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Yiwen Ding

Publications and source records attributed to Yiwen Ding.

At least 19 recordsLinked to original sources
arXiv2026

Preservation and definability for the fluted fragment

This paper investigates preservation and definability for the equality-free fluted fragment over finite relational signatures. We first prove an equirank homomorphism preservation theorem: every homomorphism-preserved fluted sentence has an existential-positive fluted equivalent of no greater quantifier rank. We then refute Purdy's claimed Los--Tarski preservation theorem for the fluted fragment. Our counterexample is a rank-three sentence over one binary relation that is preserved under extensions but has no existential fluted equivalent. Finally, a two-variable counterexample over a unary base signature shows that weak and ordinary Beth definability both fail. All three results hold over all structures and over finite structures.

math.LO↗
arXiv2025

Hodge filtration and crystalline representations of $\mathrm{GL}_n$

Let $p$ be a prime number, $n$ an integer $\geq 2$ and $\rho$ an $n$-dimensional automorphic $p$-adic Galois representation (for a compact unitary group) such that $r:=\rho\vert_{\mathrm{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)}$ is crystalline. Under a mild assumption on the Frobenius eigenvalues of $D:=D_{\mathrm{cris}}(r)$ and under the usual Taylor-Wiles conditions, we show that the locally analytic representation of $\mathrm{GL}_n(\mathbb{Q}_p)$ associated to $\rho$ in the corresponding Hecke eigenspace of the completed $H^0$ contains an explicit finite length subrepresentation which determines and only depends on $r$. This generalizes previous results of the second author which assumed that the Hodge filtration on $D$ was as generic as possible. Our approach provides a much more explicit link to this Hodge filtration (in all cases), which allows to study the internal structure of this finite length locally analytic subrepresentation.

math.NT↗
arXiv2025

Counteracting Matthew Effect in Self-Improvement of LVLMs through Head-Tail Re-balancing

Self-improvement has emerged as a mainstream paradigm for advancing the reasoning capabilities of large vision-language models (LVLMs), where models explore and learn from successful trajectories iteratively. However, we identify a critical issue during this process: the model excels at generating high-quality trajectories for simple queries (i.e., head data) but struggles with more complex ones (i.e., tail data). This leads to an imbalanced optimization that drives the model to prioritize simple reasoning skills, while hindering its ability to tackle more complex reasoning tasks. Over iterations, this imbalance becomes increasingly pronounced--a dynamic we term the "Matthew effect"--which ultimately hinders further model improvement and leads to performance bottlenecks. To counteract this challenge, we introduce four efficient strategies from two perspectives: distribution-reshaping and trajectory-resampling, to achieve head-tail re-balancing during the exploration-and-learning self-improvement process. Extensive experiments on Qwen2-VL-7B-Instruct and InternVL2.5-4B models across visual reasoning tasks demonstrate that our methods consistently improve visual reasoning capabilities, outperforming vanilla self-improvement by 3.86 points on average.

cs.CV↗
arXiv2025

AgentGym-RL: Training LLM Agents for Long-Horizon Decision Making through Multi-Turn Reinforcement Learning

Developing autonomous LLM agents capable of making a series of intelligent decisions to solve complex, real-world tasks is a fast-evolving frontier. Like human cognitive development, agents are expected to acquire knowledge and skills through exploration and interaction with the environment. Despite advances, the community still lacks a unified, interactive reinforcement learning (RL) framework that can effectively train such agents from scratch -- without relying on supervised fine-tuning (SFT) -- across diverse and realistic environments. To bridge this gap, we introduce AgentGym-RL, a new framework to train LLM agents for multi-turn interactive decision-making through RL. The framework features a modular and decoupled architecture, ensuring high flexibility and extensibility. It encompasses a wide variety of real-world scenarios, and supports mainstream RL algorithms. Furthermore, we propose ScalingInter-RL, a training approach designed for exploration-exploitation balance and stable RL optimization. In early stages, it emphasizes exploitation by restricting the number of interactions, and gradually shifts towards exploration with larger horizons to encourage diverse problem-solving strategies. In this way, the agent develops more diverse behaviors and is less prone to collapse under long horizons. We perform extensive experiments to validate the stability and effectiveness of both the AgentGym-RL framework and the ScalingInter-RL approach. Our agents match or surpass commercial models on 27 tasks across diverse environments. We offer key insights and will open-source the complete AgentGym-RL framework -- including code and datasets -- to empower the research community in developing the next generation of intelligent agents.

cs.LG↗
arXiv2025

Fuzzy Lattice-based Description Logic

Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling.

cs.LO↗
arXiv2024

MANTA: A Large-Scale Multi-View and Visual-Text Anomaly Detection Dataset for Tiny Objects

We present MANTA, a visual-text anomaly detection dataset for tiny objects. The visual component comprises over 137.3K images across 38 object categories spanning five typical domains, of which 8.6K images are labeled as anomalous with pixel-level annotations. Each image is captured from five distinct viewpoints to ensure comprehensive object coverage. The text component consists of two subsets: Declarative Knowledge, including 875 words that describe common anomalies across various domains and specific categories, with detailed explanations for < what, why, how>, including causes and visual characteristics; and Constructivist Learning, providing 2K multiple-choice questions with varying levels of difficulty, each paired with images and corresponded answer explanations. We also propose a baseline for visual-text tasks and conduct extensive benchmarking experiments to evaluate advanced methods across different settings, highlighting the challenges and efficacy of our dataset.

cs.CV↗
arXiv2024

Enhancing LLM Reasoning via Critique Models with Test-Time and Training-Time Supervision

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of $76,321$ responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at \href{https://mathcritique.github.io/}{https://mathcritique.github.io/}.

cs.CL↗
arXiv2024

Mitigating Tail Narrowing in LLM Self-Improvement via Socratic-Guided Sampling

Self-improvement methods enable large language models (LLMs) to generate solutions themselves and iteratively train on filtered, high-quality rationales. This process proves effective and reduces the reliance on human supervision in LLMs' reasoning, but the performance soon plateaus. We delve into the process and find that models tend to over-sample on easy queries and under-sample on queries they have yet to master. As iterations proceed, this imbalance in sampling is exacerbated, leading to a long-tail distribution where solutions to difficult queries almost diminish. This phenomenon limits the performance gain of self-improving models. A straightforward solution is brute-force sampling to balance the distribution, which significantly raises computational costs. In this paper, we introduce Guided Self-Improvement (GSI), a strategy aimed at improving the efficiency of sampling challenging heavy-tailed data. It leverages Socratic-style guidance signals to help LLM reasoning with complex queries, reducing the exploration effort and minimizing computational overhead. Experiments on four models across diverse mathematical tasks show that GSI strikes a balance between performance and efficiency, while also being effective on held-out tasks.

cs.CL↗
arXiv2024

Distill Visual Chart Reasoning Ability from LLMs to MLLMs

Solving complex chart Q&A tasks requires advanced visual reasoning abilities in multimodal large language models (MLLMs), including recognizing key information from visual inputs and conducting reasoning over it. While fine-tuning MLLMs for reasoning is critical, collecting and annotating charts and questions is expensive, hard to scale, and often results in low-quality annotations. To address this, we propose Code-as-Intermediary Translation (CIT), a cost-effective, efficient and scalable data synthesis method for distilling visual reasoning abilities from LLMs to MLLMs. The code serves as an intermediary that translates visual chart representations into textual representations, enabling language models to understand cross-modal information and generate reasoning chains accordingly. In this way, we can employ text-based synthesizing techniques to expand chart-plotting code and generate high-quality Q&A pairs for training models. This produces ReachQA, a dataset containing 3k reasoning-intensive charts and 20k Q&A pairs to enhance both recognition and reasoning abilities of MLLMs. Experiments show that models fine-tuned with ReachQA not only perform well on chart-related tasks but also show performance gains on general reasoning benchmarks. The code and dataset are publicly available at https://github.com/hewei2001/ReachQA.

cs.CL↗
arXiv2024

Defeasible Reasoning on Concepts

In this paper, we take first steps toward developing defeasible reasoning on concepts in KLM framework. We define generalizations of cumulative reasoning system C and cumulative reasoning system with loop CL to conceptual setting. We also generalize cumulative models, cumulative ordered models, and preferential models to conceptual setting and show the soundness and completeness results for these models.

cs.AI↗
arXiv2024

Game semantics for lattice-based modal μ-calculus

In this paper, we generalize modal $μ$-calculus to the non-distributive (lattice-based) modal $μ$-calculus and formalize some scenarios regarding categorization using it. We also provide a game semantics for the developed logic. The proof of adequacy of this game semantics proceeds by generalizing the unfolding games on the power-set algebras to the arbitrary lattices and showing that these games can be used to determine the least and the greatest fixed points of a monotone operator on a lattice. Finally, we define a notion of bisimulations on the polarities and show invariance of non-distributive modal $μ$-calculus under them.

math.LO↗
arXiv2024

$p$-adic Hodge parameters in the crystabelline representations of $\mathrm{GL}_n$

Let $K$ be a finite extension of $\mathbb{Q}_p$, and $\rho$ be an $n$-dimensional (non-critical generic) crystabelline representation of the absolute Galois group of $K$ of regular Hodge-Tate weights. We associate to $\rho$ an explicit locally $\mathbb{Q}_p$-analytic representation $\pi_1(\rho)$ of $\mathrm{GL}_n(K)$, which encodes some $p$-adic Hodge parameters of $\rho$. When $K=\mathbb{Q}_p$, it encodes the full information hence reciprocally determines $\rho$. When $\rho$ is associated to $p$-adic automorphic representations, we show under mild hypotheses that $\pi_1(\rho)$ is a subrepresentation of the $\mathrm{GL}_n(K)$-representation globally associated to $\rho$.

math.NT↗
arXiv2024

AgentGym: Evolving Large Language Model-based Agents across Diverse Environments

Building generalist agents that can handle diverse tasks and evolve themselves across different environments is a long-term goal in the AI community. Large language models (LLMs) are considered a promising foundation to build such agents due to their generalized capabilities. Current approaches either have LLM-based agents imitate expert-provided trajectories step-by-step, requiring human supervision, which is hard to scale and limits environmental exploration; or they let agents explore and learn in isolated environments, resulting in specialist agents with limited generalization. In this paper, we take the first step towards building generally-capable LLM-based agents with self-evolution ability. We identify a trinity of ingredients: 1) diverse environments for agent exploration and learning, 2) a trajectory set to equip agents with basic capabilities and prior knowledge, and 3) an effective and scalable evolution method. We propose AgentGym, a new framework featuring a variety of environments and tasks for broad, real-time, uni-format, and concurrent agent exploration. AgentGym also includes a database with expanded instructions, a benchmark suite, and high-quality trajectories across environments. Next, we propose a novel method, AgentEvol, to investigate the potential of agent self-evolution beyond previously seen data across tasks and environments. Experimental results show that the evolved agents can achieve results comparable to SOTA models. We release the AgentGym suite, including the platform, dataset, benchmark, checkpoints, and algorithm implementations. The AgentGym suite is available on https://github.com/WooooDyy/AgentGym.

cs.AI↗
arXiv2024

Towards the wall-crossing of locally $\mathbb{Q}_p$-analytic representations of $\mathrm{GL}_n(K)$ for a $p$-adic field $K$

Let $K$ be a finite extension of $\mathbb{Q}_p$. We study the locally $\mathbb{Q}_p$-analytic representations $π$ of $\mathrm{GL}_n(K)$ of integral weights that appear in spaces of $p$-adic automorphic representations. We conjecture that the translation of $π$ to the singular block has an internal structure which is compatible with certain algebraic representations of $\mathrm{GL}_n$, analogously to the mod $p$ local-global compatibility conjecture of Breuil-Herzig-Hu-Morra-Schraen. We next make some conjectures and speculations on the wall-crossings of $π$. In particular, when $π$ is associated to a two dimensional de Rham Galois representation, we make conjectures and speculations on the relation between the Hodge filtrations of $ρ$ and the wall-crossings of $π$, which have a flavour of the Breuil-Strauch conjecture. We collect some results towards the conjectures and speculations.

math.NT↗
arXiv2024

Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic

In this paper, we introduce the simulations and bisimulations on polarity-based semantics for non-distributive modal logic, which are natural generalizations of those notions on Kripke semantics for modal logic. We also generalize other important model-theoretic notions about Kripke semantics such as image-finite models, modally-saturated models, ultrafilter extension and ultrapower extension to the non-distributive setting. By using these generalizations, we prove the Hennessy-Milner theorem and the van Benthem characterization theorem for non-distributive modal logic based on polarity-based semantics.

math.LO↗
arXiv2024

Self-Demos: Eliciting Out-of-Demonstration Generalizability in Large Language Models

Large language models (LLMs) have shown promising abilities of in-context learning (ICL), adapting swiftly to new tasks with only few-shot demonstrations. However, current few-shot methods heavily depend on high-quality, query-specific demos, which are often lacking. When faced with out-of-demonstration (OOD) queries, methods that rely on hand-crafted demos or external retrievers might fail. To bridge the gap between limited demos and OOD queries, we propose Self-Demos, a novel prompting method that elicits the inherent generalizability in LLMs by query-aware demo generation. The generated demos strategically interpolate between existing demos and the given query, transforming the query from OOD to ID. To evaluate the effectiveness of our approach, we manually constructed OOD-Toolset, a dataset in the tool-using scenario with over 300 real-world APIs and 1000 instances, each consisting of three tool-use cases as demos and an OOD query. Thorough experiments on our dataset and two public math benchmarks have shown that our method can outperform state-of-the-art baselines in the OOD setting. Moreover, we conduct a range of analyses to validate Self-Demos's generalization and provide more insights.

cs.CL↗
arXiv2024

Training Large Language Models for Reasoning through Reverse Curriculum Reinforcement Learning

In this paper, we propose R$^3$: Learning Reasoning through Reverse Curriculum Reinforcement Learning (RL), a novel method that employs only outcome supervision to achieve the benefits of process supervision for large language models. The core challenge in applying RL to complex reasoning is to identify a sequence of actions that result in positive rewards and provide appropriate supervision for optimization. Outcome supervision provides sparse rewards for final results without identifying error locations, whereas process supervision offers step-wise rewards but requires extensive manual annotation. R$^3$ overcomes these limitations by learning from correct demonstrations. Specifically, R$^3$ progressively slides the start state of reasoning from a demonstration's end to its beginning, facilitating easier model exploration at all stages. Thus, R$^3$ establishes a step-wise curriculum, allowing outcome supervision to offer step-level signals and precisely pinpoint errors. Using Llama2-7B, our method surpasses RL baseline on eight reasoning tasks by $4.1$ points on average. Notebaly, in program-based reasoning on GSM8K, it exceeds the baseline by $4.2$ points across three backbone models, and without any extra data, Codellama-7B + R$^3$ performs comparable to larger models or closed-source models.

cs.AI↗