Papers

This note aims to serve as an entry point to the literature on learning in games, a topic with significant theoretical appeal and a wide range of applications – from machine learning and data science to economics and beyond. Our presentation is structured around two complementary viewpoints: We first consider a single agent – the learner – engaged in a sequential decision process in an unknown, non-stationary, and possibly adversarial environment. We then examine what happens when the environment is shaped by the decisions of several interacting agents, not necessarily aware of each other's actions or goals, and all seeking to improve their individual rewards. In this general context, we examine a family of regularized learning policies based on best-responding to the past history of play, up to a regularization penalty intended to encourage exploration and prevent over-commitment to suboptimal choices. In the single-agent setting, we present some basic regret bounds for regularized learning in adversarial multi-armed bandits; in the multi-agent setting, we describe an ergodic equilibrium convergence result for zero-sum games in the spirit of classical results on fictitious play, as well as a "folk theorem" linking strategic and dynamic notions of stability – Nash equilibria and attracting points of regularized learning, respectively. We pay special attention to the information available to the players and, through a unified analysis framework, we study both oracle- and payoff-based (bandit) methods. Our goal is to provide a coherent and comprehensible – albeit, by necessity, not comprehensive – account of some recent ideas in the field, and to discuss their implications for the study of rationality.

Generative AI models are primarily designed to imitate the data distribution, an objective that neither corrects diversity lost by a learned generator nor defines how generation should extend beyond the diversity of the data itself. We introduce Imaginative Generative AI (IGA), a framework that makes diversity part of the target-distribution design problem: among distributions close to a reference, IGA selects one whose spectral diversity reaches a prescribed level. Diversity is measured by the von Neumann entropy of the generated distribution's kernel covariance operator in a fixed representation space, providing a reference-free representation-guided measure of how broadly probability mass occupies embedding directions. The spectral entropy of the population data distribution defines an Entropy Wall. Below the wall, IGA performs diversity repair, recovering variation that a learned generator has lost while remaining within the diversity level of the data. Beyond the wall, the data distribution itself becomes infeasible, and IGA deliberately departs from it to produce distributions with greater representation-relative spectral diversity, an operational notion of imaginative generation. These regimes form a single regularization path from imitation to imagination and define an i.i.d. target distribution at each prescribed diversity level. We develop the theory of this entropy-constrained projection and show that, under a KL anchor to a pretrained generator, the optimum satisfies a self-consistent exponential-tilt relation. This characterization leads to IGA Guidance, a retraining-free inference-time method for score-based and diffusion models, including DDPM and DDIM samplers. Experiments on synthetic and vision benchmarks demonstrate diversity repair below the Entropy Wall and controlled spectral extrapolation beyond it.

Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10%, compared with 7.97% for CSI and 3.99% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications.

Large-scale learning systems often face the challenge of balancing multiple, potentially competing objectives, such as fairness, accuracy, and latency. While recent work has formalized this as an optimization problem over binary states, many real-world control parameters, such as fairness thresholds, diversity mixing rates, or resource budgets, are continuous. In this work, we extend the framework to continuous state spaces. We model the problem as minimizing a sum of linear objectives subject to movement costs that penalize system instability. We capture the local structure of the objectives using a dependency graph (or factor graph), where each objective is determined by a subset of the state attributes. To address the tension between exploration and stability, we propose Lazy Graph-LinUCB, an algorithm that performs lazy updates to minimize switching costs while maintaining near-optimal regret. Beyond stability, we introduce three advanced mechanisms to exploit the underlying graph structure: (1) an asynchronous update schedule that eliminates synchronization overhead in sparse graphs; (2) an adaptive algorithm that learns the graph structure from data; and (3) a joint estimator that leverages data sharing among correlated objectives to significantly tighten regret bounds. Empirically, we demonstrate that these structural exploitations reduce movement costs by more than a factor of three in heterogeneous systems while maintaining similar cumulative losses.

The demand for maritime surveillance has given rise to the need for monitoring fishing vessel activities, particularly in addressing the challenge of "dark vessels" that operate without Automatic Identification System (AIS) transmission. This study presents a novel approach for detecting small-scale fishing vessels using nighttime light (NTL) imagery from the SDGSAT-1 satellite, combined with deep learning techniques to enhance fishing monitoring awareness along the western coast of India. A dual-branch YOLO11 architecture was developed to exploit both the 10-meter panchromatic and 40-meter RGB imagery from SDGSAT-1. The custom model architecture was specifically optimized for small object detection in NTL imagery, featuring parallel convolutional backbones that process both modalities before concatenation for enhanced feature extraction. The dual-branch YOLO11 model demonstrated optimal performance with a precision of 0.99, recall of 0.93, F1-score of 0.96, and mAP@50 of 0.96, significantly outperforming single-branch implementations of YOLOv5s, YOLOv8s, and standard YOLO11s architectures. When applied to the western coast of India, the model detected 31525 vessel instances across the temporal dataset spanning 2022-23. Cross-matching analysis with AIS data revealed that only 7146 (22.7%) of detected vessels had corresponding AIS transmissions, while 24379 (77.3%) were identified as potential dark vessels. Spatio-temporal analysis showed peak fishing activity during January-April, with a primary activity corridor parallel to the coastline within 50-100 km, corresponding to productive continental shelf areas. This research contributes to maritime surveillance capabilities by highlighting the effectiveness of nighttime lights satellite imagery for fishing vessel detection and provides valuable insights into fishing patterns and potential regulatory compliance issues in Indian waters.

Aggregating several LLM responses to the same question can improve accuracy, but every method that does so must decide where the responses should differ. Established test-time scaling methods such as self-consistency vary only the reasoning path, resampling from a fixed input. The input modification offers several further options: the wording of the question can be rephrased, the spelling can be perturbed, and the accompanying images can be transformed. We study Test-Time Augmentation (TTA), which aggregates predictions across transformed versions of the input, and use it to ask where diversity is best injected. Comparing these options across six benchmarks at a matched number of inference calls, we find that where the diversity comes from matters more than how much of it there is. Meaning-preserving paraphrases of the input yield the largest accuracy gains (+1.80 pp over a single call) and reach peak accuracy with the fewest samples. Yet, they are not the most diverse: character-level noise makes the responses disagree far more often (37.8% versus 27.4%) while gaining less accuracy, and perturbing two modalities at once falls below the single-call baseline. Not all diversity is equally useful: perturbations that keep the meaning intact produce disagreement that aggregation can use, while those that corrupt it produce disagreement that is wrong. Overall, our results suggest that for mid-tier LLMs such as Claude Haiku, varying how a question is phrased is a better use of an inference call than varying the reasoning path. Our TTA implementation is available at github.com/aws-samples/sample-genai-reflection-for-bedrock.

The Lunar Reconnaissance Orbiter (LRO) has been collecting high-resolution images (at around 0.5-2 meters per pixel linearly with its Narrow Angle Camera) of the Moon since 2009, amassing a large dataset of images and offering researchers the opportunity to study the surface of the Moon at unprecedented scale. Here, we aim to test the abilities of the Beta-Variational Autoencoder (VAE) created by Lesnikowski et al. (2024), an unsupervised learning model which identifies anomalous features across the Moon's surface, locating not only scientifically useful geologic formations such as rockfall deposits, fresh impact craters, irregular mare patches, or volcanic pits/collapsed lava tubes, but also artificial objects such as landed spacecraft. This investigation further gauged the model's ability to locate anomalous surface features, successfully recovering two places of interest (Plaskett Crater and Paracelsus C Crater) and numerous landed technological assets at a statistically significant rate.

Density estimation underlies many unsupervised tasks on tabular data such as anomaly detection, out-of-distribution detection, and data augmentation. Although all these problems reduce to questions about where probability mass lies, they are typically solved individually by fitting a separate model to each dataset, with its own hyperparameters and tuning budget. We introduce ICED, an in-context, energy-based density estimator that removes this per-dataset cost. ICED is a transformer-based model pretrained once on a synthetic prior built specifically for density estimation under an objective that fits log-density where it is informative and preserves its ordering elsewhere. In the inference, it reads a dataset as context and returns an unnormalized log-density for any query point in a single forward pass, with no fitting, sampling, or hyperparameter selection. A single frozen ICED model then drives four tasks usually handled by four specialized pipelines: density estimation, out-of-distribution detection, unsupervised anomaly detection, and generative augmentation. Across all four, it is competitive with the strongest task-specific method, while being the only approach that needs no retraining, no tuning, and no labels to move between them. The code is available at https://github.com/gmum/iced.

Multistage stochastic model predictive control (MPC) handles uncertainty by optimizing over a scenario tree, a finite branching approximation of future outcomes constructed from sampled forecasts. To build such a tree, conventional methods focus on matching the underlying probability distribution—e.g., via Wasserstein-based scenario reduction—but improved distributional accuracy does not necessarily yield better control performance. We propose a control-oriented approach that learns scenario tree construction directly from its impact on downstream decisions. Fixing the tree topology, we formulate tree construction as a sequential assignment of sampled scenarios to leaves. This assignment is parameterized by an attention-based policy over the scenario set and trained using reinforcement learning, with closed-loop control profit as the objective. Training is stabilized by an asymmetric critic that leverages realized future trajectories. We evaluate the method on a risk-averse battery arbitrage problem. Across a range of forecast set sizes, the learned construction consistently achieves the highest profit, outperforming classical forward and backward reduction methods and certainty-equivalent (single-trajectory forecast) control. The learned policy also exhibits greater robustness on challenging instances, consistently demonstrating better tail-risk characteristics. Analysis of the resulting trees indicates that our method constructs compact, selectively branching structures that capture high-impact events while keeping most trajectories nearly deterministic. These findings highlight that the value of a scenario tree depends critically on the decisions it supports, and provide an effective framework to train scenario tree constructors merely based on the closed-loop control optimization signal.

Hallucinations are a major concern for the integration of artificial intelligence into medicine, although less explored in the realm of medical image processing. Unlike problems in natural text understanding and reasoning therewith, determining whether or not predictions derived from biomedical images and signals is less intuitively clear. This article suggests that topological errors could constitute hallucinations in a way that can be more readily measured and thus regulated. Certain of these properties for certain types of problems, such as biomedical signal segmentation, can be rephrased as linear temporal logic predicates, a number of which can be explicitly enforced using probabilistic graphical models. Our simulations show the potential of these explicitly constrained predicates for the case of automatic surgical phase recognition in robot-assisted hysterectomy, improving accuracy by approximately 10% while removing the vast majority of topological errors, suggesting that mathematical guarantees of correctness can supplement other empirical forms of regulating machine learning in medical image computing and computer-assisted interventions.

Model learning by an eavesdropper is treated as an estimation problem in a federated environment. The Fisher Information Matrix for the eavesdropper's estimation problem is driven to singularity through a signaling design; this ensures that the eavesdropper cannot learn the model. Herein, the innovation of prior designs is that model shifts are designed to maximize the difference in the model learned by Eve and the central server while satisfying a transmission power constraint for the agents. Two shift schemes are provided. MaxModShift outperforms a prior ModShift design while requiring lesser transmission power. Compared to a noise injection scheme, MaxModShift performs better while requiring a lower bandwidth secret channel and a reduced average power consumption.

In a federated learning setup for GANs, several adversarial attacks are possible. One such attack is label flipping, in which malicious clients deliberately alter label information during local training in order to manipulate the global generator. The objective of this attack is to skew the learned generation distribution so that samples conditioned on a target label are instead mapped to a source class. In this work, we investigate the effectiveness of label flipping attacks in federated GANs through both theoretical analysis and empirical evaluation. We further consider an oversampling based variant, in which malicious clients upweight poisoned samples during local training to amplify their influence on the aggregated global model. We quantify the resulting distributional shift by computing the Kullback Leibler divergence between the clean and poisoned class conditional distributions, and show both analytically and on FEMNIST, MNIST, and CIFAR10 that the semantic damage of the attack grows linearly in the effective poisoning strength while deviation from the true target distribution grows only quadratically, making the attack effective yet difficult to detect from label agnostic metrics.

The deployment of autonomous robotic systems in chemistry laboratories is accelerating experimental workflows and providing the foundational data for AI-driven scientific discovery. However, despite the success of data-driven methods in acquiring dexterous skills, safety remains a primary barrier to their deployment in high-risk domains, such as early-stage materials chemistry experiments. Specifically, learning-based policies frequently struggle to distinguish between safe and unsafe actions, leading to overconfident extrapolation and potentially catastrophic failures. To mitigate these safety risks, we propose SAFE-CHEM, an uncertainty-aware framework designed for robust, learning-based robotic chemists. Our approach leverages an ensemble of recurrent neural network-based imitation learning policies to quantify epistemic uncertainty online through the variance of action predictions. By characterising the success-conditioned density of this variance using kernel density estimation, we introduce a hybrid control architecture that autonomously switches from the learned policy to a deterministic, rule-based backup controller when uncertainty exceeds a calibrated safety threshold. We evaluate SAFE-CHEM across three fundamental laboratory manipulation tasks, where our empirical results demonstrate that this hybrid strategy improves overall task success rates and reduces critical safety violations compared to traditional single-policy baselines. Finally, we demonstrate the practical viability of the framework through zero-shot sim-to-real transfer onto a physical Franka Production 3 robot manipulator.

A CAD model is not engineering-grade merely because it looks correct. It must satisfy design requirements, respond predictably to parameter changes, support controlled edits, match a reference structural response under a declared analysis, and connect to other parts through valid joints. We present CADEngBench, a two-track benchmark for these capabilities. CADEngBench-P evaluates 300 parametric parts, each used for one zero-to-CAD task and one functional-editing task (600 tasks in total), through boundary-representation (B-Rep) validity, engineering and DFM checks, parameter-family perturbations, functional editing, and matched linear-static FEA in CalculiX. CADEngBench-A evaluates 150 body pairs through ranked joint retrieval, exact face-and-edge grounding, joint-frame prediction, and kinematic verification. Across eight multimodal, code-capable models, editing supplied CAD is substantially easier than generating it, while complex edits and matched FEA remain difficult. Assembly predictions often locate the relevant region but fail to recover the recorded joint or mating entities. These results show that CAD evaluation must test engineering behavior rather than appearance alone.

Self-evolving methods improve the capabilities of LLM agents by sampling trajectories from the underlying LLMs and learning from these trajectories. However, these methods struggle to learn beyond the inherent capability boundary of the agents, since the agents cannot sample correct trajectories on difficult examples for further improvements. In this paper, we propose a zeroth-order self-evolution framework that enables agents to learn beyond their capability boundary by perturbing LLM parameters to adapt to difficult examples without any trajectory annotations. Specifically, we perturb LoRA parameters of LLMs, run the agent, compute the losses under the perturbed and original parameters, and use the loss difference to estimate gradients and further update the LoRA parameters. We sample trajectories using the updated LLMs for supervised fine-tuning to break through the capability boundary of the agents, forming a closed self-evolution loop. We introduce a parallel perturbation inference mechanism and an adaptive lookup mechanism to reduce time consumption in zeroth-order optimization, with an answer perplexity loss that provides smooth and stable zeroth-order loss values. Experiments on multiple deep research benchmarks show that our method obtains substantially more successful trajectories and consistently outperforms strong baselines, especially on difficult examples. The code and released artifacts are available at https://github.com/hidk1911/ZOForLLMAgents.

Global medium-range weather forecasting requires modeling structured yet state-dependent interactions among heterogeneous atmospheric fields. Existing data-driven models largely learn these interactions implicitly, whereas equation-level physical constraints may inherit approximation and model-form biases. We present VeinCast, a physics-guided dynamic field graph and graph-conditioned fusion framework that jointly forecasts 69 surface and upper-air fields. Within each local window, its Physics-Guided Dynamic Field Graph combines predefined atmospheric relations with state-dependent Top-K residual edges and adapts Earth-window attention using the resulting graph context. Graph-Conditioned Latent Fusion further employs graph context and source-node centrality to guide field-to-latent aggregation, while bounded feedback preserves field-specific information. On the $1.5^\circ$ ERA5 benchmark, VeinCast demonstrates competitive forecasting performance across all 69 meteorological fields at lead times of up to 14 days, compared with representative global weather forecasting models including FuXi, Pangu-Weather, GraphCast, FengWu, and ARROW. Ablations confirm that the two modules provide complementary gains, demonstrating the effectiveness of relational-level physical guidance for data-driven weather forecasting.

Planetary geology relies on historical, interpretive reasoning to reconstruct past events from diverse observations. Here, we investigate how far this interpretive workflow can be automated by a multimodal vision-language model. Focusing on the stratigraphy of lunar basaltic mare volcanism, we train a model to generate verifiably grounded geologic interpretations directly from co-registered topographic, spectral, and geologic maps. We demonstrate that while the system successfully balances established geological priors with local visual evidence to accurately describe stratigraphy and terrain, numeric age dating derived solely from vision defaults to memorized priors. Integrating an open-book retrieval mechanism resolves this, enabling the model to faithfully cite published chronologies. Our findings delineate the necessary architecture for automated geologic inference: site evidence must be visually interpreted from local data, while quantitative historical context must be retrieved from the scientific record.

Group-based reinforcement learning objectives such as GRPO can allocate learning signal poorly across prompt difficulty: under binary rewards, group normalization induces a divergent weighting on easy prompts. We introduce Softmax Advantage Group Estimation (SoftmaxGRPO), a drop-in alternative that replaces z-score-normalized group advantages with temperature-scaled softmax advantages, keeping weights bounded regardless of prompt difficulty. For binary rewards, we derive the exact finite-group population objective and identify MaxRL as its low-temperature limit. For bounded scalar rewards, we show that the large-group update exactly optimizes a log-moment-generating-function objective, while a universal finite-group scalar objective cannot exist without additional assumptions on the reward distribution. Empirically, SoftmaxGRPO reallocates measured gradient budget away from near-solved prompts and consistently improves over GRPO under identical rewards. It reaches 51.8% on DeepMath with verifiable rewards and improves a 1.5B instruction-tuned model from 35.0% to 68.0% on Poetry using only lightweight text-similarity rewards.

Medical world models commonly learn from multimodal recordings synchronized onto a fixed-rate grid. This preprocessing resamples each native stream onto a shared time axis. Each stream has an observation clock that governs when observations are emitted or updated. When this clock depends on the latent or acquisition state, it is endogenous. In such settings, synchronization may not be neutral and can erase task-relevant evidence before the model sees the data. We introduce a four-regime taxonomy that characterizes where the evidence needed to distinguish a target event or state survives. The relevant witness may remain in the sampled values, in grid-cell update patterns, in native timing, or only in an external acquisition channel. EndoClock operationalizes this taxonomy as a conservative pretraining audit. It reports the lowest witness-bearing representation supported by the available evidence, or unresolved when no regime can be established. We illustrate this failure in echocardiography, where B-mode video write-outs cease during pulsed-wave Doppler acquisition while the corresponding measurement events remain recorded only in an external acquisition log. This work is a preliminary failure alert and executable audit. Its practical message is to preserve the native observation process long enough to determine whether synchronization has erased information required by the intended task.

On-policy self-distillation aims to improve upon reinforcement learning from verifiable rewards (RLVR) by providing token-level scores derived from privileged information, such as reference solutions or critic feedback. These scores are treated as estimates of token-level action values, yet they answer a fundamentally different question: how the model's prediction changes when its input context is enriched, rather than how the expected outcome changes when a token is changed. We examine this gap along three dimensions: (i) whether the token-level score tracks task success; (ii) whether feedback generated from the same rollout causes the score to reflect agreement with its own description, and whether using feedback from other rollouts in the group mitigates this self-referential effect; and (iii) what behavior the resulting training objective actually reinforces. In experiments on AIME 2025, the implemented score distinguishes correct from incorrect rollouts at approximately chance level (AUC=0.505); using feedback from a different rollout does not consistently improve this discrimination; and all training configurations achieve only 24.2-33.9% Avg@4, compared with 64.2% for outcome-only GRPO. Moreover, the highest-entropy token decile accounts for 57-71% of the total absolute token-advantage mass, despite the score being least informative about reasoning quality in this regime. By contrast, similar experiments on SciKnowEval Biology improves held-out Avg@8 by 28.0%, while its corresponding trajectory scores achieve AUCs of 0.81-0.92. Together, these results suggest that dense credit assignment through distillation can be effective when its likelihood-based scores are empirically validated as meaningful proxies for outcome-relevant credit. When this alignment does not hold, however, the resulting supervision can fail to generalize and may substantially underperform outcome-based RL.

Residential energy estimates are often needed before detailed envelope characteristics, equipment efficiencies, infiltration, sensor, or billing data are available. This study quantifies the trade-off between predictive accuracy and input accessibility using two nationally representative U.S. residential-energy datasets: the survey-based Residential Energy Consumption Survey (RECS) and the simulation-based ResStock dataset. Full-feature models were first used to establish dataset-specific performance benchmarks. For total-energy estimation, the models were subsequently restricted to ten low-burden variables obtainable from occupants, administrative records, or location-based weather data without an on-site energy audit. Among CatBoost, XGBoost, LightGBM, Random Forest, and Neural Networks, CatBoost consistently achieved the highest predictive performance for the full-feature analysis, reaching R2 = 0.90 for ResStock and R2 = 0.73 for RECS. When the feature set was restricted to ten homeowner-accessible inputs to simulate realistic deployment conditions, model performance converged to R2 = 0.61 for RECS and R2 = 0.62 for ResStock, showing that algorithmic complexity cannot fully compensate for missing physical and behavioral information. However, for a more homogeneous ResStock cohort consisting of single-family detached, natural-gas-heated homes in Climate Zone 6A constructed between 2000 and 2010, a reduced-input model improved accuracy to R2 = 0.85, demonstrating the value of targeted modeling for homogeneous populations. The results indicate that tree-based ensemble models can serve as high-fidelity emulators of national-scale residential energy datasets. However, careful consideration of feature availability, dataset origin (empirical vs. synthetic), and applicable use cases are also important.

Large language model-based multi-agent systems have recently shown strong potential for complex, long-horizon tasks. However, existing methods mainly rely on coarse prompt-level differentiation without parameter adaptation for diverse subtasks, resulting in insufficient inter-agent heterogeneity and limited specialized capability that bottleneck performance on tasks with complex requirements. To address this, we introduce a Task-Oriented Multi-Agent System with Mixture of Role-Subtask Experts (MoRSE) that distinguishes agents with (role, subtask)-conditional specialization at both the task structure and parameter levels. To make agents' responsibility explicit at the task structure level, we formulate a task-oriented multi-agent system that decomposes each task into a dependency-aware Directed Acyclic Graph of subtasks and assigns each agent a specific (role, subtask), introducing task-level specialization across collaborating agents. Additionally, to address the diverse role and subtask parameter adaptation demands, we propose a dynamic Mixture of (role, subtask) LoRA Experts module with a prototype-based semantic router for subtasks, augmenting agents with parameter-level specialization on a shared LLM substrate cost-effectively. Then, to co-optimize experts and router stably under sparse task rewards, we further propose a hierarchical group-relative policy optimization with two-layer credit assignment that isolates expert updates from the cross-route variance introduced by routing decisions, disentangling expert quality from routing quality. Experiments on code-generation benchmarks across three backbones demonstrate the effectiveness of our approach, with improvements in both whole-task and step-wise performance, and the gains from trained specialization generalize across held-out task categories and domains.

Federated learning (FL) must serve devices with varying computational capabilities. A fixed model cannot suit all devices, while training one model per deployment limit is costly. Federated supernet training instead learns one elastic model with differently sized subnetworks, then deploys a suitable one to each device. When client inference budgets differ, however, parameters exclusive to high-cost subnetworks are reachable by fewer clients. We propose FEAST, a federated shared-space training framework that counters this imbalance by jointly training multiple subnetworks within each client's limit. Budget-tailored sub-supernet routing sends only the relevant supernet portion, and sparse aggregation merges the returned parameter slices. The trained supernet directly serves the subnetworks used during federation and supports post-hoc extraction of additional subnetworks without federated retraining. We further show that independently assigning clients' training-data volumes and inference budgets can distort accuracy–inference-cost comparisons in heterogeneous FL simulations, and introduce a one-parameter $\gamma$-allocation protocol to control this coupling. In our experimental setup, the SuperFedNAS and DeepFedNAS supernet training procedures remain near chance at 25M and reach at most $17.09\%$ at $596$M inference MACs; FEAST reaches $71.06\%$ at $596$M, $2.4$ points above the strongest model-heterogeneous weight-sharing baseline at its largest tier. Across CIFAR-100, CINIC-10, and TinyImageNet-200, FEAST achieves the highest population-averaged accuracy among the evaluated weight-sharing methods when each client receives its largest affordable subnetwork. Sub-supernet routing reduces aggregate model-parameter traffic by $6.8\times$ relative to full-supernet transmission.

Multimodal federated learning (FL) supports collaborative modeling in privacy-sensitive health-sensing and medical settings, but realistic deployments often exhibit dual-axis modality missingness: clients have different modality sets, and individual samples may contain only subsets of the modalities available locally. Existing methods typically address these two axes separately. We propose Flux, a multimodal federated learning framework built around two complementary components. First, modality-aware confidence tempering learns sample-specific confidence for each modality through mask-aware unimodal supervision and fuses the confidence estimates from observed modalities into a sample-adaptive temperature that adjusts predictive sharpness according to evidence quality and completeness. Second, gradient-decoupled private adaptation applies this temperature only to a client-private prediction pathway, while training the shared federated model with a standard, untempered objective. This enables sample-specific, client-local confidence adaptation without allowing confidence-dependent gradients to perturb shared representation learning. Across four multimodal datasets, Flux achieves the highest average macro-F1 on every dataset, outperforming the strongest dataset-specific baseline by 0.8~2.2 points and by 1.6 points on average. Additional analyses demonstrate favorable calibration, temperature sensitivity to both modality missingness and input corruption, and more stable shared optimization under private-only tempering. Our code is available at https://github.com/AdibaOrz/Flux.

Federated learning enables privacy-preserving collaboration across distributed devices without centralizing local data. However, clients may differ not only in data distributions but also in domain knowledge and annotation capabilities. In this paper, we introduce label granularity skew, a new form of statistical heterogeneity in federated hierarchical classification, in which clients provide taxonomy-consistent labels at different levels of detail within a shared class hierarchy. To model this heterogeneity, we generate client-specific local label hierarchies using a probabilistic relational neighbor classifier and construct a WordNet-guided hierarchy via silhouette score-based coarsening. Our analysis shows that strongly coupled hierarchical models are sensitive to incomplete supervision, while the conditional softmax classifier is more robust. Based on this insight, we propose Branch-wise Decoupled Fine-Tuning (BDFT) and its federated version, FedBDFT, which fine-tune branch-wise classifiers and aggregate them through federated optimization. Experiments on CIFAR-100, TinyImageNet, and ImageNet show that FedBDFT substantially improves robustness under severe label granularity skew, with average gains of 27.9% and 56.4% at skewness levels of 0.6 and 0.9, respectively. Zero-shot results further indicate that FedBDFT better preserves hierarchical representations for unseen fine-grained classes. These findings demonstrate its effectiveness for federated hierarchical classification with heterogeneous label granularities.

Flow-matching models are now a mainstream method to image generation, but its adaptation to diverse downstream scenarios typically relies on post-training, which may cause conflicts among task-specific optimization objectives. Reinforcement learning enables direct optimization of task-specific rewards beyond the original models, yet trajectory-level optimization may incur high-variance gradients and cross-task interference. On-policy distillation (OPD) offers dense and stable supervision on student rollouts, but conventional teacher matching remains imitation-based. We propose DreOPD, a Degraded-reference extrapolative OPD method for flow-matching models that bridges these two paradigms. Our DreOPD converts implicit reward extrapolation into closed-form velocity regression, enabling extrapolative post-training with the stability of OPD. It further uses a mildly degraded reference to strengthen the teacher-reference contrast, yielding a clearer extrapolation direction. Experiments on single- and multi-teacher settings show that DreOPD outperforms OPD and multi-task RL baselines in average performance, while surpassing specialized teachers on most metrics.

On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with $\mathrm{OP}^{2}\mathrm{SD}$ (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, $\mathrm{OP}^{2}\mathrm{SD}$ improves over the base model, remains competitive with OPSD. The success of $\mathrm{OP}^{2}\mathrm{SD}$ implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.

Federated Learning (FL) enables collaborative model training across distributed client devices while preserving data privacy. However, FL faces significant challenges due to data heterogeneity, particularly in terms of label distribution skewness and variations in dataset sizes, which can lead to biased model updates and hinder convergence. To address this, we propose FedTVD, a novel FL algorithm that weights client contributions during aggregation by considering both data quality and quantity. Unlike traditional FL approaches such as FedAvg, which rely solely on dataset size for client weighting, FedTVD integrates Total Variation Distance (TVD) to measure the divergence between each client's local label distribution and a uniform global distribution. Clients with highly skewed distributions receive lower weights, preventing unbalanced datasets with imbalances from disproportionately influencing the global model. At the same time, dataset size is incorporated to ensure scalability and fairness. This dual-weighting mechanism effectively mitigates the impact of data imbalance, leading to more stable and generalized global models. Experimental results show that FedTVD consistently outperforms state-of-the-art methods across all datasets (FMNIST, CIFAR-10, and CIFAR-100) and all levels of data heterogeneity. Notably, it achieves up to 10.6% improvement over FedAvg on CIFAR-10 under highly skewed data, while maintaining top performance even under moderate and IID settings.

A score-driven filter multiplies its scaled log-likelihood score by a scale parameter. We call this coefficient the gain and learn it online. Given the current state and realised scaled score, each admissible gain selects a reachable next state and predictive density. A scalar gain moves along a line; diagonal gains control coordinatewise transmission and may change direction. We evaluate gain selection using a one-step predictive Kullback-Leibler objective. In the scalar unscaled case, the negative consecutive-score product is a stochastic gradient; the positive product used in accelerated recursions is a descent direction. Positive scalar score scaling changes only the effective learning rate. Strictly increasing, continuously differentiable gain links with positive derivative induce mirror-descent geometry, while persistence adds a Bregman pull towards a reference gain. Under convexity, compactness, integrability, and schedule conditions, projected and discounted mirror updates satisfy dynamic-regret bounds relative to time-varying, current-information comparators. Simulations isolate score scaling, link geometry, persistence, and coordinatewise gains. Across twelve equity indices, the bounded discounted-logistic gain records a lower out-of-sample mean negative log score than the constant gain in eleven markets, although market-level evidence is mixed. It also avoids the extreme transients of the numerically capped exponential-link benchmark.

Reinforcement learning (RL) has become a central post-training paradigm for eliciting reasoning capabilities in large language models, yet uniform task sampling allocates compute without regard to differences in how tasks respond to optimization. Existing task-valuation methods mostly rely on snapshot-based signals such as current pass rate or reward, which estimate how solvable a task is under the current policy. However, tasks with similar current solvability can still differ substantially in how positively they respond to further training. We study this residual axis as task learnability: a regime-conditional measure of expected positive response to continued training under a fixed RL post-training regime. By analyzing per-task reward trajectories, we find that learnability is reproducible across independently sampled training contexts and predictive of downstream utility. To make this signal practical before training begins, we propose TrajVal, a lightweight probe-based estimator that approximates per-task learnability from a short probe run and two endpoint evaluations. TrajVal can be used either as a standalone static prior for task sampling or as a multiplicative prior for existing online schedulers. Experiments on mathematical and logical reasoning benchmarks across multiple model scales show that TrajVal improves data efficiency over uniform sampling and provides complementary gains when combined with online scheduling methods.