Fan Xu
Publications
Beyond the Mean: Multi-Moment Policy Optimization for LLM Reasoning
Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader distributional structure largely uncharacterized. We propose \textbf{M}ulti-\textbf{M}oment \textbf{P}olicy \textbf{O}ptimization (MMPO), a novel policy optimization framework that jointly minimizes multiple moments of the failure-probability distribution. MMPO admits a direct operational interpretation as minimizing the expected truncated time required to obtain the first successful response. Beyond MMPO, we further develop a general moment-transformation framework that systematically induces different moment profiles and provides a unified view of a broader family of policy optimization objectives. Experiments across five mathematical reasoning benchmarks and models of different scales demonstrate that MMPO consistently outperforms strong baselines. We hope this moment-based perspective offers new insights into the design of policy optimization objectives for LLM reasoning.
DAVET: Denoising-Aware Visual Evidence Trajectory Allocation for Diffusion Vision-Language Models
Diffusion vision-language models (dVLMs) iteratively denoise masked responses while conditioning each denoising step on visual evidence, making visual conditioning a substantial recurring inference cost. Unlike autoregressive decoding, diffusion generation repeatedly revisits the entire response as uncertainty evolves. Our analysis reveals that visual evidence demand is strongly step-dependent, motivating adaptive allocation across denoising steps. Existing inference acceleration methods operate through decoding-side strategies or visual token compression via pruning and merging, but do not explicitly treat visual evidence as a resource whose demand evolves across the diffusion process. Therefore, we present Denoising-Aware Visual Evidence Trajectory Allocation (DAVET), a training-free framework that allocates visual evidence according to the evolving generation state. Starting from a phase-conditioned evidence trajectory, the proposed allocation policy uses operation demand to set an evidence reserve whose allocation at each denoising step is modulated by trajectory risk. DAVET realizes the resulting budgets through a hierarchy of evidence views constructed from a single visual encoding, separating when and how much evidence is needed from how the evidence views are constructed. Evaluated on two representative dVLMs, LLaDA-V and LaViDa, across multiple visual-understanding benchmarks, DAVET achieves an average speedup of 1.55$\times$ with an average relative performance drop of 1.86\%, showing that denoising-aware visual evidence allocation can reduce visual conditioning cost while largely preserving generation quality.
UPAIR: Diagnosing Reasoning States via Uncertainty-Progress Alignment for Selective Intervention
While test-time scaling improves the problem-solving ability of large reasoning models (LRMs) through additional inference-time computation, it can also exacerbate overthinking and underthinking, which we formulate as reasoning state--action mismatch. Resolving this mismatch requires reliable reasoning state diagnosis, yet single-signal monitors provide ambiguous evidence, while steering-based controllers often rely on outcome-labeled supervision or model-specific calibration. We introduce the Uncertainty--Progress Alignment Hypothesis, which posits that the relative transition timing of proxy answer uncertainty and latent reasoning progress distinguishes healthy, stagnant, and ready states that warrant different subsequent actions. Building on this insight, we propose UPAIR, a training-free framework that couples lightweight uncertainty monitoring with event-triggered joint diagnosis and maps the resulting state to native continuation, selective strategy switching, or verification-guided stopping. Across three LRMs and five cross-domain benchmarks, the stagnation diagnosis detects 64.3% of natural errors while flagging only 5.4% of correct samples, revealing a dynamic reasoning regularity shared across models and tasks. End to end, UPAIR improves accuracy by up to 16.67 percentage points and reduces generated tokens by up to 29.64%, demonstrating the effectiveness of its integrated diagnosis and intervention, while online diagnosis costs less than 1% of natural-generation time.
Information Gain-based Rollout Policy Optimization: An Adaptive Tree-Structured Rollout Approach for Multi-Turn LLM Agents
Reinforcement learning has become a promising paradigm for improving large language model (LLM) agents on long-horizon search tasks, where the agent must make a sequence of intermediate decisions before receiving a final outcome. However, existing methods still face a key limitation: the rollout budget is often allocated without explicitly assessing the utility of intermediate states. As a result, substantial computation may be spent on low-value states, even though different branches can vary drastically in their informativeness. In this paper, we propose Information Gain-based Rollout Policy Optimization (IGRPO), a policy optimization framework that treats intermediate-state informativeness as the organizing principle of rollout collection. Specifically, IGRPO performs budget-aware tree-structured rollouts by allocating expansion budget according to node-level informativeness, so that more informative branches are expanded more frequently while unpromising branches are progressively suppressed. We further demonstrate that the information gain-based rollout induces an explicit limiting teacher distribution over trajectories, which naturally yields a clear policy optimization target, thereby unifying adaptive tree-structured exploration with principled policy learning under a single framework. Experiments on seven challenging search-augmented QA benchmarks demonstrate that IGRPO consistently outperforms strong baselines under the same rollout budget constraints, validating the effectiveness of leveraging the induced teacher distribution to guide policy optimization for long-horizon search agents.
Breaking Model Lock-in: Cost-Efficient Zero-Shot LLM Routing via a Universal Latent Space
The rapid proliferation of Large Language Models (LLMs) has led to a fragmented and inefficient ecosystem, a state of ``model lock-in'' where seamlessly integrating novel models remains a significant bottleneck. Current routing frameworks require exhaustive, costly retraining, hindering scalability and adaptability. We introduce ZeroRouter, a new paradigm for LLM routing that breaks this lock-in. Our approach is founded on a universal latent space, a model-agnostic representation of query difficulty that fundamentally decouples the characterization of a query from the profiling of a model. This allows for zero-shot onboarding of new models without full-scale retraining. ZeroRouter features a context-aware predictor that maps queries to this universal space and a dual-mode optimizer that balances accuracy, cost, and latency. Our framework consistently outperforms all baselines, delivering higher accuracy at lower cost and latency.