arXiv subjects

Ruoran Xu

Publications and source records attributed to Ruoran Xu.

9 recordsLinked to original sources

arXiv2026

OC-OPD: Observation-coordinated Supervision for On-Policy Distillation

Reverse and forward Kullback--Leibler (KL) divergences provide complementary supervision in on-policy distillation: reverse KL refines the student's active token rankings, and forward KL allocates mass to teacher-supported candidates. At student-generated prefixes, we form a four-observation matrix by treating the student and teacher as both candidate sources and evaluators. The diagonal self-observations measure uncertainty, while source-centered cross-observations recover the two KL objectives. We establish an exact identity equating the Fisher inverse-metric coupling of their logit gradients with the sum of these contrasts, yielding a common local descent direction for distinct positive distributions. Observation-coordinated on-policy distillation (OC-OPD) uses observations to set preferences, closed-form bargaining to coordinate gradients, and distributional discrepancy to scale the update. Across three heterogeneous student settings (non-thinking generation, thinking generation, and base-model initialization), OC-OPD achieves strong gains in mathematical reasoning and transfers effectively to out-of-distribution scientific question answering and code generation. Our code is publicly available at: https://github.com/RuoranXu/OC-OPD.

cs.LG↗

arXiv2026

Better Answers, Weaker Evidence Control: Evidence Bypass in On-Policy Distillation

On-policy distillation (OPD) can improve answer accuracy while weakening responsiveness to supporting evidence. We investigate this separation in scientific-document question answering through matched document interventions that change the supported answer while preserving the question and unrelated context. We identify evidence bypass: a student retains an originally correct answer after the document changes to support a different one. On QASPER with a Qwen3-4B student, standard OPD raises original-document accuracy by 3.4 percentage points, lowers counterfactual accuracy by 5.3 points, and increases bypass by 15.7 points; the same directional pattern appears on PeerQA. Controlled perturbations localize the shift to answer-critical evidence, and bypass grows with the student's pre-distillation closed-book preference for the original answer. A factorized study of teacher targets, privileged information, divergence, and supervision density finds that explicitly supplying the teacher with annotated answer-critical spans yields the largest joint improvement in evidence response and claim support. These findings motivate Evidence-Paired OPD (EP-OPD), which combines on-policy supervision on matched documents supporting different answers to the same question with an answer-level margin that favors each document's supported answer over its paired alternative. Across both datasets and two student sizes, EP-OPD recovers 54-66% of standard OPD's counterfactual-accuracy loss while preserving 80-85% of its original-document accuracy gain. Our results establish evidence responsiveness as a distinct training and evaluation target alongside answer accuracy. Our code is publicly available at: https://github.com/RuoranXu/EP-OPD.

cs.CL↗

arXiv2026

PhysElite: How Far Are LLMs from Solving Olympiad-Level Physics Problems?

Understanding how (multimodal) large language models perform on physics problems requires benchmarks that reflect the difficulty and breadth of expert-level physical reasoning. Existing physics benchmarks remain limited in the following two important ways: (1) short of high-difficulty datasets, and (2) lack of comprehensive coverage of visual forms, knowledge points, and step-by-step solution processes. As a result, model performance on current datasets may not be fully representative of their ability to solve complex physics problems. To address these issues, we present PhysElite, a large-scale bilingual multimodal benchmark for Olympiad-level physics reasoning. PhysElite contains 11,586 Olympiad-tier problems. For each problem, we provide corresponding visual diagrams, step-by-step bilingual Chinese-English solution derivations, and the final answer. We benchmark 18 open-source and closed-source MLLMs, and find that even the strongest model reaches only 33.7% answer accuracy. We additionally conduct step-level process evaluation to diagnose where models fail in the reasoning chain. Our datasets are released at https://huggingface.co/datasets/physelite/PhysElite.

cs.AI↗

arXiv2026

Symbolic Search Is Not Exhausted: Persistent Proof-Space Exploration in Lean4

Formal theorem proving increasingly combines learned semantic guidance with verified symbolic execution. The quality of the symbolic search substrate therefore determines how much useful mathematical structure can be accumulated, reused, and exposed under a finite inference budget. We introduce ViaLean, a Lean4 prover that organizes symbolic reasoning as bounded exploration of a persistent proof-state graph. Its search preserves coverage across complementary reasoning modes, merges semantically equivalent goals, retains verified intermediate structure, and observes short symbolic futures before committing to a transition. On the complete miniF2F test split, the model-free configuration solves 122/244 problems (50.0% pass@1). Historical and recent symbolic reference points range from Lean's earlier tidy search to modern grind and SMT-backed verification, showing that proof-space organization remains a substantial source of capability. The same persistent state also provides a natural interface for neural--symbolic agents: neural reasoning can operate over verified regions and intermediate objects while Lean continuously expands and validates the local proof space.

cs.LO↗

arXiv2026

Dense Neuro-Symbolic Reasoning in a Unified Geometry State

Geometry reasoning is naturally stateful: solving a problem repeatedly alternates between structural proposals and exact deductions. We formulate this process as dense neural-symbolic coupling, in which neural guidance and symbolic execution share a typed state and communicate through executable actions at every search step. Neural proposals contribute theorem instances, constructions, and algebraic bridges; the symbolic runtime applies registered rules, propagates exact constraints, and records provenance. A nested controller allocates computation first between neural and symbolic proposal sources and then among admitted actions. We instantiate the framework in OmniGeo, a single solver for plane, analytic, and solid geometry. With Claude Sonnet 4.6, OmniGeo reaches 94.2%, 88.5%, and 89.8% on FormalGeo7K, Conic10K, and SolidFGeo, respectively (90.8% macro average), and solves 21/30 IMO-AG-30 problems.

cs.AI↗

arXiv2026

Blog: Survey of Optimizers

Neural-network optimization in 2025-2026 is no longer well described as a succession of new Adam variants. The design space has expanded from coordinates to matrices and layers, from fixed training horizons to policies over time, and from mathematical update rules to state representations that must survive sharding and low-precision computation. This survey organizes recent optimizers and training optimization methods along four largely independent axes: temporal estimation, update geometry, horizon management, and representation and systems. It connects the spectral normalization of Muon, the historical matrix statistics of Shampoo and SOAP, adaptive and hybrid matrix methods, memory-efficient optimizers, schedule-free training, small-batch corrections, and quantized optimizer states. The central empirical conclusion is deliberately non-triumphal: matrix-aware methods represent a genuine advance, but there is no context-independent replacement for AdamW. Rankings change with model scale, data-to-parameter ratio, batch size, schedule, parameter partition, tuning budget, and whether the target metric is tokens, FLOPs, wall-clock time, or memory. The practical consequence is a compositional view of optimizer design and a stricter protocol for evaluating optimizer claims.

cs.LG↗

arXiv2026

FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation

Math reasoning has achieved significant progress with the rapid advancement of Multimodal Large Language Models (MLLMs), however analytic geometry remains largely underexplored, primarily due to the scarcity of annotated samples. Existing diagram generation approaches struggle with analytic geometry: template methods cannot handle constraint-driven layouts, and generative models lack the geometric precision to render annotated conic curves correctly. We present FormalAnalyticGeo, a scalable framework for fully automatic generation of multimodal analytic geometry problems. Leveraging the rigor of formal languages, we design the framework around CDL (Condition Description Language), a formal intermediate representation that bridges free-form problem text with precise diagram rendering via a Signed Distance Field (SDF) engine. The framework employs four specialized LLM components in sequence: a Generator that produces diverse analytic geometry problems, a Formalizer that converts each problem into CDL for SDF-based rendering, a Measurer that extracts ground-truth answers through vision-based measurement on the rendered diagrams, and a Quality Verifier that checks outputs at three stages. Structured feedback from the Quality Verifier drives automatic retry, forming a closed loop that eliminates any need for human annotation. Applying FormalAnalyticGeo at scale yields AnalyticGeo7K, a dataset of over 7K verified multimodal problems, each with aligned text, diagram, formal annotation, and ground truth.Experiments show that the generated problems achieve a median ground-truth relative error of 0.70\%, with 82.3\% of answers falling within 5\% of the exact symbolic solution. Our framework and dataset will be publicly released.

cs.AI↗

arXiv2026

Singularity-aware Optimization via Randomized Geometric Probing: Towards Stable Non-smooth Optimization

Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators. In such non-smooth regimes, adaptive optimizers such as Adam suffer from gradient chattering, violent oscillations caused by conflicting signals within the Clarke subdifferential, leading to poor convergence and suboptimal generalization. To address this, we introduce Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes training by dynamically modulating step sizes based on local geometric instability. Our key contribution is the Local Geometric Instability (LGI) metric, a computationally efficient estimator of the Clarke subdifferential diameter derived from the variance of randomized directional derivatives. S-Adam incorporates an adaptive damping mechanism exp(-$λ$$ρ$) that decelerates updates in high-instability regions while preserving fast convergence in smooth basins. We provide a rigorous convergence analysis using differential inclusions, proving that S-Adam converges almost surely to ($δ$,$ε$)-Clarke stationary points at the optimal O(1/$\sqrt(T)$) rate. Empirical evaluations on Quantization-Aware Training (QAT) and high-noise small-batch learning demonstrate that S-Adam consistently outperforms AdamW and Prox-SGD, achieving accuracy gains of up to +4.54% on CIFAR-100 and +4.27% on TinyImageNet while effectively mitigating gradient oscillations.

cs.LG↗

arXiv2026

Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning

Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial diagrams and complex reasoning. To bridge this gap, we introduce Hilbert-Geo, the first unified formal language framework for solid geometry, including an extensive predicate library and a dedicated theorem bank. Based on this framework, we propose a Parse2Reason method containing two steps of first parsing then reasoning. In the parsing step, we utilize conditional description language (CDL), a formalized language composed of predicates specifically designed to construct geometric conditions, to represent both problem description (natural text) and solid diagrams (visual image). In the reasoning step, we leverage those formal CDL and the theorem bank to perform relational inference and algebraic computation, generating strictly correct, verifiable, and human-readable reasoning processes. Notably, our proposed Hilbert-Geo is also applicable to plane geometry. To advance geometric reasoning, we curate two expert-annotated dataset SolidFGeo2k and PlaneFGeo3k, which are furnished with geometric formal language annotations, solutions and answers. Extensive experiments show that our proposed method achieves the state-of-the-art (SOTA) performance 77.3% in SolidFGeo2k and 84.1% in MathVerse-Solid (one small subset in MathVerse dedicated to solid geometry), substantially outperforming leading MLLMs, such as Gemini-2.5-pro (54.2% on SolidFGeo2k) and GPT-5 (62.9% on MathVerse-Solid). In addition, our method achieves the SOTA accuracy 80.2% in PlaneFGeo3k, demonstrating the generality of the Hilbert-Geo in geometric reasoning. Our code and datasets are released at https://github.com/PremiLab-Math/Hilbert-Geo.

cs.CV↗