Evidence-Grounded Agentic Formulation Development in an Autonomous Laboratory
Michael M. Craig, Riley J. Hickman, Yingshan Ma et al. (+3 more)
Self-emulsifying drug delivery systems (SEDDS) can improve the oral bioavailability of poorly soluble drugs, but identifying high-performing formulations remains experimentally intensive. We present Andromeda 2, an agentic system that reasons over structured in-house experimental evidence and invokes computational and experimental tools to design and execute successive formulation batches. Using a miniaturized automated laboratory at a matched budget, we
benchmark it against Andromeda 1, a probabilistic optimization model deployed across dozens of live development projects, and a wet-lab design-of-experiments (DoE) campaign. For paclitaxel, Andromeda 2 achieved a 50% high-performance hit rate versus 17% for Andromeda 1 and 2% for DoE, and identified 12 formulations meeting all four target product profile (TPP) objectives versus 6 and 0, respectively. Median $AUC_{10-240}$ was 70.1, 12.0, and 3.5 mg$\cdot$min/mL, while maximum AUC was comparable between Andromeda 2 and Andromeda 1. A selected full-TPP formulation achieved an apparent effective paclitaxel loading of $19 \pm 5\%$ w/w at the first FaSSIF measurement, approximately 3.3-fold higher than the 5.7% w/w loading reported for a published paclitaxel S-SEDDS. A controlled ablation showed that access to structured in-house experimental evidence increased mean AUC by 34%.
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All authors Michael M. Craig, Riley J. Hickman, Yingshan Ma, Rémi Piché-Taillefer, Christine Allen, Pauric Bannigan
Machine Learning · Cross-listed from stat.ML
A General Kernel Framework for Non-CND Distance Measures Using |D|-Dimensional Sparse Landmark Embeddings
Marcus M. Noack, Maher B. Alghalayini and Mark D. Risser
Kernel methods, and Gaussian Processes (GPs) in particular, require a Hilbertian distance measure—one whose square is conditionally negative definite (CND)—to guarantee positive semi-definiteness (PSD) of the kernel
matrix; a condition that fails for many natural input spaces, including smooth
manifolds and spaces of probability distributions. We propose the Sparse Landmark
Embedding (SLE) kernel, which eliminates this requirement entirely. Each input is embedded into a sparse feature vector via compactly supported bump functions centered at all |D| training points; applying any standard PSD kernel in this
embedding space yields a kernel that is provably PSD for arbitrary distance measures. The compact support automatically controls
embedding sparsity, keeping kernel
matrices well-conditioned and computationally tractable despite the high ambient dimension. We provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show that the SLE kernel matches or substantially exceeds domain-specific baselines in both predictive accuracy and uncertainty quantification using geodesic and Wasserstein distances.
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Machine Learning
Probabilistic Linear Explanations
Frederic Koriche, Jean-Marie Lagniez and Chi Tran
Formal explainability provides mathematically grounded justifications for individual predictions. However, abductive explanations often exceed human cognitive limits by involving too many features, while probabilistic relaxations have remained largely limited to categorical classification. We present a unified framework for probabilistic explainability based on sparse, anchored linear models, applicable to both binary classification and continuous regression. By mapping instances to the Boolean hypercube, our linear explanations strictly generalize subset-based approaches: they capture both the magnitude and direction of feature contributions while enforcing a prescribed sparsity budget $k$. We show that minimizing the relevance error for such explanations is \ClassNPPP-hard when the underlying model is a neural network, and we relate this intractable objective to a tractable surrogate—the fidelity error. For a parameterized family of local distributions, the relevance error of any $k$-sparse explanation is bounded by its fidelity error up to a multiplicative factor that remains small locally. We address the resulting empirical problem using two complementary approaches: a Mixed Integer Programming (MIP) formulation that yields provably optimal empirical solutions while maintaining
polynomial sample complexity, and a
polynomial-time Iterative Hard Thresholding (IHT)
algorithm with provable approximation guarantees. Empirical evaluations show that, unlike state-of-the-art baselines such as LIME and MAPLE, our explanations satisfy both the anchoring and sparsity constraints by construction, while consistently achieving lower relevance error.
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Machine Learning
Double descent is the principle of least action
Congzhou M Sha
The test error of a model plotted against its number of parameters $d$ falls, peaks when the model can just fit the training data, and falls again, exhibiting the double descent phenomenon. We explain the phenomenon with statistical mechanics. The training trajectory of a
stochastic gradient-based method is a particle wandering over the energy landscape of the training loss at an induced temperature $T$, and a run that has equilibrated visits every parameter vector of a given training loss equally often, the fundamental postulate of statistical mechanics, with probability given by the Boltzmann distribution. Because training starts at an initial point and has only finite time to diffuse, it carries an effective weight decay, which makes every parameter a quadratic degree of freedom. The equipartition
theorem then distributes the energy among the $d$ degrees of freedom in shares of $T/2$, so at a fixed training loss adding parameters lowers the temperature and drives the Boltzmann distribution toward the stationary path. Finally, adding parameters can only lower the $L^2$ norm of the stationary path, so a solution sampled at fixed loss is less likely to be large with increasing $d$, effectively increasing weight regularization.
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Machine Learning
RLLBC-Lib: An Educational Code Library for Reinforcement Learning and Learning-Based Control
Bernd Frauenknecht, Emma Cramer, Artur Eisele et al. (+9 more)
Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.
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All authors Bernd Frauenknecht, Emma Cramer, Artur Eisele, Paul Kruse, Lukas Kesper, Jonas Hertrampf, Ramil Sabirov, Jyotirmaya Patra, Johannes Berger, Paul Brunzema, Friedrich Solowjow, Sebastian Trimpe
Machine Learning · Cross-listed from cs.MA
Social Laws for Multi-agent Coordination in Stochastic Environments
Rolando Fernandez, Caleb Probine, Tyler Lee et al. (+5 more)
In multi-
agent environments, coordinating
agents to prevent interference and ensure robust individual performance is a critical challenge. Previous research on social laws for multi-
agent systems has primarily focused on deterministic, goal-based settings. This paper extends the concept of social laws to
stochastic, reward-based environments, proposing a formalism for defining and verifying their robustness under various conditions. We introduce the notion of $\alpha$-robustness, a measure of the guaranteed utility each
agent retains while pursuing its optimal single
agent policy, assuming all
agents obey the social law. We then present an approach for robustness verification of social laws in
stochastic settings, based on a reduction to solving a series of Markov decision processes. Empirical evaluations on toy environments illustrate the potential of our framework.
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All authors Rolando Fernandez, Caleb Probine, Tyler Lee, Jeffrey Chen, Erez Karpas, Muhammad Arrasy Rahman, Peter Stone, Ufuk Topcu
Machine Learning · Cross-listed from hep-ph
Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion
Lining Mao, Yvonne Peters, Ethan Simpson et al. (+1 more)
In particle
collider experiments, event reconstruction is the task of inferring the kinematics of short-lived particles produced in the hard scatter from the stable final states recorded by detectors. We decompose event reconstruction into two primary tasks: assigning measured jets and charged
leptons to parent particles, and predicting unmeasured
neutrino kinematics. We present VyPER, a novel
geometric learning framework that represents
collider events as hypergraphs with a physics-inspired
topology. VyPER combines the supervised classification of hyperedges for particle assignment with a
diffusion model for predicting
neutrino kinematics, leveraging a joint loss function to optimize both reconstruction tasks within a unified framework. We showcase VyPER across several
proton-
proton collision processes, comparing its performance to existing analytical and machine-learning-based reconstruction techniques. In doing so, we demonstrate that accurate event reconstruction is achievable across a diverse range of Standard Model physics processes, opening new avenues for precision measurements in the
Higgs boson, electroweak, and top-
quark sectors.
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All authors Lining Mao, Yvonne Peters, Ethan Simpson, Zihan Zhang
Machine Learning
Higher-order pruning of experts in mixture-of-experts language models
Alex M. Tseng, Prannay Kaul, Luca Zancato et al. (+2 more)
Mixture-of-Experts (MoE)
language models suffer from large parameter counts, which create a significant
memory bottleneck. Expert
pruning is the most direct approach for reducing this parameter count, yet existing methods make
pruning decisions for each expert independently, and assume experts' contributions are purely additive. In reality, expert usage in MoEs is inherently cooperative. We derive HOPE (Higher-Order
Pruning of Experts), a second-order
pruning objective which provably minimizes an upper bound on the error resulting from
pruning. We show that REAP (a state-of-the-art first-order
pruning method) is a special case of HOPE where interaction terms are ignored. Across three frontier MoE models (up to 122B parameters), two distinct calibration sets, and multiple
benchmarks (including math, instruction following, coding, and an agentic suite), we demonstrate that HOPE produces better
pruning decisions than existing methods, and its advantage is most pronounced at high
pruning rates and on challenging agentic workloads. At 50%
pruning, HOPE outperforms all baselines and achieves an average rank of 1.58 out of 5 methods (versus 2.42 for the next-best method, REAP), with gains of up to +6.1% on agentic coding. Over all conditions, HOPE again achieves the best average rank and surpasses every other method in the majority of head-to-head comparisons. By preserving cooperative expert structure that first-order methods ignore, HOPE enables aggressive compression with minimal degradation, particularly on complex tasks where diverse expert combinations are invoked over long sequences.
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All authors Alex M. Tseng, Prannay Kaul, Luca Zancato, Wei Xia, Stefano Soatto
Machine Learning · Cross-listed from stat.ML
Fast Learning Rates for Physics-Informed Kernel Methods
Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti et al. (+1 more)
In physics-informed machine learning, a target function $u^*$ is learned from noisy value observations $y_i=u^*(x_i)+ \varepsilon_i$, together with differential information, given either by noisy observations $d_j=(Du^*)(z_j)+\xi_j$ or by a known physical constraint $Du^*=v$. We consider the setting where $D$ is a linear differential operator and analyze a physics-informed kernel
estimator $\hat u$ combining $n$ value observations and $m$ differential observations. In this context, we ask how much can differential information improve predictions, and how does this improvement depend quantitatively on $n$, $m$, and $D$. We prove finite-sample bounds, supported by numerical simulations, revealing a two-regime structure for the prediction error. When $m$ is limited, the rate depends jointly on $n$ and $m$; when $m$ exceeds a problem-dependent threshold, the rate saturates and matches the oracle rate obtained when the perfect constraint $D \hat u = Du^*$ is imposed. Examples are discussed for Sobolev spaces which are reproducing kernel
Hilbert spaces and include partial
Laplacian constraints on the
torus and gradient observations on bounded domains. These examples illustrate the range of possible learning rate improvements — from the standard nonparametric $n^{-1/4}$ to the parametric rate $n^{-1/2}$. Finally, we derive physically consistent rates in a stronger norm that jointly controls the errors in $\hat u$ and $D\hat u$.
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All authors Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti, Lorenzo Rosasco
Machine Learning · Cross-listed from math.AP
Learning Lyapunov Operators for Nonlinear Systems
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández et al. (+1 more)
Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting their reuse across systems. In this paper, we study the Lyapunov solution operator that maps a vector field to the corresponding Lyapunov function defined by a dissipation-based Lyapunov PDE. We establish that, on compact subsets of the domain of attraction and under exponential stability assumptions, this operator is well-defined, unique, and continuous with respect to perturbations of both the vector field and the dissipation function. These results provide a theoretical foundation for approximating Lyapunov functions uniformly over families of nonlinear systems. Building on these theoretical foundations, we employ
Fourier Neural Operators (FNOs) as a data-driven approximation of the Lyapunov solution operator. Numerical experiments demonstrate that a single trained operator can accurately approximate the numerical Lyapunov functions across parameterized families of dynamics. This illustrates the potential of neural operators for approximating Lyapunov functions.
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All authors Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández, Jun Liu
Machine Learning
Preventing Model Collapse: A Fisher-Rao Perspective on the Dynamics of Training with Synthetic Data
Matteo Marchi, João Pedro Silvestre, Bahman Gharesifard et al. (+1 more)
Large
Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true underlying data distribution. Training on a mixture of synthetic and fresh human data is a logical countermeasure and can prevent model collapse. However, it is an open question as to what is the exact minimum required ratio of human-to-synthetic data to maintain training stability. In this paper, we establish rigorous theoretical guarantees on the minimum rate of human data required to prevent model collapse. Although previous work established a formal lower bound for this ratio, such bound can be vacuous for very high dimensions, as the analysis relies on the usual Euclidean metric in R^n and is not adapted to the space of categorical probability distributions. Instead, in this paper we explicitly leverage the information-
geometric structure of the probability simplex by analyzing the dynamics of the process under the Fisher-Rao metric. We derive quantitative contraction and invariance bounds that are stable and do not become trivial as the dimensions increase. Thus, we show that the effective required data ratio to prevent model collapse is different than previously implied.
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All authors Matteo Marchi, João Pedro Silvestre, Bahman Gharesifard, Paulo Tabuada
Machine Learning
Physics-based prediction, uncertainty quantification and decision-making for IN718 crystallographic texture intensity across LPBF defocus regimes
Yisheng Lu, John Riris, Jie Song et al. (+2 more)
Reliable prediction of crystallographic texture in
laser powder bed fusion is critical for linking process conditions with anisotropic response and for qualification. However, black-box models may fail under shift and cannot distinguish weak data support from loss of physical validity. This study develops a two-stage physics-based model for <001> || BD (build direction) texture in Inconel 718. Stage 1 maps process variables to melting mode and melt pool geometry. Stage 2 predicts texture by combining an empirical physics model with a random-forest residual model. A k-nearest-neighbor weight attenuates residual corrections for poorly supported queries, while a study-specific areal beam-power-density criterion withholds predictions outside the adopted conduction envelope. Conformal intervals are evaluated on the retained physics-valid set, and SHAP and Sobol analyses assess residual sensitivity. Under a controlled leave-one-defocus-out evaluation, the physics anchor achieved R^2 = 0.778, against -0.001 for the black-box model and 0.750 for the gated hybrid. Under leave-one-group-out cross-validation, the gated hybrid reached R^2 = 0.592 against 0.538 for the black-box model. Retained-set coverage was 92.9% at a mean full width of 3.65 multiples of a uniform distribution (MUD) under grouped cross-validation and 100% at a width of 3.21 MUD under transfer to a withheld +80 mm defocus regime. An illustrative mapping produced a retained BD elastic-modulus span of 127-187 GPa. On nine conditions from a separately built sample set, the framework withheld three, attenuated three, and matched the measured ordering for the rest. Separating data applicability, physics validity, and predictive uncertainty into distinct decisions lets the framework transfer where an unconstrained model does not, and withhold predictions where no model class performs adequately.
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All authors Yisheng Lu, John Riris, Jie Song, Yao Fu, Jie Chen
Machine Learning · Cross-listed from cs.CV
Decodable but Misrouted: Sparse Features Uncover a Readout Gap in Vision-Language Models for Harmful Meme Detection
Girish A. Koushik, Diptesh Kanojia and Helen Treharne
When large
vision-
language models misclassify harmful memes, the failure may reflect missing internal evidence or an inability to route represented evidence to their outputs. We distinguish these cases in Gemma-3 and Qwen3.5 using sparse autoencoders, role-conditioned probes, causal interventions, and recovery experiments across six harmful content
benchmarks, with additional Spanish and Hindi-English code-mixed evaluations. Sparse readouts outperform native prediction on all six primary binary tasks: Qwen averages $0.740$ versus $0.432$ for native macro-F1, residual reconstruction reaches $0.486$, and Gemma improves from $0.532$ to $0.714$. These gains measure how accessible the label is to a supervised readout; they do not show that the model's native generation already applies such a decision rule. Under the evaluated scales, Qwen silent-feature ablation is $24-63$ times more probe-sensitive, whereas routed-feature patching on literal yes/no tasks is $16-140$ times more output-sensitive. Native-only threshold calibration explains much, but not all of the gap: on five tasks with matched probe scores, it recovers $69.8$% of the raw native-to-probe difference, while direct routing adds $0.094$ mean macro-F1 beyond calibrated native scoring. Joint gold-label, probe-KL, and pairwise LoRA supervision improves dedicated FHM prediction, but a gold-only adapter performs better on the shared seven-task mean. A case study of Gemma-3-12B on the Facebook Hateful Memes
dataset finds a distributed rank-32 image-
prompt interaction, reaching $0.756$ versus $0.685$ native macro-F1. Robustness controls show that the signal is not explained solely by accompanying OCR and depends on paired visual evidence, and that it extends beyond English. In many of the errors we study, the evidence is represented but does not reach the answer; therefore, routing is a common bottleneck in harmful meme classification.
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Machine Learning · Cross-listed from cs.AI
Infinite-Parameter LLMs: Generating and Adapting Weights from Live Data
Jinli Hu, Ross M. Clarke, Yichuan Zhang et al. (+1 more)
Scaling laws hold that
language models grow more capable with more parameters and more training data. Mixture-of-Experts (MoE) architectures are a remarkable demonstration of these laws, activating only a fraction of an enormous parameter bank for each
token. But this success is built on static pretraining data — the facts and corrections supplied by users during live interactions are a significant untapped source of potential improvement for a deployed model, but cannot be exploited by conventional architectures whose weights are frozen after training. Instead, this newfound knowledge must be placed in the context (by instruction or
retrieval) and re-read on every request, only to be discarded afterwards. We seek instead to learn from live interactions by dynamically updating model weights. Inspired by MoEs, we propose the Infinite-Parameter LLM. A compact hypernetwork turns the online data into low-rank modulations of a shared base network, so feed-forward weights are generated from live data, not read from static
memory. Whereas existing weight generators are held fixed after reading the context once, we form a
Bayesian belief over the generator's latent state and update it online, such that the effective weights are re-derived as our belief evolves during the session. Although the model's
memory footprint is constant, the feasible space of generated weights is thus effectively infinite. Representing live data in the weights rather than the
prompt amortises compute, frees the context window, persists updates across turns, and can generalise better than in-context use. Our evaluation protocol applies this methodology to in-context learning and
retrieval.
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All authors Jinli Hu, Ross M. Clarke, Yichuan Zhang, José Miguel Hernández-Lobato
Machine Learning
Interpretable Multi-Instance Learning Enables Early Prediction of Key Molecular Alterations from Routine Flow Cytometry in Acute Myeloid Leukemia
Jonathan Legrand, Aguirre Mimoun, Baudouin Denis de Senneville et al. (+3 more)
Background: Molecular testing for NPM1 and FLT3-ITD mutations guides critical early treatment decisions in acute myeloid leukemia (AML), but results can take weeks, long after these decisions must be made. Flow cytometry, already performed within hours of admission as part of routine care, may carry enough signal to predict these mutations directly, without added cost or delay. Methods: We developed an interpretable multi-instance learning classifier based on a decision tree, in which each patient sample is modeled as a collection of individual
cells and mutation status is inferred from
cell-level predictions. The model was benchmarked against a random forest trained on clinical variables and a deep convolutional neural network adapted for multitube flow cytometry data. Performance was assessed by cross-validation on a discovery cohort of 197 patients and tested on an independent cohort of 161 patients, using the area under the receiver operating characteristic curve (AUROC) and positive predictive value. Results: In cross-validation on the discovery cohort, the MIL model achieved mean AUROCs of 0.96 (SD=0.05) for NPM1 and 0.86 (SD=0.10) for FLT3-ITD, outperforming the clinical baseline and matching deep learning approaches. The model then successfully generalized to the independent test cohort of 161 patients, reaching AUROCs of 0.90 (NPM1) and 0.82 (FLT3-ITD), with positive predictive values of 0.87 and 0.68, respectively.
Cell-level interpretation recovered established immunophenotypic signatures (CD33${}^{+}$ /CD34___ for NPM1-mutated cases, CD33${}^{+}$ /low side-scatter for FLT3-ITD), directly linking model predictions to known biology. Conclusions: These results show that an interpretable model applied to data already collected in routine care can predict AML molecular status within hours, offering a practical route to earlier, biology-informed treatment decisions.
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All authors Jonathan Legrand, Aguirre Mimoun, Baudouin Denis de Senneville, Audrey Bidet, Pierre-Yves Dumas, Christèle Etchegaray
Machine Learning
WaveTLM: Reliable Time-Series Language Modeling through Task Compilation
Jiahui Chen, Bingke Zhu, Hongyu Pan et al. (+1 more)
Time-series
language models provide a shared natural-
language interface across temporal tasks, but plausible text does not guarantee reliable task outputs. Responses may appear reasonable while hallucinating the required object: numerical sequences can violate shape, scale, channel order, or temporal
alignment, and textual decisions can fall outside the legal label space. We formulate reliable time-series
language modeling, separating task-object reliability from predictive quality. We introduce ExecTS-QA, a contract-grounded
benchmark spanning
forecasting, imputation, classification, anomaly detection, and waveform analysis. We further propose WaveTLM, a unified compiler-executor model whose task compiler transforms user requests, visible arguments, and wave-grounded evidence into typed task states, while task-native executors construct numerical tensors, legal decisions, or structured records. On ExecTS-QA, a single WaveTLM checkpoint achieves 99.40% contract-valid coverage, compared with 37.83% for the strongest evaluated string-first baseline, while retaining balanced predictive performance across all five task families. Evaluations on SciTS, TSQA, IRTS-ToolBench, and ARFBench provide additional evidence of transfer. The code, construction scripts, and ExecTS-QA
dataset will be publicly released upon publication. These results show that task compilation can convert plausible
language generation into reliable time-series outputs.
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All authors Jiahui Chen, Bingke Zhu, Hongyu Pan, Yingying Chen
Machine Learning
A Convergence Framework for Deep $V$-Learning: Error Propagation and Sharp Action-Gap Bounds
Yury Kolomeytsev
We establish convergence bounds for deep $V$-learning with horizon $H$. The
algorithm fits a scalar value function to targets from executed transitions and selects actions using a predictive model and the value function. For current observed-successor targets with fresh true-kernel outcomes, the conditional mean is $\mathcal{T}^\beta V$, which averages over behavior-policy actions. The Bellman optimality update is $\mathcal{T} V$. We decompose the update error into six residuals: fitting, transition reuse, target construction, replay, action selection, and exploration. Under $L^s$ concentrability, their $L^p$ norms ($p=s/(s-1)$) control expected $L^1$ policy loss. The bound explicitly weights residuals from only the last $H-1$ update blocks, plus an initialization term for shorter runs. We quantify the cost of a shared sampling distribution across horizon levels. For statistical error bounds of order $n^{-\nu}$, we derive optimal continuous allocations and an integer allocation whose objective is within a factor $2^\nu$ of the constrained optimum. A margin condition with exponent $\alpha$ gives action error of order $\Lambda^{1+\alpha/p}$, where $\Lambda$ combines network drift and score error; a one-step construction proves the exponent sharp. Bounds on the distance between frozen and optimal scores transfer an optimal-gap condition to frozen-iterate gap bounds while retaining the mass of optimal ties. Survival probabilities and coverage conditions at deployment yield bounds for policies selected with approximate scores. Separate spatial ReLU networks per horizon level give a conditional neural regression rate, and the finite-state case gives a log-free expected fit rate. These results give expected policy-loss consistency for the fixed-horizon generative-reset approximate-ERM procedure with exact action scores and provide an explicit residual-decay criterion for FIFO/interleaved SGD.
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Machine Learning · Cross-listed from cs.AI
CERA-MoA: Co-Evolving Routing Mechanisms with Continually Learning LLM Agents
Jiaxuan Jiang, Liyuan He and Zhixuan Fang
Current Mixture-of-
Agents (MoA) paradigms generally treat query routing and
agent fine-tuning as separate processes, limiting their ability to respond to evolving
agent capabilities. This disconnect prevents routing strategies from adapting to evolving
agent capabilities during post-training and prevents
agents from achieving synergistic data-driven specialization. To resolve this, we introduce CERA-MoA (Co-Evolving Router with continually learning
Agents for Mixture-of-
Agents), an iterative reinforcement learning framework where the dynamic router and independent
agent policies co-evolve. We design a predictive familiarity
estimator that leverages mid-layer hidden states to evaluate semantic competence among
agents, avoiding the overhead of full rollouts. Based on these familiarity scores, a cumulative-threshold adaptive routing mechanism dynamically activates a tailored minimal
agent subset, achieving a trade-off between task performance and efficiency. By proactively allocating targeted training samples to
agents based on their evolving competence, CERA-MoA promotes capability differentiation. Extensive experiments across various domains demonstrate that CERA-MoA outperforms state-of-the-art static-
agent routing and fix-workflow fine-tuning baselines.
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Machine Learning · Cross-listed from eess.SP
Stable Filters for Generative Modeling of Graph Signals
Martin Schmidt and Gonzalo Mateos
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While recent graph-aware Schrödinger bridge models incorporate
topology information directly into their reference dynamics, it is unclear how perturbations of the graph propagate through these dynamics and affect the resulting generated distributions. In this paper, we analyze the structural stability of graph-aware continuous-time generative models whose drift combines a graph filter with a learned graph neural network. We derive explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions. Motivated by these bounds, we introduce a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat
diffusion, while boosting structural stability. Experiments on synthetic and fMRI signals show our stable filters enhance structural robustness while matching or exceeding the generative quality of the heat equation baseline.
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