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Bin Dong

Publications and source records attributed to Bin Dong.

At least 19 recordsLinked to original sources
arXiv2026

Compact Attention: Exploiting Structured Spatio-Temporal Sparsity for Fast Video Generation

The quadratic computational complexity of self-attention mechanisms imposes a critical constraint on transformer-based video generation, particularly for synthesizing ultra-long and high-definition sequences. While most sparse attention techniques employ fixed or heuristic patterns, they often struggle to accommodate the heterogeneous and layer-specific redundancies inherent in video diffusion transformers (VDiTs). We find that different attention heads consistently concentrate most of their attention mass in different coarse query-key regions, a behavior we call functional specialization. Although individual attention values vary with the generated content, these regions remain similar across prompts and random seeds. Leveraging these insights, we introduce Compact Attention, a hardware-aware sparse attention framework for efficient long-video synthesis. We quantify this stability and use it to construct searchable, reusable, head-specific masks. Based on the observation, we propose a deformable dual-window sparse pattern mechanism that flexibly approximates local and axial attention regions within one tile-aligned mask family. To avoid manually choosing a mask for each head, we develop a recall-driven offline auto-search algorithm that identifies high-quality sparse masks while leveraging temporal stability for mask reuse. Extensive evaluations on Wan2.1 (14B) and Hunyuan-Video demonstrate that Compact Attention achieves 2.25x/3.03x attention speedups over FlashAttention-2 and 1.20x/1.74x over FlashAttention-3, respectively, while maintaining visual quality and temporal consistency comparable to full-attention baselines. Project Page: https://yo-ava.github.io/Compact-Attention.github.io/

cs.CV↗
arXiv2026

Reap: Uncovering Monte Carlo proof search with a lightweight model

We present Reap, an open framework for learning and analyzing formal proof search in Lean4. Reap implements policy-value-guided Monte Carlo Tree Search directly in Lean, sharing proof-state transitions, AND-OR search, and replay verification between inference and training rollouts. Structured action logs expose how neural predictions and tactic execution interact during search. Using this framework, we train Reaper-1, a 1.7B-parameter policy-value model, through continued pre-training, supervised tactic learning, and iterative search-based reinforcement learning. Using a separate premise selector, the final system solves 79.9% of miniF2F-test at pass@32, establishing state-of-the-art performance among open provers of comparable size while remaining competitive with substantially larger models. Beyond improved solve rates, our results suggest that RL strengthens the prover's ability to organize proofs around useful intermediate results, favoring substantial advances over repeated local adjustments. This more directed proof construction is accompanied by increasingly elaborate tactic programs: fewer explicit search decisions are needed, while more work is performed within each decision. The resulting trade-off between search effort and tactic execution cost provides insight into how learning changes the prover's problem-solving strategy.

cs.AI↗
arXiv2026

An AI-Assisted Formalization of the Poincaré Conjecture

We present an AI-assisted Lean 4 formalization of the Poincaré conjecture. The project began with limited reusable formal infrastructure for the geometric analysis behind the proof. To organize this work, we combined a proof blueprint prepared by mathematicians with explicit milestone statements. These milestones enabled parallel agent work and gave mathematicians clear points to locate blockers and provide effective mathematical guidance. Our analysis identifies the human interventions and organizational choices behind this workflow. The project provides a starting point toward reusable infrastructure for future formalization projects; such infrastructure, once developed, could eventually reduce the cost of verifying mathematical results in geometric analysis.

cs.AI↗
arXiv2026

Constructing Rational Curves via Jets on Projective Varieties with Non-Nef Canonical Bundle

We give an algebraic proof in characteristic zero of the Miyaoka--Mori criterion: every point of a curve of negative canonical degree on a smooth projective variety lies on a rational curve. Our jet technique gives, in addition, an effective numerical decomposition of the original curve class. For each prescribed point, the decomposition contains a rational curve through that point, with a positive coefficient independent of the point and with anticanonical degree at most $\dim X+1$. Together with BDPP cone duality, this recovers the projective uniruledness criterion over $\mathbb C$. The main result of this paper was obtained using the Pharos system. A detailed report on the use of Pharos and on the Lean~4 formalization of the main arguments is given in the Appendix B, written by Bin Dong, Guoxiong Gao, Zeming Sun, and Bin Wu.

math.AG↗
arXiv2026

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with adequate accuracy, and limitations of the traditional solvers and specialized neural operators motivate the development of foundation models for solving PDEs. This paper introduces PDEformer-2, a versatile foundation model for two-dimensional PDEs. Based on our previous one-dimensional PDEformer-1 model, PDEformer-2 receives the PDE form as network input via computational graph representation, which has the flexibility to encode most common PDEs. The mesh-free predicted solutions can be directly queried at arbitrary spatio-temporal coordinates. A large (40TB) diverse dataset is employed to pretrain the current model, making it capable of simultaneously addressing PDEs with different symbolic forms, domain shapes, boundary conditions, number of variables, and time-dependency. Accurate zero-shot prediction is allowed for PDEs that resemble the pretraining ones. When adapted to new unseen PDEs, PDEformer-2 demonstrates faster learning than many specialized models, and has smaller errors given limited (less than 100) samples. Additionally, PDEformer-2 can be employed in the inverse problems thanks to its fast and differentiable nature and produces reasonable results in our experiments to recover coefficient scalars and fields of a PDE.

math.NA↗
arXiv2026

CiUNet: A Hybrid Swin-CNN UNet for Medical Image Segmentation

Medical image segmentation requires high accuracy and robustness, yet practical commercial deployment also demands privacy preservation and computational efficiency. In this context, the U-Net architecture, which can be inherently decoupled into independent encoder and decoder components, serves as a natural commercial choice. However, pure Transformer-based variants like Swin-UNet often suffer from insufficient local detail capture and limited interpretability. In this paper, we propose a lightweight hybrid architecture built upon the Swin-UNet framework. Our model integrates a parallel CNN encoder to complement the shallow layer reasoning of Swin Transformers with local texture features. To bridge the semantic gap and enhance fine-grained spatial detail recovery, we design an asymmetric feature fusion strategy and introduce cross-layer skip (XSkip) connections that explicitly propagate shallow CNN features into the decoder. We further incorporate novel loss functions and an auxiliary supervision head (Aux-Head) to strengthen training stability, boundary delineation, and intermediate feature interpretability. Extensive experiments on the Synapse multi-organ segmentation dataset demonstrate that our approach achieves state-of-the-art competitive Dice scores and Hausdorff distances, offering an accurate, efficient, and interpretable solution for clinical deployment.

eess.IV↗
arXiv2026

Xemo-Talker: Unlock Emotions Explicitly for Audio-Driven Talking Portrait Synthesis

Precise emotion control in audio-driven talking heads remains a challenge due to the reliance on implicit emotion regulation in existing systems, which often leads to indirect and insufficient control. Additionally, training with explicit emotion-related losses across the entire motion space poses significant difficulties due to the inherent trade-off between accurate lip synchronization and fine-grained emotion control. In this paper, we reveal a key finding: although emotional cues are distributed throughout the motion space, concentrating discriminative supervision on less-principal components achieves a better emotion-lip synchronization balance, as principal components mainly encode high-energy articulation and pose variations. Building on this insight, we propose Xemo-Talker, which first learns a neutral speech-to-motion mapping for stable articulation and lip synchronization, and then introduces a lightweight emotion branch guided by less-principal subspace supervision. To enhance emotion control, we design a Tri-Loss consisting of inter-class separation, intra-class compactness, and less-principal contrastive learning. Given an audio input, a reference image, and an emotion label, Xemo-Talker achieves state-of-the-art emotion classification accuracy while maintaining competitive lip synchronization and high inference efficiency, with performance approaching that measured on real videos.The source code is publicly available at https://github.com/chaolongy/Xemo-Talker.

cs.CV↗
arXiv2026

Building AI That Works: ESnet's Pragmatic Approach to AI-Driven Operational Excellence

The ORBIT (Operations Responses and Business Intelligence Toolkit) project was initiated to assess agentic AI for the upcoming ESnet 7 initiative and to address persistent operational pain points in the Network Operations Center (NOC) workflow. ESnet operators experience slow retrieval from siloed data sources, incidents described in lengthy and difficult-to-parse tickets, and context loss across shift handoffs. These challenges increase cognitive load and prolong incident resolution times. ORBIT therefore targets routine automation, cross-source synthesis, and actionable insights delivered directly within operators' existing tooling. ORBIT is an agentic AI system integrated into ServiceNow, ESnet's primary incident management platform. The design uses a modular, layered architecture comprising a centralized reasoning hub, tool access via MCPs for ESnet data sources, a semantic search layer, and an operator-facing chat interface. To manage the complexity and stochasticity of the AI toolchain, ORBIT follows industry best practices by structuring task logic as versioned, tested "skills" that guide the system in performing bounded responsibilities. This improves reliability and predictability compared to fully unconstrained agent behavior. Key results show that ORBIT successfully delivered all six initial tasks, and the architecture enabled rapid development of two additional tasks proposed by NOC engineers. We observed strong organic adoption of general-purpose infrastructure components, especially the chat interface and LiteLLM model gateway, including high request volumes from outside the project. Experiments with skills indicate that this approach can reduce task completion steps while eliminating observed error modes.

cs.NI↗
arXiv2026

Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.

cs.AI↗
arXiv2026

InverseScope: Scalable Activation Inversion for Interpreting Large Language Models

Understanding the internal representations of large language models (LLMs) is a central challenge in interpretability research. Existing feature interpretability methods often rely on strong structural assumptions--such as linearity or sparsity--that may not hold in practice. In this work, we introduce InverseScope, an assumption-light and scalable framework for interpreting neural activations via input inversion. Given a target activation, InverseScope characterizes its encoded information by generating natural-language inputs that produce nearby activations, grounding abstract internal states in concrete language. To overcome the prohibitive cost of sampling in high-dimensional activation spaces, we propose a novel control-layer conditioning architecture that substantially improves sample efficiency compared to prior token-prepending approaches. We demonstrate that InverseScope reveals rich geometric structure in LLM representation spaces, including sentence-level linear analogies. The framework scales to state-of-the-art open-source models of up to 14B parameters and generalizes to out-of-distribution inputs, enabling systematic analysis of activation neighborhoods.

cs.LG↗
arXiv2026

Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph

Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their inability to synthesize new definitions. To tackle these issues, we present Aria (Agent for Retrieval and Iterative Autoformalization), a system for conjecture-level formalization in Lean that emulates human expert reasoning via a two-phase Graph-of-Thought process: recursively decomposing statements into a dependency graph and then constructing formalizations from grounded concepts. To ensure semantic correctness, we introduce AriaScorer, a checker that retrieves definitions from Mathlib for term-level grounding, enabling rigorous and reliable verification. We evaluate Aria on diverse benchmarks. On ProofNet, it achieves 91.6% compilation success rate and 68.5% final accuracy, surpassing previous methods. On FATE-X, a suite of challenging algebra problems from research literature, it outperforms the best baseline with 44.0% vs. 24.0% final accuracy. On a dataset of homological conjectures, Aria reaches 42.9% final accuracy while all other models score 0%.

cs.AI↗
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

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↗
arXiv2026

Iteris: Agentic Research Loops for Computational Mathematics

Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.

cs.AI↗
arXiv2026

Automated Conjecture Resolution with Formal Verification

Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework that integrates natural language reasoning with formal verification to tackle research-level mathematical problems. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas combines reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with LeanSearch, translates informal arguments into formalized Lean 4 projects through task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Additional case studies illustrate the capabilities of Rethlas in informal mathematical reasoning and discovery, as well as the ability of Archon to formalize research-level proofs in Lean 4. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent can autonomously fill nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, reduce human effort, and support human-AI collaborative mathematical research.

cs.LG↗
arXiv2026

LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while premise-selection systems predict useful lemmas one tactic step at a time. Neither recovers the full premise set an entire theorem requires. We present LeanSearch v2, a two-mode retrieval system for this task. Its standard mode applies a hierarchy-informalized Mathlib corpus with an embedding-reranker pipeline, achieving state-of-the-art single-query retrieval without domain-specific fine-tuning (nDCG@10 of 0.62 vs. 0.53 for the next-best system). Its reasoning mode builds on standard mode as its retrieval substrate, targeting global premise retrieval through iterative sketch-retrieve-reflect cycles. On a 69-query benchmark of research-level Mathlib theorems, reasoning mode recovers 46.1% of ground-truth premise groups within 10 retrieved candidates, outperforming strong reasoning retrieval systems (38.0%) and premise-selection baselines (9.3%) on the same benchmark. In a controlled downstream evaluation with a fixed prover loop, replacing alternative retrievers with LeanSearch v2 yields the highest proof success (20% vs. 16% for the next-best system and 4% without retrieval), confirming that retrieval quality propagates to proof generation. We have open-sourced all code, data, and benchmarks. Code and data: https://github.com/frenzymath/LeanSearch-v2 . The standard mode is publicly available with API access at https://leansearch.net/ .

cs.IR↗
arXiv2026

MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers

Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model. By contrast, explicit solver logic is easier to understand and integrate, but is usually hand-designed rather than learned from solver feedback. We study whether the automatic design of MILP solver logic can instead be cast as LLM-guided closed-loop search over executable white-box components evaluated directly by end-to-end solver behavior. To this end, we propose a closed-loop program evolution framework for MILP solver auto-design, implemented through PySCIPOpt, and instantiate it on the joint design of a cut selector and a branching rule. Candidate programs are iteratively generated, loaded into SCIP, and evaluated by direct execution on MILP instances, with the resulting feedback guiding performance-based selection, targeted repair, diagnostic reflection, and diversity-aware population maintenance. The method outputs explicit solver components that can be inspected, modified, and deployed within standard solver workflows. Across four benchmark families, we find that LLM-guided program evolution can discover competitive domain-specialized policies in several settings.

cs.AI↗
arXiv2026

AI for Mathematics: Progress, Challenges, and Prospects

AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully automated formal logic, they faced severe scalability limitations due to the combinatorial explosion of the search space. The recent integration of data-driven approaches has revitalized this pursuit. In this review, we provide a systematic overview of AI4Math, highlighting its primary focus on developing AI models to support mathematical research. Crucially, we emphasize that this is not merely the application of AI to mathematical activities; it also encompasses the development of stronger AI systems where the rigorous nature of mathematics serves as a premier testbed for advancing general reasoning capabilities. We categorize existing research into two complementary directions: problem-specific modeling, involving the design of specialized architectures for distinct mathematical tasks, and general-purpose modeling, focusing on foundation models capable of broader reasoning, retrieval, and exploratory workflows. We conclude by discussing key challenges and prospects, advocating for AI systems that go beyond facilitating formal correctness to enabling the discovery of meaningful results and unified theories, recognizing that the true value of a proof lies in the insights and tools it offers to the broader mathematical landscape.

math.HO↗