arXiv subjects
Publications and source records attributed to Li Cai.
Let $G$ be a split reductive group over a $p$-adic field. We give germ expansions of Kloosterman integrals for $G$. As an application, we prove that Bessel distributions are regular for all generic representations on $G$ provided that Kloosterman sums for any Levi subgroups of $G$ have nontrivial bounds.
Cross-domain task-oriented dialogue requires reasoning over implicit and explicit feasibility constraints while planning long-horizon, multi-turn actions. Large language models (LLMs) can infer such constraints but are unreliable over long horizons, while Reinforcement learning (RL) optimizes long-horizon behavior yet cannot recover constraints from raw dialogue. Naively coupling LLMs with RL is therefore brittle: unverified or unstructured LLM outputs can corrupt state representations and misguide policy learning. Motivated by this, we propose Verified LLM-Knowledge empowered RL (VLK-RL), a hybrid framework that makes LLM-derived constraint reasoning usable for RL. VLK-RL first elicits candidate constraints with an LLM and then verifies them via a dual-role cross-examination procedure to suppress hallucinations and cross-turn inconsistencies. The verified constraints are mapped into ontology-aligned slot-value representations, yielding a structured, constraint-aware state for RL policy optimization. Experiments across multiple benchmarks demonstrate that VLK-RL significantly improves generalization and robustness, outperforming strong single-model baselines on long-horizon tasks.
Evaluating agentic AI on open-ended professional tasks faces a fundamental dilemma between rigor and flexibility. Static rubrics provide rigorous, reproducible assessment but fail to accommodate diverse valid response strategies, while LLM-as-a-judge approaches adapt to individual responses yet suffer from instability and bias. Human experts address this dilemma by combining domain-grounded principles with dynamic, claim-level assessment. Inspired by this process, we propose JADE, a two-layer evaluation framework. Layer 1 encodes expert knowledge as a predefined set of evaluation skills, providing stable evaluation criteria. Layer 2 performs report-specific, claim-level evaluation to flexibly assess diverse reasoning strategies, with evidence-dependency gating to invalidate conclusions built on refuted claims. Experiments on BizBench show that JADE improves evaluation stability and reveals critical agent failure modes missed by holistic LLM-based evaluators. We further demonstrate strong alignment with expert-authored rubrics and effective transfer to HealthBench and DR.BENCH, covering medical and 10-domain professional evaluation settings. Code and data are available at https://github.com/smiling-world/JADE.
Let $\mathcal{O}$ be the ring of integers for some number field $F$. Let $\chi(x)\in \mathcal{O}[x]$ be a regular monic polynomial of degree $n$. We study the asymptotic count of integral $n\times n$ matrices over $\mathcal{O}$ with the characteristic polynomial $\chi$ and bounded archimedean norm. Previous works establish such an asymptotic with a positive leading constant. Our main result determines this constant in terms of the leading Laurent coefficients at $s=1$ of Dedekind zeta functions attached to orders in $F[x]/(\chi(x))$. The proof combines a refinement of the equi-distribution property of orbits with a reformulation of the counting problem in terms of generalized $\kappa$-orbital integrals. These orbital integrals are then transferred by the endoscopic fundamental lemma and related to zeta functions of orders.
In this work, we unify different constructions of Kan's loop group $GX$ for a reduced simplicial set $X$ topologically, by identifying its geometric realization $|GX|$ as different submonoids of $\Omega|X|$, the monoid of based Moore loops on $|X|$. Then we construct a cubical subcomplex $|CX|\subset |GX|$ as a submonoid and prove that after inverting all elements of degree $0$ in $CX$, the inclusion $|S^{-1}CX|\subset |GX|$ is a (weak) homotopy equivalence. Our construction is functorial and explicit, without using inductions.
AFSI is a novel, open-source fluid-structure interaction (FSI) solver that extends the capabilities of the FEniCS finite element library through an immersed boundary (IB) framework. Designed to simulate large deformations in hyperelastic materials (such as cardiac tissue), AFSI avoids the need for expensive remeshing by coupling a Lagrangian representation of the solid with an Eulerian description of the surrounding fluid. This approach retains the full expressiveness of FEniCS's variational formulations, function spaces, and time integration schemes. Implemented in a hybrid Python/C++ architecture, AFSI allows users to define geometries, constitutive models (e.g., the Holzapfel-Ogden law for myocardium), and strain energy functions directly in Python, while delegating performance-critical tasks such as assembly and linear solvers to optimized C++ backends. Its concise and modular Python API facilitates the setup of FSI simulations, enabling users to easily modify discretization strategies or analyze results using standard FEniCS post-processing tools. By combining the flexibility of FEniCS with a robust immersed boundary formulation, AFSI empowers rapid prototyping of complex nonlinear solid-fluid interaction problems, making it a powerful tool for simulating biomechanical systems and other applications involving highly deformable structures in flow.
In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the central critical value of symmetric cube $L$-functions. We also deduce from the local multiplicity one result that there exist cuspidal automorphic forms with prescribed local components and non-vanishing central symmetric cube $L$-values.
The immersed boundary (IB) method has become a leading approach in cardiac fluid-structure interaction (FSI) modeling due to its ability to handle large deformations and complex geometries without requiring mesh regeneration. However, the use of nonlinear, fiber-reinforced hyperelastic materials for modeling soft cardiac tissues introduces challenges in computational efficiency, particularly due to the additional projection steps required for stability in the IB framework. These steps often involve sparse matrix storage and computation, which can degrade GPU performance. In this work, we present a novel, fully GPU-accelerated, matrix-free IB method for FSI in anatomically realistic cardiac models. By employing nodal coupling, our method eliminates the need for projection operations in the finite element space. Additionally, we solve the Navier-Stokes equations using Chorin's projection method combined with a matrix-free geometric multigrid solver, ensuring the entire FSI algorithm remains matrix-free and highly compatible with GPU acceleration. Our implementation features several GPU-specific optimizations, including the use of constant memory to store values of nodal basis functions and their derivatives at quadrature points, and texture memory to efficiently implement the semi-Lagrangian discretization of convection terms. These innovations maximize GPU utilization while preserving the complex mechanical behavior of soft cardiac tissue. Benchmark tests demonstrate that our GPU-accelerated solver achieves a $50\times$-$100\times$ speedup compared to a 20-core CPU implementation, with comparable accuracy.
We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Euler system. This uniformly recovers many of the known Euler systems, and in the twisted Friedberg--Jacquet setting, we produce a new split anticyclotomic Euler system.
Recent advances in Multi-modal Large Language Models (MLLMs), such as LLaVA-series models, are driven by massive machine-generated instruction-following data tuning. Such automatic instruction collection pipelines, however, inadvertently introduce significant variability in data quality. This paper introduces a novel instruction curation algorithm, derived from two unique perspectives, human and LLM preference alignment, to compress this vast corpus of machine-generated multimodal instructions to a compact and high-quality form: (i) For human preference alignment, we have collected a machine-generated multimodal instruction dataset and established a comprehensive set of both subjective and objective criteria to guide the data quality assessment critically from human experts. By doing so, a reward model was trained on the annotated dataset to internalize the nuanced human understanding of instruction alignment. (ii) For LLM preference alignment, given the instruction selected by the reward model, we propose leveraging the inner LLM used in MLLM to align the writing style of visual instructions with that of the inner LLM itself, resulting in LLM-aligned instruction improvement. Extensive experiments demonstrate that we can maintain or even improve model performance by compressing synthetic multimodal instructions by up to 90%. Impressively, by aggressively reducing the training instructions from 158k to 14k (9$\times$ smaller), our model consistently outperforms its full-size dataset counterpart across various MLLM benchmarks. Our project is available at https://github.com/DCDmllm/Align2LLaVA.
Empathetic response generation endows agents with the capability to comprehend dialogue contexts and react to expressed emotions. Previous works predominantly focus on leveraging the speaker's emotional labels, but ignore the importance of emotion cause reasoning in empathetic response generation, which hinders the model's capacity for further affective understanding and cognitive inference. In this paper, we propose a cause-aware empathetic generation approach by integrating emotions and causes through a well-designed Chain-of-Thought (CoT) prompt on Large Language Models (LLMs). Our approach can greatly promote LLMs' performance of empathy by instruction tuning and enhancing the role awareness of an empathetic listener in the prompt. Additionally, we propose to incorporate cause-oriented external knowledge from COMET into the prompt, which improves the diversity of generation and alleviates conflicts between internal and external knowledge at the same time. Experimental results on the benchmark dataset demonstrate that our approach on LLaMA-7b achieves state-of-the-art performance in both automatic and human evaluations.
Multilingual Knowledge Graph Completion (mKGC) aim at solving queries like (h, r, ?) in different languages by reasoning a tail entity t thus improving multilingual knowledge graphs. Previous studies leverage multilingual pretrained language models (PLMs) and the generative paradigm to achieve mKGC. Although multilingual pretrained language models contain extensive knowledge of different languages, its pretraining tasks cannot be directly aligned with the mKGC tasks. Moreover, the majority of KGs and PLMs currently available exhibit a pronounced English-centric bias. This makes it difficult for mKGC to achieve good results, particularly in the context of low-resource languages. To overcome previous problems, this paper introduces global and local knowledge constraints for mKGC. The former is used to constrain the reasoning of answer entities, while the latter is used to enhance the representation of query contexts. The proposed method makes the pretrained model better adapt to the mKGC task. Experimental results on public datasets demonstrate that our method outperforms the previous SOTA on Hits@1 and Hits@10 by an average of 12.32% and 16.03%, which indicates that our proposed method has significant enhancement on mKGC.
Retrieval-Augmented Generation (RAG) methods augment the input of Large Language Models (LLMs) with relevant retrieved passages, reducing factual errors in knowledge-intensive tasks. However, contemporary RAG approaches suffer from irrelevant knowledge retrieval issues in complex domain questions (e.g., HotPot QA) due to the lack of corresponding domain knowledge, leading to low-quality generations. To address this issue, we propose a novel Collaborative Retrieval-Augmented Generation framework, DuetRAG. Our bootstrapping philosophy is to simultaneously integrate the domain fintuning and RAG models to improve the knowledge retrieval quality, thereby enhancing generation quality. Finally, we demonstrate DuetRAG' s matches with expert human researchers on HotPot QA.
Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this task. This paper advances beyond conventional approaches by introducing more expressive quaternion representations for TKGC within hypercomplex space. Unlike existing quaternion-based methods, our study focuses on capturing time-sensitive relations rather than time-aware entities. Specifically, we model time-sensitive relations through time-aware rotation and periodic time translation, effectively capturing complex temporal variability. Furthermore, we theoretically demonstrate our method's capability to model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns. Comprehensive experiments on public datasets validate that our proposed approach achieves state-of-the-art performance in the field of TKGC.
Knowledge graphs have garnered significant research attention and are widely used to enhance downstream applications. However, most current studies mainly focus on static knowledge graphs, whose facts do not change with time, and disregard their dynamic evolution over time. As a result, temporal knowledge graphs have attracted more attention because a large amount of structured knowledge exists only within a specific period. Knowledge graph representation learning aims to learn low-dimensional vector embeddings for entities and relations in a knowledge graph. The representation learning of temporal knowledge graphs incorporates time information into the standard knowledge graph framework and can model the dynamics of entities and relations over time. In this paper, we conduct a comprehensive survey of temporal knowledge graph representation learning and its applications. We begin with an introduction to the definitions, datasets, and evaluation metrics for temporal knowledge graph representation learning. Next, we propose a taxonomy based on the core technologies of temporal knowledge graph representation learning methods, and provide an in-depth analysis of different methods in each category. Finally, we present various downstream applications related to the temporal knowledge graphs. In the end, we conclude the paper and have an outlook on the future research directions in this area.
Complex Query Answering (CQA) is a challenge task of Knowledge Graph (KG). Due to the incompleteness of KGs, query embedding (QE) methods have been proposed to encode queries and entities into the same embedding space, and treat logical operators as neural set operators to obtain answers. However, these methods train KG embeddings and neural set operators concurrently on both simple (one-hop) and complex (multi-hop and logical) queries, which causes performance degradation on simple queries and low training efficiency. In this paper, we propose Query to Triple (Q2T), a novel approach that decouples the training for simple and complex queries. Q2T divides the training into two stages: (1) Pre-training a neural link predictor on simple queries to predict tail entities based on the head entity and relation. (2) Training a query encoder on complex queries to encode diverse complex queries into a unified triple form that can be efficiently solved by the pretrained neural link predictor. Our proposed Q2T is not only efficient to train, but also modular, thus easily adaptable to various neural link predictors that have been studied well. Extensive experiments demonstrate that, even without explicit modeling for neural set operators, Q2T still achieves state-of-the-art performance on diverse complex queries over three public benchmarks.
In both local and global settings, we establish explicit relations between Ichino triple product period and Waldspurger toric periods for CM forms via the theta lifting and the see-saw principle.
Entity alignment (EA) aims to find the equivalent entity pairs between different knowledge graphs (KGs), which is crucial to promote knowledge fusion. With the wide use of temporal knowledge graphs (TKGs), time-aware EA (TEA) methods appear to enhance EA. Existing TEA models are based on Graph Neural Networks (GNN) and achieve state-of-the-art (SOTA) performance, but it is difficult to transfer them to large-scale TKGs due to the scalability issue of GNN. In this paper, we propose an effective and efficient non-neural EA framework between TKGs, namely LightTEA, which consists of four essential components: (1) Two-aspect Three-view Label Propagation, (2) Sparse Similarity with Temporal Constraints, (3) Sinkhorn Operator, and (4) Temporal Iterative Learning. All of these modules work together to improve the performance of EA while reducing the time consumption of the model. Extensive experiments on public datasets indicate that our proposed model significantly outperforms the SOTA methods for EA between TKGs, and the time consumed by LightTEA is only dozens of seconds at most, no more than 10% of the most efficient TEA method.