arXiv subjects

Zhaoyu Li

Publications and source records attributed to Zhaoyu Li.

At least 19 recordsLinked to original sources

arXiv2026

One-Step Retrieval Framework for Real-Time Sponsored Search Ads Using Hierarchical Text Representations

Traditional retrieval systems typically use multi-stage cascading architectures (MCA), where each module is optimized independently, leading to inconsistent objectives and the premature elimination of high-potential candidates. Recent LLM-based generation methods offer end-to-end solutions but use discrete semantic identifiers (SIDs) to retrieve ads, which are not learned by the base LLM and require memorization of numerous SID-to-ad mappings during SFT, suffering from limited generalization to unseen ads, high maintenance and update costs. The one-to-one mapping between SIDs and advertisements leads to inefficient decoding. Moreover, these methods rely on a small reward model (e.g. pctr) for relevance and ranking, limiting the LLM's ability to fully assess ads' commercial value. To address these challenges, we propose A uNified Generation-discriminative-ranking reaL-time rEtrieval (ANGLE) framework. ANGLE uses LLM-generated hierarchical textual representations, which consist of commercial intent that provide high-level overviews and ad abstract that deliver fine-grained details. Additionally, ANGLE integrates retrieval, relevance, and ranking directly within a single LLM, enabling precise and efficient ranking of ads by leveraging the full capabilities of the LLM. We applied ANGLE to the real-world search scenarios, achieving a 1.81% increase in consumption and a 2.16% increase in gross merchandise volume (GMV). We also conducted offline evaluations of ANGLE and seven baselines, with ANGLE outperforming all across key metrics such as HR and ACR.

cs.IR↗

arXiv2026

P$^{3}$: Joint Program-and-Proof Planning for Verified Code Generation

Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction. The de facto workflow decouples the two halves of the problem: first synthesize a program, then attempt to prove it correct. We observe that this sequential pipeline can be both ineffective and inefficient in practice. A program generated without anticipating its proof can be subtly incorrect or structurally difficult to verify, forcing the LLM into brittle repair loops that alternate between patching the code and patching the proof. Inspired by Dijkstra's view that a program and its correctness argument should be developed hand in hand, we propose $P^3$, an LLM-based agentic workflow that first derives a unified program-and-proof plan from the specification, then elaborates the implementation and proof scaffold under this shared plan. To evaluate verified code generation in realistic settings, we further introduce Lean4Commit0, a repository-derived, library-level benchmark built by extracting core APIs from real-world software repositories and translating their requirements, including relational specifications across APIs, into Lean tasks. Using four frontier LLM backends, we evaluate $P^3$ on Verina, AlgoVeri, and our Lean4Commit0 benchmark, where it achieves the highest solve rate in every benchmark--model setting. Compared with the stronger baseline, it improves solve rates by 4.6--11.2 percentage points and reduces per-task API cost by up to roughly 40\% and wall-clock time by up to roughly 37\% on the difficult subset of each benchmark. A targeted ablation further shows gains of 3.3--8.3 points over implementation-only planning, isolating the benefit of planning the program and proof jointly.

cs.AI↗

arXiv2026

Theory-Level Autoformalization: From Isolated Statements to Unified Formal Knowledge Bases

Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web of axioms, definitions, and lemmas before target theorems can even be stated. In this position paper, we argue for theory-level autoformalization: formalizing complete theories, including all their inter-dependencies, as structured libraries. We examine the significance of this shift, address alternative views, identify open challenges, and propose three promising paths forward. Our survey of autoformalization is available at https://github.com/marcusm117/Awesome-Autoformalization.

cs.AI↗

arXiv2026

Overview of Cross-Component In-loop Filters in Video Coding Standards

In-loop filters have been comprehensively explored during the development of video coding standards due to their remarkable noise-reduction capability. In the early stage of video coding, in-loop filters, such as Deblocking Filter, Sample Adaptive Offset, and Adaptive Loop Filter, were performed separately for each component. Recently, cross-component filters were studied to improve the chroma fidelity by exploiting correlations between the luma and chroma channels. This paper summarizes the cross-component filters used in the state-of-the-art video coding standard. Specifically, it includes the Cross-Component Adaptive Loop Filter and Cross-Component Sample Adaptive Offset. Cross-component filters aim to reduce compression artifacts based on the correlation between different components and provide more accurate pixel reconstruction values. In this paper, we introduce the origin, development, and status of cross-component filters in the current video coding standards. Finally, we had some discussions on the further evolutions of cross-component filters.

cs.CV↗

arXiv2026

Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry

Euclidean geometry is a compelling testbed for AI reasoning, as it demands the combination of intuitive diagram understanding, axiomatic deduction, and algebraic computation. Yet, existing approaches typically address only a subset of these abilities or struggle with competition-level problems. We introduce \textit{Euclid-Omni}, a unified neuro-symbolic framework that couples a formal geometry system with Large Language Models (LLMs) and Vision-Language Models (VLMs) to tackle both calculation- and proving-style problems, in formal and natural languages, up to Olympiad-level difficulty. At its core, we develop \textit{Euclidea}, a versatile symbolic geometry solver that automatically generates reasoning steps through deductive inference and algebraic computation. Building on this, we develop a data-generation pipeline that synthesizes symbolic problems and solutions, renders diagrams, and translates them into natural language, producing large-scale, diverse datasets for training LLMs and VLMs across a wide range of reasoning settings. Experiments show that VLMs trained on our synthetic data achieve superior performance on calculation tasks, and that LLMs combined with \textit{Euclidea} are competitive with state-of-the-art systems on Olympiad-level proving problems, despite using orders of magnitude less compute and training data. Code and scripts are publicly available at https://github.com/20171130/Euclid-Omni

cs.AI↗

arXiv2026

DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent

We introduce DreamProver, an agentic framework that leverages a "wake-sleep" program induction paradigm to discover reusable lemmas for formal theorem proving. Existing approaches either rely on fixed lemma libraries, which limit adaptability, or synthesize highly specific intermediate lemmas tailored to individual theorems, thereby lacking generality. DreamProver addresses this gap through an iterative two-stage process. In the wake stage, DreamProver attempts to prove theorems from a training set using the current lemma library while proposing new candidate lemmas. In the "sleep" stage, it abstracts, refines, and consolidates these candidates to compress and optimize the library. Through this alternating cycle, DreamProver progressively evolves a compact set of high-level, transferable lemmas that can be effectively used to prove unseen theorems in related domains. Experimental results demonstrate that DreamProver substantially improves proof success rates across a diverse set of mathematical benchmarks, while also producing more concise proofs and reducing computational cost.

cs.AI↗

arXiv2026

Variational Bayesian Personalized Ranking

Pairwise learning underpins implicit collaborative filtering, yet its effectiveness is often hindered by sparse supervision, noisy interactions, and popularity-driven exposure bias. In this paper, we propose Variational Bayesian Personalized Ranking (VarBPR), a tractable variational framework for implicit-feedback pairwise learning that offers principled exposure controllability and theoretical interpretability. VarBPR reformulates pairwise learning as variational inference over discrete latent indexing variables, explicitly modeling noise and indexing uncertainty, and divides training into two stages: variational inference and variational learning. In the variational inference stage, we develop a variational formulation that integrates preference alignment, denoising, and popularity debiasing under a unified ELBO/regularization objective, deriving closed-form posteriors with clear control semantics: the prior encodes a target exposure pattern, while temperature/regularization strength controls posterior-prior adherence. As a result, exposure controllability becomes an endogenous and interpretable outcome of variational inference. In the variational learning stage, we propose a posterior-compression objective that reduces the ideal ELBO's computational complexity from polynomial to linear, with the approximation justified by an explicit Jensen-gap upper bound. Theoretically, we provide interpretable generalization guarantees by identifying a structural error component and revealing the opportunity cost of prioritizing certain exposure patterns (e.g., long-tail), offering a concrete analytical lens for designing controllable recommender systems. Empirically, We validate VarBPR across popular backbones; it demonstrates consistent gains in ranking accuracy, enables controlled long-tail exposure, and preserves the linear-time complexity of BPR.

cs.IR↗

arXiv2026

Learning to Disprove: Formal Counterexample Generation with Large Language Models

Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost exclusively on proof construction, often neglecting the equally important task of finding counterexamples. In this paper, we address this gap by fine-tuning large language models (LLMs) to reason about and generate counterexamples. We formalize this task as formal counterexample generation, which requires LLMs not only to propose candidate counterexamples but also to produce formal proofs that can be automatically verified in the Lean 4 theorem prover. To enable effective learning, we introduce a symbolic mutation strategy that synthesizes diverse training data by systematically extracting theorems and discarding selected hypotheses, thereby producing diverse counterexample instances. Together with curated datasets, this strategy enables a multi-reward expert iteration framework that substantially enhances both the effectiveness and efficiency of training LLMs for counterexample generation and theorem proving. Experiments on three newly collected benchmarks validate the advantages of our approach, showing that the mutation strategy and training framework yield significant performance gains.

cs.AI↗

arXiv2025

Unveiling a young thick disk in the Milky Way

The thickness of a galaxy's disk provides a valuable probe of its formation and evolution history. Observations of the Milky Way and local galaxies have revealed an ubiquitous disk structure with two distinctive components: an old thick disk and a relatively young thin disk. The formation of this dual-disk structure and the mechanisms that develop the thickness of the disk are still unclear. Whether the disk thickness inherit from the birth environment or is established through secular dynamical heating after formation is under debate. In this work we identify a relatively young ($\sim$6.6 billion years old) geometric thick disk in the Milky Way, with a scale height of $0.64$ kpc at the Solar Circle. This young thick component exhibits comparable thickness and flaring strength to the canonical old thick disk but is more radially extended and systematically younger. We also identify thin disk components that formed before and after this young thick disk. Detailed analysis of the solar vicinity structure suggests that the young thick disk marks the onset of a new phase of upside-down disk formation. These findings strongly discount the role of secular dynamical heating and support a turbulent, bursty birth environment as the primary mechanism behind thick disk formation. The existence of two thick disk components suggests that the Milky Way has undergone at least two episodes of turbulent and bursty star formation, likely triggered by galaxy mergers.

astro-ph.GA↗

arXiv2025

LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation

Recent years have witnessed the rapid development of Neuro-Symbolic (NeSy) AI systems, which integrate symbolic reasoning into deep neural networks. However, most of the existing benchmarks for NeSy AI fail to provide long-horizon reasoning tasks with complex multi-agent interactions. Furthermore, they are usually constrained by fixed and simplistic logical rules over limited entities, making them far from real-world complexities. To address these crucial gaps, we introduce LogiCity, the first simulator based on customizable first-order logic (FOL) for an urban-like environment with multiple dynamic agents. LogiCity models diverse urban elements using semantic and spatial concepts, such as IsAmbulance(X) and IsClose(X, Y). These concepts are used to define FOL rules that govern the behavior of various agents. Since the concepts and rules are abstractions, they can be universally applied to cities with any agent compositions, facilitating the instantiation of diverse scenarios. Besides, a key feature of LogiCity is its support for user-configurable abstractions, enabling customizable simulation complexities for logical reasoning. To explore various aspects of NeSy AI, LogiCity introduces two tasks, one features long-horizon sequential decision-making, and the other focuses on one-step visual reasoning, varying in difficulty and agent behaviors. Our extensive evaluation reveals the advantage of NeSy frameworks in abstract reasoning. Moreover, we highlight the significant challenges of handling more complex abstractions in long-horizon multi-agent scenarios or under high-dimensional, imbalanced data. With its flexible design, various features, and newly raised challenges, we believe LogiCity represents a pivotal step forward in advancing the next generation of NeSy AI. All the code and data are open-sourced at our website: https://jaraxxus-me.github.io/LogiCity/

cs.AI↗

arXiv2025

Dynamic Backtracking in GFlowNets: Enhancing Decision Steps with Reward-Dependent Adjustment Mechanisms

Generative Flow Networks (GFlowNets or GFNs) are probabilistic models predicated on Markov flows, and they employ specific amortization algorithms to learn stochastic policies that generate compositional substances including biomolecules, chemical materials, etc. With a strong ability to generate high-performance biochemical molecules, GFNs accelerate the discovery of scientific substances, effectively overcoming the time-consuming, labor-intensive, and costly shortcomings of conventional material discovery methods. However, previous studies rarely focus on accumulating exploratory experience by adjusting generative structures, which leads to disorientation in complex sampling spaces. Efforts to address this issue, such as LS-GFN, are limited to local greedy searches and lack broader global adjustments. This paper introduces a novel variant of GFNs, the Dynamic Backtracking GFN (DB-GFN), which improves the adaptability of decision-making steps through a reward-based dynamic backtracking mechanism. DB-GFN allows backtracking during the network construction process according to the current state's reward value, thereby correcting disadvantageous decisions and exploring alternative pathways during the exploration process. When applied to generative tasks involving biochemical molecules and genetic material sequences, DB-GFN outperforms GFN models such as LS-GFN and GTB, as well as traditional reinforcement learning methods, in sample quality, sample exploration quantity, and training convergence speed. Additionally, owing to its orthogonal nature, DB-GFN shows great potential in future improvements of GFNs, and it can be integrated with other strategies to achieve higher search performance.

cs.LG↗

arXiv2025

Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data for formal proofs is limited, posing a significant challenge to LLM-based tactic generation. To address this, we introduce a neuro-symbolic tactic generator that synergizes the mathematical intuition learned by LLMs with domain-specific insights encoded by symbolic methods. The key aspect of this integration is identifying which parts of mathematical reasoning are best suited to LLMs and which to symbolic methods. While the high-level idea of neuro-symbolic integration is broadly applicable to various mathematical problems, in this paper, we focus specifically on Olympiad inequalities (Figure~1). We analyze how humans solve these problems and distill the techniques into two types of tactics: (1) scaling, handled by symbolic methods, and (2) rewriting, handled by LLMs. In addition, we combine symbolic tools with LLMs to prune and rank the proof goals for efficient proof search. We evaluate our framework on 161 challenging inequalities from multiple mathematics competitions, achieving state-of-the-art performance and significantly outperforming existing LLM and symbolic approaches without requiring additional training data.

cs.AI↗

arXiv2024

Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency

Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models (LLMs) have unveiled their promising capabilities to formalize even competition-level math problems. However, we observe a considerable discrepancy between pass@1 and pass@k accuracies in LLM-generated formalizations. To address this gap, we introduce a novel framework that scores and selects the best result from k autoformalization candidates based on two complementary self-consistency methods: symbolic equivalence and semantic consistency. Elaborately, symbolic equivalence identifies the logical homogeneity among autoformalization candidates using automated theorem provers, and semantic consistency evaluates the preservation of the original meaning by informalizing the candidates and computing the similarity between the embeddings of the original and informalized texts. Our extensive experiments on the MATH and miniF2F datasets demonstrate that our approach significantly enhances autoformalization accuracy, achieving up to 0.22-1.35x relative improvements across various LLMs and baseline methods.

cs.CL↗

arXiv2024

Decoupling Training-Free Guided Diffusion by ADMM

In this paper, we consider the conditional generation problem by guiding off-the-shelf unconditional diffusion models with differentiable loss functions in a plug-and-play fashion. While previous research has primarily focused on balancing the unconditional diffusion model and the guided loss through a tuned weight hyperparameter, we propose a novel framework that distinctly decouples these two components. Specifically, we introduce two variables ${x}$ and ${z}$, to represent the generated samples governed by the unconditional generation model and the guidance function, respectively. This decoupling reformulates conditional generation into two manageable subproblems, unified by the constraint ${x} = {z}$. Leveraging this setup, we develop a new algorithm based on the Alternating Direction Method of Multipliers (ADMM) to adaptively balance these components. Additionally, we establish the equivalence between the diffusion reverse step and the proximal operator of ADMM and provide a detailed convergence analysis of our algorithm under certain mild assumptions. Our experiments demonstrate that our proposed method ADMMDiff consistently generates high-quality samples while ensuring strong adherence to the conditioning criteria. It outperforms existing methods across a range of conditional generation tasks, including image generation with various guidance and controllable motion synthesis.

cs.CV↗

arXiv2024

Neuro-symbolic Learning Yielding Logical Constraints

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural network training, symbol grounding, and logical constraint synthesis into a coherent and efficient end-to-end learning process. The capability of this framework comes from the improved interactions between the neural and the symbolic parts of the system in both the training and inference stages. Technically, to bridge the gap between the continuous neural network and the discrete logical constraint, we introduce a difference-of-convex programming technique to relax the logical constraints while maintaining their precision. We also employ cardinality constraints as the language for logical constraint learning and incorporate a trust region method to avoid the degeneracy of logical constraint in learning. Both theoretical analyses and empirical evaluations substantiate the effectiveness of the proposed framework.

cs.AI↗

arXiv2024

A Survey on Deep Learning for Theorem Proving

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large language models, has sparked a notable surge of research exploring these techniques to enhance the process of theorem proving. This paper presents a comprehensive survey of deep learning for theorem proving by offering (i) a thorough review of existing approaches across various tasks such as autoformalization, premise selection, proofstep generation, and proof search; (ii) an extensive summary of curated datasets and strategies for synthetic data generation; (iii) a detailed analysis of evaluation metrics and the performance of state-of-the-art methods; and (iv) a critical discussion on the persistent challenges and the promising avenues for future exploration. Our survey aims to serve as a foundational reference for deep learning approaches in theorem proving, inspiring and catalyzing further research endeavors in this rapidly growing field. A curated list of papers is available at https://github.com/zhaoyu-li/DL4TP.

cs.AI↗

arXiv2024

APPL: A Prompt Programming Language for Harmonious Integration of Programs and Large Language Model Prompts

Large Language Models (LLMs) have become increasingly capable of handling diverse tasks with the aid of well-crafted prompts and integration of external tools, but as task complexity rises, the workflow involving LLMs can be complicated and thus challenging to implement and maintain. To address this challenge, we propose APPL, A Prompt Programming Language that acts as a bridge between computer programs and LLMs, allowing seamless embedding of prompts into Python functions, and vice versa. APPL provides an intuitive and Python-native syntax, an efficient parallelized runtime with asynchronous semantics, and a tracing module supporting effective failure diagnosis and replaying without extra costs. We demonstrate that APPL programs are intuitive, concise, and efficient through three representative scenarios: Chain-of-Thought with self-consistency (CoT-SC), ReAct tool use agent, and multi-agent chat. Experiments on three parallelizable workflows further show that APPL can effectively parallelize independent LLM calls, with a significant speedup ratio that almost matches the estimation.

cs.AI↗

arXiv2024

Autoformalizing Euclidean Geometry

Autoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean geometry provides an interesting and controllable domain for studying autoformalization. In this paper, we introduce a neuro-symbolic framework for autoformalizing Euclidean geometry, which combines domain knowledge, SMT solvers, and large language models (LLMs). One challenge in Euclidean geometry is that informal proofs rely on diagrams, leaving gaps in texts that are hard to formalize. To address this issue, we use theorem provers to fill in such diagrammatic information automatically, so that the LLM only needs to autoformalize the explicit textual steps, making it easier for the model. We also provide automatic semantic evaluation for autoformalized theorem statements. We construct LeanEuclid, an autoformalization benchmark consisting of problems from Euclid's Elements and the UniGeo dataset formalized in the Lean proof assistant. Experiments with GPT-4 and GPT-4V show the capability and limitations of state-of-the-art LLMs on autoformalizing geometry problems. The data and code are available at https://github.com/loganrjmurphy/LeanEuclid.

cs.LG↗