arXiv subjects

Wotao Yin

Publications and source records attributed to Wotao Yin.

At least 19 recordsLinked to original sources

arXiv2026

Log-Driven Semantic Tuning for Mixed Integer Programming Solvers

Automated configuration of mixed-integer programming (MIP) solvers largely relies on black-box optimization. Each trial requires an expensive solver run and provides only a scalar outcome, so tuning can require many such evaluations. Human experts take a different approach. They inspect solver logs, identify performance bottlenecks, and adjust the parameters that address them. We propose Log-Driven Semantic Tuning (LDST), which uses a large language model (LLM) to automate this process. LDST extracts compact diagnostics from solver logs, uses the LLM to propose sparse edits to the current best configuration based on parameter meanings and observed solver behavior, and validates each proposal before execution. A regime-adaptive objective selects the tuning signal according to the information available from a time-limited run, while a log-based completion signal estimates completion time from branch-and-bound tree growth recorded in ordinary solver logs, so that solved and unsolved runs share one time scale. On 215 instances from five benchmark sets, LDST reduces geometric-mean loss by 43.9% on easy instances and 16.7% on intermediate instances relative to the best of SMAC3, RBFOpt, and random search. In both regimes, LDST achieves a lower loss with 10 proposals than any of these baselines achieves with 50. Configurations that LDST tunes on a single instance also transfer better than baseline configurations to unseen instances of the same family.

math.OC↗

arXiv2026

Diagnosing the Reference Gap: What Visual Scaffolds Can and Cannot Fix in Multimodal Reasoning

Multimodal large language models can recognize visual content yet struggle to reason reliably over it across multiple steps. In counting, a model may see all objects but lose track of which ones it has counted. We argue that such failures, commonly attributed to perception, reveal a reference gap: the failure to bind language to the relevant visual entities, regions, or locations. Motivated by the theory of visual routines, we test whether external references such as numbering can narrow this gap. We introduce ReGap-Bench, a paired benchmark of five visual reasoning tasks in which the scene, question, and answer are fixed and only the reference varies. Results show that task-matched references improve accuracy by up to 25\%, while mismatched references provide little benefit or even hurt performance. These findings identify the reference gap as a bottleneck distinct from visual perception and show that constructing task-appropriate visual references can serve as a training-free visual skill for improving multimodal reasoning.

cs.CV↗

arXiv2026

Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization

Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-L fine-tuning on CIFAR-100.

cs.LG↗

arXiv2026

ScholarStack: Layered Research Asset Orchestration and Cross-Task Reuse for Scientific Agents

Scientific agents support a range of literature-based research tasks, such as retrieval, question answering, evidence-grounded generation, and claim assessment. Most existing systems, however, are organized around individual tasks: the same papers are repeatedly retrieved, segmented, and interpreted, and the understanding built in one task is difficult to reuse in the next. We present ScholarStack, a layered research asset framework that compiles a paper collection into reusable, versioned, and provenance-preserving assets at three complementary levels: source-grounded paper-level statements, domain-level organization, and evidence-grounded cross-paper syntheses. A common access interface returns task-specific views at the evidence granularity each task requires, preserving study conditions, source traceability, and verification status. We instantiate the framework on four task families spanning ten task settings, comparing agents that use the compiled assets with task-specific baselines under matched base models. Quality gains concentrate on tasks that require cross-paper evidence, such as multi-paper question answering and literature review generation, and query-time token cost falls on every task where it is measured, with assets compiled once and reused across tasks. These results suggest that layered research assets can serve as shared infrastructure for scientific agents, shifting literature-based assistance from isolated document processing toward cumulative, evidence-grounded workflows.

cs.AI↗

arXiv2026

Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

AI agents are becoming increasingly capable of generating scientific code, but generating code is not the same as improving the algorithms behind it. For numerical solvers, execution feedback can expose poor performance, but rarely reveals its underlying cause and how to address it. We introduce Auto-Diagnosis and Skill Discovery (ADSD), a framework that links numerical diagnosis to reusable solver self-improvement. ADSD follows a diagnosis-first paradigm that first explains why a solver performs poorly, then uses this diagnosis to guide the discovery of appropriate numerical methods. The resulting knowledge is packaged into reusable solver skills, turning solver improvement from trial-and-error editing into a structured process of diagnosis, discovery, and implementation. Across four challenging numerical domains--power flow equation, AC optimal power flow control, stiff ordinary differential equations, and heterogeneous diffusion PDEs--ADSD consistently improves solver accuracy, robustness, and efficiency. On GOC-500 power flow, for example, ADSD reduces mean solver error by nearly $71\times$, with improvements further transferring to unseen grid topologies and operating regimes.

cs.AI↗

arXiv2026

A Zeroth-Order Paradigm for LLM Preference Alignment

Direct preference alignment methods are widely used to align large language models (LLMs) with human preferences because of their computational and memory efficiency. However, likelihood displacement motivates alternative ways to extract information from preference pairs with small likelihood margins. In this paper, we propose and analyze Comparison-based Preference Optimization (ComPO), a zeroth-order alignment method based on comparison oracles. ComPO extracts directional information from these pairs without directly optimizing a differentiable preference loss on them. We establish a convergence guarantee for its basic offline scheme under smoothness, gradient sparsity, and compatibility between the oracle and a latent objective. We further introduce online ComPO, which retains the offline comparison mechanism and uses unlabeled policy generations for reverse-KL control relative to a reference policy. Following the coverage perspective of preference fine-tuning, we establish a performance guarantee for a basic constrained scheme under local coverage and in-distribution pairwise reward accuracy. Experiments on Mistral, Llama, Gemma-2, Qwen3, and Gemma-3 models demonstrate improvements over existing direct alignment methods, including length-controlled win rates, with pair-level diagnostics providing evidence consistent with mitigating likelihood displacement.

cs.CL↗

arXiv2026

From Search to Synthesis: Training LLMs as Zero-Shot Workflow Generators

Large language models (LLMs) excel across a wide range of tasks, yet their instance-specific solutions often lack the structural consistency needed for reliable deployment. Workflows that encode recurring algorithmic patterns at the task level provide a principled framework, offering robustness across instance variations, interpretable traces for debugging, and reusability across problem instances. However, manually designing such workflows requires significant expertise and effort, limiting their broader application. While automatic workflow generation could address this bottleneck, existing methods either produce instance-specific solutions without learning task-level patterns, or cannot generalize beyond their training configurations. We present MetaFlow, which casts workflow generation as a meta-learning problem: given a task and an operator set, the model learns to compose solution strategies. MetaFlow trains in two stages: supervised fine-tuning on synthetic workflow data, followed by reinforcement learning with verifiable rewards (RLVR) that uses execution feedback across problem instances in the task to improve end-to-end success. The resulting model produces effective workflows for trained tasks and exhibits strong generalization to untrained tasks and novel operator sets. Across benchmarks in question answering, code generation, and mathematical reasoning, MetaFlow achieves performance comparable to state-of-the-art baselines on in-domain tasks with single inference, while demonstrating remarkable zero-shot generalization capabilities on out-of-domain tasks and operator sets.

cs.LG↗

arXiv2026

Restarted Reflected Halpern Acceleration for Augmented Primal-Dual Methods

We study linearly constrained composite convex optimization with a smooth term and a proximable nonsmooth term. We develop a unified augmented primal-dual framework with primal-dual hybrid gradient-type and augmented Chambolle-Pock-type metric choices, including a fully augmented Chambolle-Pock-type family that retains the augmented quadratic term. The exact scheme admits a degenerate proximal-point form; the linearized scheme admits a preconditioned forward-backward form. These representations allow reflected Halpern acceleration to be analyzed directly in primal-dual variables. For the shadow iterates, we prove convergence to Karush-Kuhn-Tucker (KKT) points and nonergodic O(1/k) bounds for the KKT residual and objective gap, with a scalar worst-case example. We show that finite identification belongs to the shadow sequence rather than to the anchored Halpern state. After identification, an affine-face model yields an exact reduced residual identity and a local-sharpness criterion. Finally, we prove linear convergence of restart anchors under fixed-point sharpness on the visited restart set, with local or tail convergence when sharpness follows from local error bounds. Experiments on linear and convex quadratic programs illustrate augmentation and linearization.

math.OC↗

arXiv2026

Expressive Power of Implicit Models: Rich Equilibria and Test-Time Scaling

Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing memory needs for the same level of performance compared to explicit models. While it is empirically known that these compact models can often match or even exceed the accuracy of larger explicit networks by allocating more test-time compute, the underlying mechanism remains poorly understood. We study this gap through a nonparametric analysis of expressive power. We provide a strict mathematical characterization, showing that a simple and regular implicit operator can, through iteration, progressively express more complex mappings. We prove that for a broad class of implicit models, this process lets the model's expressive power scale with test-time compute, ultimately matching a much richer function class. The theory is validated across four domains: image reconstruction, scientific computing, operations research, and LLM reasoning, demonstrating that as test-time iterations increase, the complexity of the learned mapping rises, while the solution quality simultaneously improves and stabilizes.

cs.LG↗

arXiv2026

Automating Reformulation for Parallel ADMM

Many real-world optimization models contain exploitable sparsity and block structure, but this structure is often obscured in algebraic form, limiting the effectiveness of modern parallel algorithms. We propose an automatic pipeline that converts a generic multiblock problem into a canonical two-block formulation suitable for parallel Alternating Direction Method of Multipliers (ADMM). The method constructs a coupling graph, applies an edge-subdivision-based bipartization to obtain a bipartite representation, and produces an ADMM-ready decomposition with independent subproblems. Fast graph-traversal heuristics, a new mixed-integer linear program (MILP), and a learning-based graph neural network (GNN) surrogate model are developed to guide edge subdivision. Numerical experiments demonstrate that the resulting reformulations yield strong parallel ADMM performance. The entire pipeline is implemented in the open-source Julia package PDMO.jl.

math.OC↗

arXiv2026

DeepVision-103K: A Visually Diverse, Broad-Coverage, and Verifiable Mathematical Dataset for Multimodal Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) has been shown effective in enhancing the visual reflection and reasoning capabilities of Large Multimodal Models (LMMs). However, existing datasets are predominantly derived from either small-scale manual construction or recombination of prior resources, which limits data diversity and coverage, thereby constraining further gains in model performance. To this end, we introduce \textbf{DeepVision-103K}, a comprehensive dataset for RLVR training that covers diverse K12 mathematical topics, extensive knowledge points, and rich visual elements. Models trained on DeepVision achieve strong performance on multimodal mathematical benchmarks, and generalize effectively to general multimodal reasoning tasks. Further analysis reveals enhanced visual perception, reflection and reasoning capabilities in trained models, validating DeepVision's effectiveness for advancing multimodal reasoning. Data: \href{https://huggingface.co/datasets/skylenage/DeepVision-103K}{this url}.

cs.LG↗

arXiv2026

ALiA: Adaptive Linearized ADMM

We propose ALiA, a novel adaptive variant of the alternating direction method of multipliers (ADMM). Specifically, ALiA is a variant of function-linearized proximal ADMM (FLiP ADMM), which generalizes the classical ADMM by leveraging the differentiable structure of the objective function, making it highly versatile. Notably, ALiA features an adaptive stepsize selection scheme that eliminates the need for backtracking linesearch. Motivated by recent advances in adaptive gradient and proximal methods, we establish point convergence of ALiA for convex and differentiable objectives. Furthermore, by introducing negligible computational overhead, we develop an alternative stepsize selection scheme for ALiA that improves the convergence speed both theoretically and empirically. Extensive numerical experiments on practical datasets confirm the accelerated performance of ALiA compared to standard FLiP ADMM. Additionally, we demonstrate that ALiA either outperforms or matches the practical performance of existing adaptive methods across problem classes where it is applicable.

math.OC↗

arXiv2026

Deeply Learned Robust Matrix Completion for Large-scale Low-rank Data Recovery

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fix-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.

cs.LG↗

arXiv2026

Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward

This paper examines the exploration-exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: spurious rewards, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and entropy minimization, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.

cs.LG↗

arXiv2026

Subsampled Ensemble Can Improve Generalization Tail Exponentially

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on ensembling. By selecting the most frequently generated model from the base learner when repeatedly applied to subsamples, we can attain exponentially decaying tails for the excess risk, even if the base learner suffers from slow (i.e., polynomial) decay rates. This tail enhancement power of ensembling applies to base learners that have reasonable predictive power to begin with and is stronger than variance reduction in the sense of exhibiting rate improvement. We demonstrate how our ensemble methods can substantially improve out-of-sample performances in a range of numerical examples involving heavy-tailed data or intrinsically slow rates.

math.OC↗

arXiv2025

ComPO: Preference Alignment via Comparison Oracles

Direct alignment methods are increasingly used for aligning large language models (LLMs) with human preferences. However, these methods suffer from the issues of verbosity and likelihood displacement, which can be driven by the noisy preference pairs that induce similar likelihood for preferred and dispreferred responses. The contributions of this paper are two-fold. First, we propose a new preference alignment method based on zeroth-order, comparison-based optimization via comparison oracles and provide convergence guarantees for its basic scheme. Second, we improve our method using some heuristics and conduct the experiments to demonstrate the flexibility and compatibility of practical scheme in improving the performance of LLMs using noisy preference pairs. Evaluations are conducted across multiple base and instruction-tuned models (Mistral-7B, Llama-3-8B and Gemma-2-9B) with benchmarks (AlpacaEval 2, MT-Bench and Arena-Hard). Experimental results show the effectiveness of our method as an alternative to addressing the limitations of existing direct alignment methods. A highlight of our work is that we evidence the importance of designing specialized methods for preference pairs with distinct likelihood margin, which complements the recent findings in Razin et al (2025).

cs.CL↗

arXiv2025

Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs

Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix decomposition or use the preconditioned conjugate gradient method. For relatively large instances, these methods cannot achieve the real-time requirement unless there is an effective preconditioner. Recently, graph neural networks (GNNs) opened new possibilities for QP. Some promising empirical studies of applying GNNs for QP tasks show that GNNs can capture key characteristics of an optimization instance and provide adaptive guidance accordingly to crucial configurations during the solving process, or directly provide an approximate solution. However, the theoretical understanding of GNNs in this context remains limited. Specifically, it is unclear what GNNs can and cannot achieve for QP tasks in theory. This work addresses this gap in the context of linearly constrained QP tasks. In the continuous setting, we prove that message-passing GNNs can universally represent fundamental properties of convex quadratic programs, including feasibility, optimal objective values, and optimal solutions. In the more challenging mixed-integer setting, while GNNs are not universal approximators, we identify a subclass of QP problems that GNNs can reliably represent.

cs.LG↗

arXiv2025

AdapThink: Adaptive Thinking Preferences for Reasoning Language Model

Reinforcement Learning (RL)-based post-training has significantly advanced the complex reasoning capabilities of language models, fostering sophisticated self-reflection processes. However, this ``slow thinking'' paradigm presents a critical challenge to reasoning efficiency: models may expend excessive computation on simple questions and shift reasoning prematurely for complex ones. Previous mechanisms typically rely on static length budgets or predefined rules, lacking the adaptability for varying question complexities and models' evolving capabilities. To this end, we propose AdapThink, an adaptive post-training framework designed to induce more efficient thinking while maintaining the performance of reasoning language models. Specifically, AdapThink incorporates two key mechanisms: 1) A group-relative reward function that leverages model confidence and response's characteristic to dynamically adjust the preference of reflection-related transition words without resorting to a fixed length preference. 2) A diversity-aware sampling mechanism that balances the training group's solution accuracy with reasoning diversity via an entropy-guided score. Experiments on several mathematical reasoning datasets with DeepSeek-distilled models demonstrate AdapThink's advantages in enabling adaptive reasoning patterns and mitigating the inefficiencies.

cs.LG↗