LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor $ρ$, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a $χ^2$-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Return-to-Go Is More Than a Number: Q-Guided Alignment for Return-Conditioned Supervised Learning

Conditioned Sequence Models (CSMs) learn policies by treating return-to-go (RTG) as a control signal. However, existing CSMs often treat the RTGs as simple numerical inputs rather than aligning them with the performance of their policies. In this paper, we propose Q-ALIGN DT, a framework that enforces this alignment by ensuring the $Q$-value of the output policy is consistent with the input RTG. By leveraging a $Q$ function to provide dense guidance to CSMs and further fine-tuning it using an RTG-perturbation technique with the CSM, our method ensures that higher RTGs are consistently mapped to trajectories with higher expected returns. Theoretically, we show that Q-ALIGN DT can efficiently learn the desired policy and output a near-optimal one when the RTG is sufficiently high. Empirically, we demonstrate through extensive experiments that Q-ALIGN DT achieves superior controllability and performance across the D4RL benchmark. Remarkably, our model effectively learns a structured family of policies that maintains precise alignment and generalizes to tasks like velocity-tracking where prior methods fail.

Moment Matching Q-Learning

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these models suffer from prolonged inference latency, which imposes a significant computational bottleneck in RL with iterative sampling. To overcome this limitation, we propose a new framework named Moment Matching Q-Learning (MoMa QL), which utilizes a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD) that intend to match all orders of statistics between the original and target distribution. By enforcing strong regularization on all moment statistics, this algorithm guarantees distribution-level convergence for conditional score function and remains stable under various hyperparameters. Empirically, we show that our method MoMa QL is more computationally efficient with a comparable if not competitive performance in various D4RL tasks. Remarkably, by accelerating the action sampling process for flow-based policies, MoMa QL demonstrates superior performance in offline-to-online RL tasks because of faster and stronger adaptability for online interactive finetuning.

AutoResearchClaw: Self-Reinforcing Autonomous Research with Human-AI Collaboration

Automating scientific discovery requires more than generating papers from ideas. Real research is iterative: hypotheses are challenged from multiple perspectives, experiments fail and inform the next attempt, and lessons accumulate across cycles. Existing autonomous research systems often model this process as a linear pipeline: they rely on single-agent reasoning, stop when execution fails, and do not carry experience across runs. We present AutoResearchClaw, a multi-agent autonomous research pipeline built on five mechanisms: structured multi-agent debate for hypothesis generation and result analysis, a self-healing executor with a \textsc{Pivot}/\textsc{Refine} decision loop that transforms failures into information, verifiable result reporting that prevents fabricated numbers and hallucinated citations, human-in-the-loop collaboration with seven intervention modes spanning full autonomy to step-by-step oversight, and cross-run evolution that converts past mistakes into future safeguards. On ARC-Bench, a 25-topic experiment-stage benchmark, AutoResearchClaw outperforms AI Scientist v2 by 54.7%. A human-in-the-loop ablation across seven intervention modes reveals that precise, targeted collaboration at high-leverage decision points consistently outperforms both full autonomy and exhaustive step-by-step oversight. We position AutoResearchClaw as a research amplifier that augments rather than replaces human scientific judgment. Code is available at https://github.com/aiming-lab/AutoResearchClaw.

Wasserstein Equilibrium Decoding for Reliable Medical Visual Question Answering

Small vision-language models (2-8B) are well-suited for clin- ical deployment due to privacy constraints, limited connectivity, and low-latency requirements favouring on-device or on-premise inference. However, their limited capacity exacerbates the generation of plausible but incorrect outputs. We extend game-theoretic decoding, previously restricted to text-only, closed-ended NLP tasks, to vision-language mod- els for open-ended Medical VQA. We introduce a semantically aware Wasserstein stopping criterion that replaces lexical order matching, en- abling convergence based on semantic consensus among near-synonymous candidate answers and avoiding unnecessary iterations caused by clini- cally equivalent ranking swaps. On VQA-RAD and PathVQA, we ob- tain consistent, statistically significant improvements over greedy and discriminative baselines. On VQA-RAD, we improve Qwen3-VL-2B by +3.5 percentage points (p < 0.01), surpassing the greedy 4B model, with similar trends at larger scales. On PathVQA, Gemma-3-4B with BDG matches MedGemma-4B under greedy decoding despite no domain- specific fine-tuning. At accuracy parity with classic BDG, the Wasser- stein criterion reduces average convergence iterations by approximately 20%, improving inference efficiency while preserving the game-theoretic equilibrium behaviour. Code is available at https://github.com/luca-hagen/ Wasserstein-BDG-medical-VQA.

OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning

We study {on-policy self-distillation} (OPSD), where a language model improves its reasoning ability by distilling privileged teacher distributions along its own on-policy trajectories. Despite the performance gains of OPSD, we identify a common but often overlooked mismatch between teacher and student responses: self-reflected teacher responses can be shifted by reflection-induced bias and response templates, leading to miscalibrated token-level supervision. To mitigate this issue, we propose \methodname, an outcome-guided logit-steering framework that leverages verifiable outcome rewards to contrast successful and failed on-policy trajectories and calibrate teacher logits. By combining outcome-level correctness with dense token-level guidance through logit steering, \methodname stabilizes self-distillation and improves reasoning performance over standard OPSD and other variants across diverse benchmarks.

GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations

Herding -- where agents align their behaviors and act collectively -- is a central driver of market fragility and systemic risk. Existing approaches to quantify herding rely on price-correlation statistics, which inherently lag because they only detect coordination after it has already moved realised returns. We propose GeomHerd, a forward-looking geometric framework that bypasses this observability lag by quantifying coordination directly on upstream agent-interaction graphs. To generate these graphs, we treat a heterogeneous LLM-driven multi-agent simulator -- each financial trader instantiated by a persona-conditioned LLM call -- as a forecastable world, and evaluate the geometric pipeline on the Cividino--Sornette continuous-spin agent-based substrate as our headline financial testbed. By tracking the discrete Ollivier--Ricci curvature of these action graphs, GeomHerd captures the structural topology of emerging coordination. Theoretically, we establish a mean-field bridge mapping our graph-theoretic metric to CSAD, the classical macroscopic herding statistic, linking GeomHerd to downstream price-dispersion measurement. Empirically, GeomHerd anticipates herding long before aggregate market baselines: on the continuous-spin substrate, our primary detector fires a median of 272 steps before order-parameter onset; a contagion detector ($β_{-}$) recalls 65% of critical trajectories 318 steps early; and on co-firing trajectories the agent-graph signal precedes price-correlation-graph baselines by 40 steps. As a complementary indicator, the effective vocabulary of agent actions contracts during cascades. The geometric signature transfers out-of-domain to the Vicsek self-driven-particle model, and a curvature-conditioned forecasting head reduces cascade-window log-return MAE over detector-conditioned and price-only baselines.

Provably Efficient Offline-to-Online Value Adaptation with General Function Approximation

We study value adaptation in offline-to-online reinforcement learning under general function approximation. Starting from an imperfect offline pretrained $Q$-function, the learner aims to adapt it to the target environment using only a limited amount of online interaction. We first characterize the difficulty of this setting by establishing a minimax lower bound, showing that even when the pretrained $Q$-function is close to optimal $Q^\star$, online adaptation can be no more efficient than pure online RL on certain hard instances. On the positive side, under a novel structural condition on the offline-pretrained value functions, we propose O2O-LSVI, an adaptation algorithm with problem-dependent sample complexity that provably improves over pure online RL. Finally, we complement our theory with neural-network experiments that demonstrate the practical effectiveness of the proposed method.

Provable and Practical In-Context Policy Optimization for Self-Improvement

We study test-time scaling, where a model improves its answer through multi-round self-reflection at inference. We introduce In-Context Policy Optimization (ICPO), in which an agent optimizes its response in context using self-assessed or externally observed rewards without modifying its parameters. To explain this ICPO process, we theoretically show that with sufficient pretraining under a novel Fisher-weighted logit-matching objective, a single-layer linear self-attention model can provably imitate policy-optimization algorithm for linear bandits. Building on this theory, we propose Minimum-Entropy ICPO (ME-ICPO), a practical algorithm that iteratively uses its response and self-assessed reward to refine its response in-context at inference time. By selecting the responses and their rewards with minimum entropy, ME-ICPO ensures the robustness of the self-assessed rewards via majority voting. Across standard mathematical reasoning tasks, ME-ICPO attains competitive, top-tier performance while keeping inference costs affordable compared with other inference-time algorithms. Overall, ICPO provides a principled understanding of self-reflection in LLMs and yields practical benefits for test-time scaling for mathematical reasoning.

Your Self-Play Algorithm is Secretly an Adversarial Imitator: Understanding LLM Self-Play through the Lens of Imitation Learning

Self-play post-training methods has emerged as an effective approach for finetuning large language models and turn the weak language model into strong language model without preference data. However, the theoretical foundations for self-play finetuning remain underexplored. In this work, we tackle this by connecting self-play finetuning with adversarial imitation learning by formulating finetuning procedure as a min-max game between the model and a regularized implicit reward player parameterized by the model itself. This perspective unifies self-play imitation and general preference alignment within a common framework. Under this formulation, we present a game-theoretic analysis showing that the self-play finetuning will converge to it's equilibrium. Guided by this theoretical formulation, we propose a new self-play imitation finetuning algorithm based on the $χ^2$-divergence variational objective with bounded rewards and improved stability. Experiments on various of language model finetuning tasks demonstrate consistent improvements over existing self-play methods and validate our theoretical insights.