Sparse but Critical: A Token-Level Analysis of Distributional Shifts in RLVR Fine-Tuning of LLMs

Reinforcement learning with verifiable rewards (RLVR) has significantly improved reasoning in large language models (LLMs), yet the token-level mechanisms underlying these improvements remain unclear. We present a systematic empirical study of RLVR's distributional effects organized around three main analyses: (1) token-level characterization of distributional shifts between base and RL models, (2) the impact of token-level distributional shifts on sequence-level reasoning performance through cross-sampling interventions, and (3) fine-grained mechanics of these shifts at the token level. We find that RL fine-tuning induces highly sparse and targeted changes, with only a small fraction of token distributions exhibiting meaningful divergence between the base and RL policies. We further characterize the structure and evolution of these shifts through analyses of token entropy, positional concentration, and reallocation of probability mass. To assess the functional importance of these sparse changes, we conduct cross-sampling experiments that selectively swap token choices between the base and RL models with varying intervention budgets. We show that inserting only a small fraction of RL-sampled tokens into base generations progressively recovers RL performance gains, while injecting a similarly small number of base token choices into otherwise RL-generated sequences collapses performance to base levels, isolating a small set of token-level decisions directly responsible for RLVR's performance gains. Finally, we explore divergence-weighted variants of the advantage signal as a diagnostic intervention, finding that they can yield improvements over baselines. Together, our results shed light on the distributional changes induced by RLVR and provide a fine-grained, token-level lens for understanding RLVR fine-tuning as a targeted refinement process.

On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the \textbf{magnitude} of these updates, largely overlooking their \textbf{direction}. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference $Δ\log p$ between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that $Δ\log p$ more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a \textit{test-time extrapolation} method that amplifies the policy along the learned $Δ\log p$ direction to improve reasoning accuracy without further training; (2) a \textit{training-time reweighting} method that focuses learning on low-probability (corresponding to higher $Δ\log p$) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

SoundMind: RL-Incentivized Logic Reasoning for Audio-Language Models

While large language models have shown reasoning capabilities, their application to the audio modality, particularly in large audio-language models (ALMs), remains significantly underdeveloped. Addressing this gap requires a systematic approach, involving a capable base model, high-quality reasoning-oriented audio data, and effective training algorithms. In this study, we present a comprehensive solution: we introduce the Audio Logical Reasoning (ALR) dataset, consisting of 6,446 text-audio annotated samples specifically designed for complex reasoning tasks. Building on this resource, we propose SoundMind, a rule-based reinforcement learning (RL) algorithm tailored to endow ALMs with deep bimodal reasoning abilities. By training Qwen2.5-Omni-7B on the ALR dataset using SoundMind, our approach achieves state-of-the-art performance in audio logical reasoning. This work highlights the impact of combining high-quality, reasoning-focused datasets with specialized RL techniques, advancing the frontier of auditory intelligence in language models. Our code and the proposed dataset are available at https://github.com/xid32/SoundMind.

KCES: Training-Free Defense for Robust Graph Neural Networks via Kernel Complexity

Graph Neural Networks (GNNs) have achieved impressive success across a wide range of graph-based tasks, yet they remain highly vulnerable to small, imperceptible perturbations and adversarial attacks. Although numerous defense methods have been proposed to address these vulnerabilities, many rely on heuristic metrics, overfit to specific attack patterns, and suffer from high computational complexity. In this paper, we propose Kernel Complexity-Based Edge Sanitization (KCES), a training-free, model-agnostic defense framework. KCES leverages Graph Kernel Complexity (GKC), a novel metric derived from the graph's Gram matrix that characterizes GNN generalization via its test error bound. Building on GKC, we define a KC score for each edge, measuring the change in GKC when the edge is removed. Edges with high KC scores, typically introduced by adversarial perturbations, are pruned to mitigate their harmful effects, thereby enhancing GNNs' robustness. KCES can also be seamlessly integrated with existing defense strategies as a plug-and-play module without requiring training. Theoretical analysis and extensive experiments demonstrate that KCES consistently enhances GNN robustness, outperforms state-of-the-art baselines, and amplifies the effectiveness of existing defenses, offering a principled and efficient solution for securing GNNs.

Music's Multimodal Complexity in AVQA: Why We Need More than General Multimodal LLMs

While recent Multimodal Large Language Models exhibit impressive capabilities for general multimodal tasks, specialized domains like music necessitate tailored approaches. Music Audio-Visual Question Answering (Music AVQA) particularly underscores this, presenting unique challenges with its continuous, densely layered audio-visual content, intricate temporal dynamics, and the critical need for domain-specific knowledge. Through a systematic analysis of Music AVQA datasets and methods, this position paper identifies that specialized input processing, architectures incorporating dedicated spatial-temporal designs, and music-specific modeling strategies are critical for success in this domain. Our study provides valuable insights for researchers by highlighting effective design patterns empirically linked to strong performance, proposing concrete future directions for incorporating musical priors, and aiming to establish a robust foundation for advancing multimodal musical understanding. This work is intended to inspire broader attention and further research, supported by a continuously updated anonymous GitHub repository of relevant papers: https://github.com/xid32/Survey4MusicAVQA.

Judging with Many Minds: Do More Perspectives Mean Less Prejudice?

LLM-as-Judge has emerged as a scalable alternative to human evaluation, enabling large language models (LLMs) to provide reward signals in trainings. While recent work has explored multi-agent extensions such as multi-agent debate and meta-judging to enhance evaluation quality, the question of how intrinsic biases manifest in these settings remains underexplored. In this study, we conduct a systematic analysis of four diverse bias types: position bias, verbosity bias, chain-of-thought bias, and bandwagon bias. We evaluate these biases across two widely adopted multi-agent LLM-as-Judge frameworks: Multi-Agent-Debate and LLM-as-Meta-Judge. Our results show that debate framework amplifies biases sharply after the initial debate, and this increased bias is sustained in subsequent rounds, while meta-judge approaches exhibit greater resistance. We further investigate the incorporation of PINE, a leading single-agent debiasing method, as a bias-free agent within these systems. The results reveal that this bias-free agent effectively reduces biases in debate settings but provides less benefit in meta-judge scenarios. Our work provides a comprehensive study of bias behavior in multi-agent LLM-as-Judge systems and highlights the need for targeted bias mitigation strategies in collaborative evaluation settings.

Achieving Domain-Independent Certified Robustness via Knowledge Continuity

We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language, respectively). Most existing approaches that seek to certify robustness, especially Lipschitz continuity, lie within the continuous domain with norm and distribution-dependent guarantees. In contrast, our proposed definition yields certification guarantees that depend only on the loss function and the intermediate learned metric spaces of the neural network. These bounds are independent of domain modality, norms, and distribution. We further demonstrate that the expressiveness of a model class is not at odds with its knowledge continuity. This implies that achieving robustness by maximizing knowledge continuity should not theoretically hinder inferential performance. Finally, to complement our theoretical results, we present several applications of knowledge continuity such as regularization, a certification algorithm, and show that knowledge continuity can be used to localize vulnerable components of a neural network.

This Looks Like Those: Illuminating Prototypical Concepts Using Multiple Visualizations

We present ProtoConcepts, a method for interpretable image classification combining deep learning and case-based reasoning using prototypical parts. Existing work in prototype-based image classification uses a ``this looks like that'' reasoning process, which dissects a test image by finding prototypical parts and combining evidence from these prototypes to make a final classification. However, all of the existing prototypical part-based image classifiers provide only one-to-one comparisons, where a single training image patch serves as a prototype to compare with a part of our test image. With these single-image comparisons, it can often be difficult to identify the underlying concept being compared (e.g., ``is it comparing the color or the shape?''). Our proposed method modifies the architecture of prototype-based networks to instead learn prototypical concepts which are visualized using multiple image patches. Having multiple visualizations of the same prototype allows us to more easily identify the concept captured by that prototype (e.g., ``the test image and the related training patches are all the same shade of blue''), and allows our model to create richer, more interpretable visual explanations. Our experiments show that our ``this looks like those'' reasoning process can be applied as a modification to a wide range of existing prototypical image classification networks while achieving comparable accuracy on benchmark datasets.