arXiv subjects

Kang Liu

Publications and source records attributed to Kang Liu.

At least 19 recordsLinked to original sources

arXiv2026

Keepace.ai: A Technical Report on a Large Language Model for Sports and Health

Large language models hold promise for delivering safe, scientifically grounded, and personalized exercise guidance at scale, yet the sports-and-health domain still lacks curated training corpora and rigorous evaluation benchmarks. Keepace.ai is a domain-specialized LLM built on Qwen3.5-27B through post-training, currently optimized for Chinese-language exercise guidance across three tasks: workout plan generation, sports-and-health knowledge QA, and personal sports data analysis. In internal rubric-based evaluations designed with domain experts, Keepace.ai outperforms its base model and larger general-purpose baselines, with the most pronounced improvements in exercise safety, boundary compliance, structured output completeness, and scientific accuracy. This report summarizes the current design, data pipeline, safety-first evaluation framework, and evaluation results of Keepace.ai.

cs.CL↗

arXiv2026

SkillPyramid: A Hierarchical Skill Consolidation Framework for Self-Evolving Agents

Recent AI agents can flexibly invoke skills to solve complex tasks, but their long-term improvement is fundamentally constrained by a lack of systematic skill construction, accumulation, and transfer. In particular, without a unified framework for skill consolidation, agents tend to redundantly construct similar capabilities across different tasks, are unable to effectively transform experience into reusable assets, and struggle to generalize task-specific skills to novel scenarios. To address this limitation, we propose SkillPyramid, a skill consolidation framework that reuses existing skill experience for broader task generalization. Operating on a hierarchical skill topology, SkillPyramid further introduces a self-evolution mechanism that enables agents to compose, validate, and incorporate new skills during task execution. Experiments on ALFWorld, WebShop, and ScienceWorld across four backbone models show that SkillPyramid substantially increases the average reward by 38.0% and reduces execution steps by 27.7%. Overall, our method transforms a skill collection from a static resource pool into a dynamic evolution system.

cs.AI↗

arXiv2026

When Retrieval Partially Conflicts with Skills: Understanding Procedural Hallucination in Language Models

Language models increasingly use skills that provide reusable instructions and procedures for task execution. After a relevant skill has been selected, the model may need to apply its governing procedure together with retrieved task context. When the retrieved context is useful but contains cues that violate the skill, the model must retain compatible information while rejecting the conflicting cues. We study failures in which the model adopts such cues and produces a retrieval-supported but skill-invalid answer, which we call procedural hallucination. We introduce SourceClash, a matched benchmark with 1,271 bundles and 6,355 prompts across ten procedural domains. Each bundle fixes the task, skill specification, and answer space while varying the relation between the skill and retrieval. Across nine models, valid-answer rates average 25.7% under conflicting retrieval, compared with 78.2% and 72.8% under two supportive retrieval settings. Mechanistic analysis of open-weight models shows that the answer-preference difference typically reaches its maximum shortly after generation begins. Residual replacement moves the model toward valid answers, while attention decomposition attributes most of the repair to value vectors. Intervention at the identified value pathway also improves final answer validity. These results characterize how partly conflicting retrieval changes skill-guided generation.

cs.AI↗

arXiv2026

AtomSD: Procedural Atom-Guided Self-Distillation for LLM Agents

Large language models (LLMs) possess broad factual knowledge and strong reasoning capabilities, but solving complex tasks also requires procedural knowledge about how to act. Existing approaches often represent procedural knowledge through trajectories or bundled skills, limiting flexible reuse across interaction histories. This paper introduces Procedural Atoms, fine-grained and independently applicable units that represent Intent, When, Do, and Avoid guidance. Building on this representation, we propose AtomSD, an Atom-guided Self-Distillation framework in which the learner continually extracts Procedural Atoms from its own successful trajectories and distills them into the evolving policy through Atom-conditioned supervision and task-reward optimization. Comprehensive experiments show that AtomSD consistently outperforms strong reward-based and distillation methods, exceeding the state-of-the-art baseline by up to 9.31 points in average performance. Further analyses demonstrate that the proposed Procedural Atoms provide effective guidance, highlighting the value of atom-level procedural knowledge for policy learning.

cs.CL↗

arXiv2026

RuleTrek: Benchmarking Agentic Rule Reasoning in Complex Scenarios

Large language models (LLMs) increasingly tackle complex real-world tasks in specialized domains. However, identifying and correctly applying domain-specific rules remains challenging when scenario information is distributed across multiple files. Existing rule-reasoning benchmarks typically represent scenarios using only a few factual statements, simplifying the identification and application of relevant rules. To address this gap, this paper introduces \textbf{RuleTrek}, a multi-domain benchmark for agentic rule reasoning in complex scenarios. Its rule-grounded construction pipeline extracts structured rule graphs, generates and incrementally composes rule-specific sub-scenarios while ensuring consistency and solvability. To systematically evaluate agentic rule reasoning in complex scenarios, RuleTrek assesses three capabilities in interactive workspaces: Rule Identification (RI), Rule Deduction (RD), and End-to-End Rule Reasoning (E2E). Experiments on 11 frontier LLMs show that the highest RI and RD scores are only 62.47\% and 60.43\%, respectively, while E2E scores range from 26.97\% to 55.29\%. These results demonstrate that current LLM agents face substantial challenges in rule reasoning over complex scenarios. We make our code and dataset publicly available at \href{https://github.com/yuan247/RuleTrek}{RuleTrek}.

cs.AI↗

arXiv2026

Learning from Hetero Density for Cryo-EM Protein Reconstruction

Reconstructing protein structures from cryo-electron microscopy (cryo-EM) maps is essential for understanding macromolecular assemblies. Although learning-based methods have improved protein reconstruction, information from hetero components remains underused. Our analysis finds both false predictions and reference protein sites near hetero components; filtering nearby candidates can improve or impair chain construction. We introduce CryoCue, a framework that uses hetero information to guide protein reconstruction. An anchor-supervised detector learns hetero representations across five component classes. Multiscale hetero features guide backbone localization, while predicted hetero candidates condition structure refinement through their class, confidence, and frame-relative geometry. Experiments show that CryoCue improves backbone localization near hetero components and achieves more accurate protein structure reconstruction.

cs.LG↗

arXiv2026

A PDE Perspective on Generative Diffusion Models

Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mathematical foundations remain only partially understood, particularly regarding the stability and consistency of the stochastic and partial differential equations underlying their dynamics. In this work, we develop a partial differential equation (PDE) framework for score-based diffusion processes associated with the heat flow of a compactly supported data measure. After establishing weak well-posedness on positive-time intervals, we derive a sharp one-sided divergence bound for the score and use it to obtain sharp uniform $L^p$-stability estimates for the generative Fokker--Planck equation. This bound is the Euclidean form of the Li--Yau differential inequality. Through entropy stability methods, we prove that the generated laws converge in the $2$-Wasserstein distance at rate $\sqrt t$ as $t\to0^+$ to a probability measure supported on the data support. This holds for both deterministic and stochastic generation, for positive terminal densities with finite absolute entropy and second moment. In the deterministic case, almost every trajectory converges to a point of the data support; for empirical data, we further obtain a trajectory-wise square-root rate. These results clarify how exact-score dynamics concentrate on the data support without necessarily recovering the data distribution. An explicitly solvable case identifies the limiting weights and their dependence on Gaussian initialization, while a relative-entropy estimate quantifies the effect of score approximation. Together, these findings connect the stability and concentration mechanisms with score learning and early stopping, providing a mathematical perspective on the balance between imitation fidelity and generative diversity.

math.OC↗

arXiv2026

Sharp Initialization Guarantees for the Heavy-Ball Method

The heavy-ball method can accelerate convergence near the minimizer, but it may also enter persistent oscillations on general strongly convex objectives. How should it be initialized to reliably realize this local advantage? We study the initialization neighborhood in which convergence can be guaranteed using only curvature and regularity bounds. This neighborhood shrinks as momentum approaches one; for Lipschitz-continuous Hessians, its radius is of the same order as damping. Matching upper and lower bounds show that this initialization requirement cannot be relaxed uniformly over the function class. We then derive a startup rule based on the current gradient: a finite gradient-descent warm-up enters the guaranteed region before switching to heavy-ball. With parameters optimal for strongly convex quadratics, the subsequent iterates satisfy an accelerated local asymptotic rate bound. Code is available at https://anonymous.4open.science/r/HeavyBall-811D/.

math.OC↗

arXiv2026

Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning

In federated learning (FL), a central server typically allocates training efforts to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To study this setting, we propose a potential game framework in which each client's payoff is determined by its individual effort and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated by a reward factor. We first establish the existence of Nash equilibria (NEs) and then investigate their uniqueness in a stationary setting. We show that the NEs depend nonlinearly on the reward factor and exhibit a nonsmooth transition at a critical value, where the stationary potential loses strict curvature, leading to nonunique NEs and a jump between low-effort and high-effort branches. Furthermore, we prove the convergence of the best-response algorithm for computing NEs in our FL game. Finally, we apply the clients' rational efforts derived from the NEs to FL training with various datasets and models, thereby validating the effectiveness of the identified critical reward factor. The source code is available at https://github.com/DCN-FAU-AvH/FL-Potential-Game

cs.LG↗

arXiv2026

Dual Certified White-Box Inference for Input Convex Neural Networks

Input convex neural networks (ICNNs) are used to learn convex objectives whose minimizers define decisions, making efficient and reliable optimization central to inference. At nonsmooth inputs, automatic differentiation returns a single derivative rather than the full subdifferential governing optimality and descent. Second-order cone ICNNs (SOC-ICNNs) admit an exact representation as value functions of parametric second-order cone programs, providing a white-box approach to recovering their full subdifferentials from optimal dual multipliers and deriving explicit Hessians on smooth regions. Building on this representation, we develop dual-certified inference (DCI), which combines the network and feasible set geometries to obtain exact stationarity certificates and tangent common descent directions. DCI uses local curvature for Newton acceleration and an exact proximal safeguard. We establish global convergence and, under standard regularity conditions, local quadratic convergence near structurally nondegenerate interior minimizers. Numerical experiments validate the recovered geometry and demonstrate the reliability and efficiency of DCI. Code is avaliable at https://anonymous.4open.science/r/DCI-ICNN-507D/

cs.LG↗

arXiv2026

Information Limits of Low-Rank Approximation Certification

Low-rank approximation can require additional matrix--vector products to verify that its error meets a prescribed tolerance. We characterize this certification cost for both relative matrix error and mean-square output error. For a single approximation matrix candidate, we determine the exact dimension-uniform minimax query constant as the allowed failure probability vanishes. Our main result concerns reusing validation responses as the approximation space expands. For a candidate family constructed independently of validation, one batch supports an entire nested path without increasing the query budget with the number of checks. Across $W$ paths, a concentration bound exploiting shared residual energy yields a $\sqrt{\log(W+1)}$ dependence. A matching lower bound establishes its optimality for fixed interior error targets and sufficiently small separation gaps. Finally, we compare two uniformly valid certificates on the same dispersed-spectrum family. Optimizing the validation budget within each rule family yields costs of orders $N^{1/3}$ and $N^{2/3}$ for validation and construction beyond the true target. Code is available at https://anonymous.4open.science/r/Low-rank-approximation-1275/

math.OC↗

arXiv2026

GAMEGO: Training Game-Dev Agents with Synthetic Trajectories Anchored in Real-World Assets

Recent advances in Large Language Models (LLMs) have demonstrated remarkable capabilities in web front-end execution, with browser-based game generation emerging as a particularly prominent frontier. While previous efforts frequently rely on complex multi-turn workflows or focus on static game evaluation benchmarks, this work targets direct end-to-end real-world game synthesis driven by coding agents. However, generating complex games directly from sparse user queries often forces coding agents to make underspecified assumptions, yielding incomplete mechanics, disconnected gameplay flows, and limited visual aesthetics. To resolve this issue, this paper presents GameGo, a scalable framework that systematically transforms brief game seeds into comprehensive Product Requirements Documents grounded in industry game-development practices. To retain core gameplay constraints without restricting design exploration, GameGo uses task-specific dynamic compression to maximize information density while preserving instruction following. Based on this pipeline, GameGoData is constructed with 55,060 development trajectories across 2D, 2.5D, and 3D games, alongside GameGoBench, a benchmark comprising 124 diverse game queries. Training GameGoCoder on GameGoData yields a model that outperforms matched baselines and is comparable to frontier models across gamedev benchmarks. All code, datasets, and models will be made publicly available.

cs.AI↗

arXiv2026

Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging

Merging pretrained models has emerged as an effective approach for consolidating diverse capabilities into a single unified model. However, prevailing merging methods typically treat each task vector as an indivisible merging unit, overlooking the heterogeneous geometric changes encoded within it. This treatment can induce cross-component coupling: when merging decisions are derived from statistics of the complete task vector, the geometric characteristics of one component may influence how another is selected, weighted, or combined, potentially degrading the quality of the merged model. To address this issue, we propose DiGA, a Disentangled Geometry-Aware model merging framework. Using the pretrained weights as a shared geometric reference, DiGA orthogonally decomposes each task vector into components corresponding to distinct geometric attributes. Rather than merging the task vectors as a whole, DiGA aggregates corresponding components independently within their respective subspaces and subsequently recombines them into a unified update. This component-wise formulation preserves the geometric identity of each component and prevents the characteristics of one component from interfering with the aggregation of another. Furthermore, DiGA can be incorporated into a broad range of existing model merging methods. Extensive experiments across diverse models, tasks, and merging methods demonstrate that DiGA improves merged-model performance and reduces capability degradation. Our repository is on https://github.com/wzj1718/DiGA.

cs.CL↗

arXiv2026

Finite-time boundary collision in planar linear quadratic regulator gradient flows

Policy gradient methods for the linear quadratic regulator optimize feedback gains using a cost over an infinite horizon. When this cost is evaluated at one fixed initial state, it need not diverge near every part of the stability boundary. We study whether the Euclidean gradient flow can reach this boundary in finite optimization time. For controllable planar systems with one input and positive definite quadratic weights, an exact representation of the cost yields a necessary and sufficient condition for the existence of such a collision. The condition reduces to a scalar root calculation and includes the critical case, where a double direction root attracts an open set of stabilizing gains. For a triangular family, the criterion gives an explicit algebraic parameter region, and every trajectory either converges to the Riccati gain or collides with the stability boundary. A sharp threshold for compact cost sublevels provides a convergence certificate. Along every colliding trajectory, the stability margin and the smallest eigenvalue of the accumulated state Gramian vanish linearly, although the Gramian remains positive definite before collision. Numerical experiments examine the dependence on initialization, slow passage near a critical direction, and the effect of adding excitation in a second state direction.

math.OC↗

arXiv2026

WeVisDoc: From Coverage to Capability for Robust End-to-End Document Parsing

Document parsing converts document images into structured content and requires reliable performance across diverse layouts and acquisition conditions. Yet training corpora are biased toward common document types and clean digital pages, while expanding coverage alone does not specify how to address a parser's remaining weaknesses. We present WeVisDoc, a two-stage data-centric framework for robust end-to-end document parsing. Stage I broadens semantic, structural, and appearance coverage through heterogeneous data and structure-preserving degradation synthesis. Stage II uses a held-out probe to measure the Stage I parser's residual errors within fixed visual-structural clusters. These diagnostics guide targeted data construction and reallocation of the target-token budget. WeVisDoc-4B achieves an Overall score of 95.38 on OmniDocBench v1.6 and a mean Overall score of 75.54 across the three PureDocBench tracks, ranking first among the compared end-to-end parsers in all four settings. Compared with Stage I, Stage II improves Overall scores for the 2B and 4B models on both benchmarks, with larger gains on the degraded PureDocBench tracks, including a 4.03-point gain for the 4B model on the Real Degraded track.

cs.CV↗

arXiv2026

Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints

This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constraint observations can produce a biased augmented multiplier signal, shifting the equilibria of the mean dynamics. For componentwise inequalities, we give a necessary and sufficient condition for preserving the Karush-Kuhn-Tucker (KKT) equilibria and construct a convex example with a locally exponentially stable equilibrium that violates complementarity. To address this bias, constraint values are estimated recursively before forming the augmented multiplier signal. For smooth convex conic problems, a joint energy analysis establishes boundedness of the primal, dual, and estimation states, vanishing estimation error, and almost sure convergence of the primal-dual iterates to a single KKT point under global regularity and bounded conditional second moments. The result allows nonunique solutions and multipliers while keeping the number of samples per iteration fixed. Numerical studies illustrate the predicted equilibrium bias and examine convergence with nonunique KKT points and nonlinear constraints.

math.OC↗

arXiv2026

Can one regularizer reproduce posterior means at two noise levels?

Consider Gaussian denoising with a fixed prior and varying noise variance. When the prior has a density, maximum a posteriori estimation uses its negative logarithm as a fixed regularizer; only the weight of the quadratic data term changes with the noise variance. We ask whether a fixed regularizer can also recover the posterior mean. Although a suitable regularizer exists at each variance, we prove that no single regularizer works at two distinct positive variances for any compactly supported prior other than a point mass. This holds even for nonconvex and nonsmooth regularizers. A residual computed from two denoiser evaluations gives positive lower bounds on the uniform approximation error and excess mean squared error of estimators using a common regularizer. Numerical examples illustrate these bounds and the cost of reusing a regularizer across noise levels.

math.ST↗

arXiv2026

SAEScientist-Bench: Can AI Agents Conduct Autonomous SAE Interpretability Research?

While research on recursive self-improvement (RSI) has predominantly automated model training pipelines, reliable autonomous development demands a missing pillar: post-hoc monitoring and auditing to understand what models learn and ensure safe alignment. Mechanistic interpretability tools are essential to bridge this gap, among which Sparse Autoencoders (SAEs) serve as a cornerstone by isolating interpretable features for model inspection and steering. In this paper, we introduce SAEScientist-Bench to evaluate whether AI agents can act as scientists utilizing SAE tools for autonomous mechanistic discovery. Given a target concept, an agent designs contrastive probes and navigates a Gemma Scope dictionary of 131K+ features in Gemma-2-9B-IT to discover the optimal feature, evaluated against curated expert reference features anchored on Neuronpedia across activation rank, concept selectivity on contrastive texts, and causal steering. Across 10 agent configurations and 20 tasks, frontier agents demonstrate genuine discovery capabilities and lead different evaluation dimensions, but remain well behind the expert baseline, approaching expert levels on separating target concepts from contrastive controls while lagging substantially in causal generation steering. Further analysis reveals that although agents can design contrasts to rule out spurious candidates, they frequently misinterpret experimental measurements. These results establish experimental model understanding as a measurable capability for closed-loop autonomous AI R&D. Our code is available at https://github.com/Trae1ounG/SAEScientist.

cs.AI↗