GRASP: Deterministic argument ranking in interaction graphs

Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from rhetorical appeal. However, we show that holistic judging - a common LLM-as-a-Judge practice where a model provides a global verdict on a debate - suffers from substantial inter-model disagreement. We argue that this instability arises from collapsing a debate's complex interaction structure into a single opaque score. To address this, we propose GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates stable local interaction judgments into a global ranking via a convergent attack--defense propagation operator. We show that local interaction judgments are more reproducible than holistic rankings in LLM-as-a-Judge evaluations, allowing GRASP to produce more consistent global rankings. We further show that GRASP scores do not correlate with human "convincingness" labels, highlighting a vital sociotechnical distinction: GRASP does not measure persuasion, factuality, or rhetorical appeal, but structural sufficiency - a defense-aware notion of argument robustness over the explicit interaction graph. Overall, GRASP offers a transparent and auditable alternative to holistic LLM judging.

Split the Differences, Pool the Rest: Provably Efficient Multi-Objective Imitation

This work investigates multi-objective imitation learning: the problem of recovering policies that lie on the Pareto front given demonstrations from multiple Pareto-optimal experts in a Multi-Objective Markov Decision Process (MOMDP). Standard imitation approaches are ill-equipped for this regime, as naively aggregating conflicting expert trajectories can result in dominated policies. To address this, we introduce Multi-Output Augmented Behavioral Cloning (MA-BC), an algorithm that systematically partitions divergent expert data while pooling state-action pairs where no behavior conflict is observed. Theoretically, we prove that MA-BC converges to Pareto-optimal policies at a faster statistical rate than any learner that considers each expert dataset independently. Furthermore, we establish a novel lower bound for multi-objective imitation learning, demonstrating that MA-BC is minimax optimal. Finally, we empirically validate our algorithm across diverse discrete environments and, guided by our theoretical insights, extend and evaluate MA-BC on a continuous Linear Quadratic Regulator (LQR) control task.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives

In this work, we develop proximal preconditioned gradient methods with a focus on spectral gradient methods providing a proximal extension to the Muon and Scion optimizers. We introduce a family of stochastic algorithms that can handle a wide variety of convex and nonconvex constraints and study its convergence under heavy-tailed noise, through a novel analysis tailored to the geometry of the proposed methods. We further propose a variance-reduced version, which achieves faster convergence under standard noise assumptions. Finally, we show that the polynomial iterations used in Muon are more accurately captured by a nonlinear preconditioner than by the ideal matrix sign, leading to a convergence analysis that more faithfully reflects practical implementations.

On the Role of Batch Size in Stochastic Conditional Gradient Methods

We study the role of batch size in stochastic conditional gradient methods under a $μ$-Kurdyka-Łojasiewicz ($μ$-KL) condition. Focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion), we derive a new analysis that explicitly captures the interaction between stepsize, batch size, and stochastic noise. Our study reveals a regime-dependent behavior: increasing the batch size initially improves optimization accuracy but, beyond a critical threshold, the benefits saturate and can eventually degrade performance under a fixed token budget. Notably, the theory predicts the magnitude of the optimal stepsize and aligns well with empirical practices observed in large-scale training. Leveraging these insights, we derive principled guidelines for selecting the batch size and stepsize, and propose an adaptive strategy that increases batch size and sequence length during training while preserving convergence guarantees. Experiments on NanoGPT are consistent with the theoretical predictions and illustrate the emergence of the predicted scaling regimes. Overall, our results provide a theoretical framework for understanding batch size scaling in stochastic conditional gradient methods and offer guidance for designing efficient training schedules in large-scale optimization.

Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving these tasks depends on the way data is coupled with noise. A recent approach uses minibatch optimal transport (OT) to reassign noise-data pairs in each training step to streamline sampling trajectories and thus accelerate inference. However, its optimization is restricted to individual minibatches, limiting its effectiveness on large datasets. To address this shortcoming, we introduce LOOM-CFM (Looking Out Of Minibatch-CFM), a novel method to extend the scope of minibatch OT by preserving and optimizing these assignments across minibatches over training time. Our approach demonstrates consistent improvements in the sampling speed-quality trade-off across multiple datasets. LOOM-CFM also enhances distillation initialization and supports high-resolution synthesis in latent space training.

Multi-agent imitation learning with function approximation: Linear Markov games and beyond

In this work, we present the first theoretical analysis of multi-agent imitation learning (MAIL) in linear Markov games where both the transition dynamics and each agent's reward function are linear in some given features. We demonstrate that by leveraging this structure, it is possible to replace the state-action level "all policy deviation concentrability coefficient" (Freihaut et al., arXiv:2510.09325) with a concentrability coefficient defined at the feature level which can be much smaller than the state-action analog when the features are informative about states' similarity. Furthermore, to circumvent the need for any concentrability coefficient, we turn to the interactive setting. We provide the first, computationally efficient, interactive MAIL algorithm for linear Markov games and show that its sample complexity depends only on the dimension of the feature map $d$. Building on these theoretical findings, we propose a deep MAIL interactive algorithm which clearly outperforms BC on games such as Tic-Tac-Toe and Connect4.

Matching Multiple Experts: On the Exploitability of Multi-Agent Imitation Learning

Multi-agent imitation learning (MA-IL) aims to learn optimal policies from expert demonstrations of interactions in multi-agent interactive domains. Despite existing guarantees on the performance of the resulting learned policies, characterizations of how far the learned polices are from a Nash equilibrium are missing for offline MA-IL. In this paper, we demonstrate impossibility and hardness results of learning low-exploitable policies in general $n$-player Markov Games. We do so by providing examples where even exact measure matching fails, and demonstrating a new hardness result on characterizing the Nash gap given a fixed measure matching error. We then show how these challenges can be overcome using strategic dominance assumptions on the expert equilibrium. Specifically, for the case of dominant strategy expert equilibria, assuming Behavioral Cloning error $ε_{\text{BC}}$, this provides a Nash imitation gap of $\mathcal{O}\left(nε_{\text{BC}}/(1-γ)^2\right)$ for a discount factor $γ$. We generalize this result with a new notion of best-response continuity, and argue that this is implicitly encouraged by standard regularization techniques.

Easy Data Unlearning Bench

Evaluating machine unlearning methods remains technically challenging, with recent benchmarks requiring complex setups and significant engineering overhead. We introduce a unified and extensible benchmarking suite that simplifies the evaluation of unlearning algorithms using the KLoM (KL divergence of Margins) metric. Our framework provides precomputed model ensembles, oracle outputs, and streamlined infrastructure for running evaluations out of the box. By standardizing setup and metrics, it enables reproducible, scalable, and fair comparison across unlearning methods. We aim for this benchmark to serve as a practical foundation for accelerating research and promoting best practices in machine unlearning. Our code and data are publicly available.

MaD-Mix: Multi-Modal Data Mixtures via Latent Space Coupling for Vision-Language Model Training

Vision-Language Models (VLMs) are typically trained on a diverse set of multi-modal domains, yet current practices rely on costly manual tuning. We propose MaD-Mix, a principled and computationally efficient framework that derives multi-modal data mixtures for VLM training. MaD-Mix formulates data mixing as modality-aware domain alignment maximization and obtains closed-form multi-modal alignment scores from the Fenchel dual through inter-modal coupling variables. MaD-Mix systematically handles domains with missing modalities, allowing for the integration of language-only domains. Empirical evaluations across 0.5B and 7B models demonstrate that MaD-Mix accelerates VLM training across diverse benchmarks. MaD-Mix matches human-tuned data mixtures using 22% fewer training steps in image-text instruction tuning. In complex tri-modal video-image-text scenarios, where manual tuning becomes impractical, MaD-Mix boosts average accuracy over uniform weights, with negligible mixture computation overhead (< 1 GPU-hour), enabling scalable mixture design for modern VLM pipelines.

Provably avoiding over-optimization in Direct Preference Optimization without knowing the data distribution

We introduce PEPO (Pessimistic Ensemble based Preference Optimization), a single-step Direct Preference Optimization (DPO)-like algorithm to mitigate the well-known over-optimization issue in preference learning without requiring the knowledge of the data-generating distribution or learning an explicit reward model. PEPO achieves pessimism via an ensemble of preference-optimized policies trained on disjoint data subsets and then aggregates them through a worst case construction that favors the agreement across models. In the tabular setting, PEPO achieves sample complexity guarantees depending only on a single-policy concentrability coefficient, thus avoiding the all-policy concentrability which affects the guarantees of algorithms prone to over-optimization, such as DPO. The theoretical findings are corroborated by a convincing practical performance, while retaining the simplicity and the practicality of DPO-style training.