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Lei Fu

Publications and source records attributed to Lei Fu.

At least 19 recordsLinked to original sources
arXiv2026

Arithmetic hypergeometric $\mathcal {D}$-modules and exponential sums on reductive groups

For a finite family of representations of a reductive group, we define a Laurent polynomial on the group. The exponential sum associated this Laurent polynomial is called a hypergeometric exponential sum. We introduce an arithmetic hypergeometric $\mathcal D$-module to study the hypergeometric exponential sum. It is an overholonomic arithmetic $\mathcal D$-module with a Frobenius structure so that the trace of the Frobenius at a rational point is the exponential sum. Over the locus where the Laurent polynomial is nondegenerate, the arithmetic hypergeometric $\mathcal {D}$-module defines an $F$-isocrystal overconvergent along the degenerate locus. As an application, we get an estimation of the hypergeometric exponential sum.

math.AG↗
arXiv2026

ARCANA: A Reflective Multi-Agent Program Synthesis Framework for ARC-AGI-2 Reasoning

We present ARCANA, a collaborative multi agent framework for solving ARC AGI 2 tasks under strict test time and hardware constraints. ARCANA decomposes each task into iterative perception, hypothesis generation, symbolic execution, and reflective refinement. A perceptual grounding agent builds object centric scene graphs from raw grids, a latent program policy proposes diverse DSL programs, a symbolic executor verifies candidates on demonstrations, and a reflective agent synthesizes failure driven feedback for the next turn. These agents communicate through a shared differentiable blackboard and are scheduled by a learned meta controller. The design combines structured program search with adaptive multi turn correction, improving reasoning efficiency and solution quality on challenging abstract transformation tasks.

cs.AI↗
arXiv2026

Dependency-Aware Chain-of-Thought Compression for Financial Reasoning

Chain of thought prompting improves complex reasoning, but its long intermediate traces create substantial inference cost and hinder practical deployment in financial settings. We present a Hierarchical Semantic Distillation Network, HSDN, for compressing reasoning chains while preserving answer accuracy and logical coherence. The framework combines semantic segmentation, dependency graph construction, dual encoder importance scoring, constrained segment selection, and local boundary rewriting. A frozen Qwen3 4B model is used only for feature extraction and final answer generation, while the compression process remains structured and interpretable. On the AFAC2025 benchmark, HSDN achieves 91.0% accuracy with 68.4% compression, outperforming strong compression baselines in overall score and reasoning coherence. The results show that graph guided compression is effective for high stakes financial reasoning tasks.

cs.AI↗
arXiv2026

The GKZ hypergeometric $\mathcal D$-module

For an $(n\times N)$-matrix $A$ of rank $n$ with integer entries, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the $A$-hypergeometric system. We define the stable GKZ hypergeometric $\mathcal D$-module using cohomological functors, which is closely related to the $A$-hypergeometric $\mathcal D$-module and the $\mathcal D$-module underlying the better behaved GKZ system introduced by Borisov and Horja. We prove the stable GKZ hypergeometric $\mathcal D$-module is holonomic and is an integrable connection of rank $n!\mathrm{vol}(\Delta_\infty)$ on the Zariski open subset parametrizing nondegenerate Laurent polynomials, where $\Delta_\infty$ is the Newton polytope at $\infty$.

math.AG↗
arXiv2025

Companion Agents: A Table-Information Mining Paradigm for Text-to-SQL

Large-scale Text-to-SQL benchmarks such as BIRD typically assume complete and accurate database annotations as well as readily available external knowledge, which fails to reflect common industrial settings where annotations are missing, incomplete, or erroneous. This mismatch substantially limits the real-world applicability of state-of-the-art (SOTA) Text-to-SQL systems. To bridge this gap, we explore a database-centric approach that leverages intrinsic, fine-grained information residing in relational databases to construct missing evidence and improve Text-to-SQL accuracy under annotation-scarce conditions. Our key hypothesis is that when a query requires multi-step reasoning over extensive table information, existing methods often struggle to reliably identify and utilize the truly relevant knowledge. We therefore propose to "cache" query-relevant knowledge on the database side in advance, so that it can be selectively activated at inference time. Based on this idea, we introduce Companion Agents (CA), a new Text-to-SQL paradigm that incorporates a group of agents accompanying database schemas to proactively mine and consolidate hidden inter-table relations, value-domain distributions, statistical regularities, and latent semantic cues before query generation. Experiments on BIRD under the fully missing evidence setting show that CA recovers +4.49 / +4.37 / +14.13 execution accuracy points on RSL-SQL / CHESS / DAIL-SQL, respectively, with larger gains on the Challenging subset +9.65 / +7.58 / +16.71. These improvements stem from CA's automatic database-side mining and evidence construction, suggesting a practical path toward industrial-grade Text-to-SQL deployment without reliance on human-curated evidence.

cs.CL↗
arXiv2025

Memory-Augmented Knowledge Fusion with Safety-Aware Decoding for Domain-Adaptive Question Answering

Domain-specific question answering (QA) systems for services face unique challenges in integrating heterogeneous knowledge sources while ensuring both accuracy and safety. Existing large language models often struggle with factual consistency and context alignment in sensitive domains such as healthcare policies and government welfare. In this work, we introduce Knowledge-Aware Reasoning and Memory-Augmented Adaptation (KARMA), a novel framework designed to enhance QA performance in care scenarios. KARMA incorporates a dual-encoder architecture to fuse structured and unstructured knowledge sources, a gated memory unit to dynamically regulate external knowledge integration, and a safety-aware controllable decoder that mitigates unsafe outputs using safety classification and guided generation techniques. Extensive experiments on a proprietary QA dataset demonstrate that KARMA outperforms strong baselines in both answer quality and safety. This study offers a comprehensive solution for building trustworthy and adaptive QA systems in service contexts.

cs.CL↗
arXiv2025

ROSBag MCP Server: Analyzing Robot Data with LLMs for Agentic Embodied AI Applications

Agentic AI systems and Physical or Embodied AI systems have been two key research verticals at the forefront of Artificial Intelligence and Robotics, with Model Context Protocol (MCP) increasingly becoming a key component and enabler of agentic applications. However, the literature at the intersection of these verticals, i.e., Agentic Embodied AI, remains scarce. This paper introduces an MCP server for analyzing ROS and ROS 2 bags, allowing for analyzing, visualizing and processing robot data with natural language through LLMs and VLMs. We describe specific tooling built with robotics domain knowledge, with our initial release focused on mobile robotics and supporting natively the analysis of trajectories, laser scan data, transforms, or time series data. This is in addition to providing an interface to standard ROS 2 CLI tools ("ros2 bag list" or "ros2 bag info"), as well as the ability to filter bags with a subset of topics or trimmed in time. Coupled with the MCP server, we provide a lightweight UI that allows the benchmarking of the tooling with different LLMs, both proprietary (Anthropic, OpenAI) and open-source (through Groq). Our experimental results include the analysis of tool calling capabilities of eight different state-of-the-art LLM/VLM models, both proprietary and open-source, large and small. Our experiments indicate that there is a large divide in tool calling capabilities, with Kimi K2 and Claude Sonnet 4 demonstrating clearly superior performance. We also conclude that there are multiple factors affecting the success rates, from the tool description schema to the number of arguments, as well as the number of tools available to the models. The code is available with a permissive license at https://github.com/binabik-ai/mcp-rosbags.

cs.RO↗
arXiv2025

Human or Robot? Evidence from Last-Mile Delivery Service

As platforms increasingly deploy robots alongside human labor in last-mile logistics, little is known about how contextual features like product attributes, environmental conditions, and psychological mechanisms shape consumer preference in real-world settings. To address this gap, this paper conducts an empirical study on consumer choice between human versus robot service, analyzing 241,517 package-level choices from Alibaba's last-mile delivery stations. We identify how product privacy sensitivity, product value, and environmental complexity affect consumer preference. Our findings reveal that consumers are significantly more likely to choose robot delivery for privacy-sensitive packages (11.49%) and high-value products (0.97% per 1% increase in value), but prefer human couriers under adverse weather conditions (1.63%). These patterns are robust to alternative specifications and controls. These results also underscore that delivery choices are shaped not only by functional considerations but also by psychological concerns, highlighting the need for context-aware service design that aligns strategies with consumer perceptions.

econ.GN↗
arXiv2025

Towards Embodied Agentic AI: Review and Classification of LLM- and VLM-Driven Robot Autonomy and Interaction

Foundation models, including large language models (LLMs) and vision-language models (VLMs), have recently enabled novel approaches to robot autonomy and human-robot interfaces. In parallel, vision-language-action models (VLAs) or large behavior models (LBMs) are increasing the dexterity and capabilities of robotic systems. This survey paper reviews works that advance agentic applications and architectures, including initial efforts with GPT-style interfaces and more complex systems where AI agents function as coordinators, planners, perception actors, or generalist interfaces. Such agentic architectures allow robots to reason over natural language instructions, invoke APIs, plan task sequences, or assist in operations and diagnostics. In addition to peer-reviewed research, due to the fast-evolving nature of the field, we highlight and include community-driven projects, ROS packages, and industrial frameworks that show emerging trends. We propose a taxonomy for classifying model integration approaches and present a comparative analysis of the role that agents play in different solutions in today's literature.

cs.RO↗
arXiv2025

Consistency between Bulk and Boundary Causalities in Asymptotically Anti-de Sitter Spacetimes

We investigate the consistency between bulk and boundary causalities in static, spherically symmetric, asymptotically anti-de Sitter (AdS) spacetimes. We derive a general formula that provides sufficient conditions for time advance, where bulk propagation arrives earlier than any boundary propagation. As an application, we show that in Reissner--Nordstr\"{o}m--anti de Sitter spacetime, no geodesic satisfies the sufficient conditions for time advance even in the super-extremal case. Furthermore, we demonstrate that the Einstein--Euler--Heisenberg theory exhibits time advance when one or a linear combination of the coupling constants is positive and below an upper bound determined by the AdS length scale.

gr-qc↗
arXiv2025

Research on the Design of a Short Video Recommendation System Based on Multimodal Information and Differential Privacy

With the rapid development of short video platforms, recommendation systems have become key technologies for improving user experience and enhancing platform engagement. However, while short video recommendation systems leverage multimodal information (such as images, text, and audio) to improve recommendation effectiveness, they also face the severe challenge of user privacy leakage. This paper proposes a short video recommendation system based on multimodal information and differential privacy protection. First, deep learning models are used for feature extraction and fusion of multimodal data, effectively improving recommendation accuracy. Then, a differential privacy protection mechanism suitable for recommendation scenarios is designed to ensure user data privacy while maintaining system performance. Experimental results show that the proposed method outperforms existing mainstream approaches in terms of recommendation accuracy, multimodal fusion effectiveness, and privacy protection performance, providing important insights for the design of recommendation systems for short video platforms.

cs.IR↗
arXiv2024

Research on Optimizing Real-Time Data Processing in High-Frequency Trading Algorithms using Machine Learning

High-frequency trading (HFT) represents a pivotal and intensely competitive domain within the financial markets. The velocity and accuracy of data processing exert a direct influence on profitability, underscoring the significance of this field. The objective of this work is to optimise the real-time processing of data in high-frequency trading algorithms. The dynamic feature selection mechanism is responsible for monitoring and analysing market data in real time through clustering and feature weight analysis, with the objective of automatically selecting the most relevant features. This process employs an adaptive feature extraction method, which enables the system to respond and adjust its feature set in a timely manner when the data input changes, thus ensuring the efficient utilisation of data. The lightweight neural networks are designed in a modular fashion, comprising fast convolutional layers and pruning techniques that facilitate the expeditious completion of data processing and output prediction. In contrast to conventional deep learning models, the neural network architecture has been specifically designed to minimise the number of parameters and computational complexity, thereby markedly reducing the inference time. The experimental results demonstrate that the model is capable of maintaining consistent performance in the context of varying market conditions, thereby illustrating its advantages in terms of processing speed and revenue enhancement.

cs.LG↗
arXiv2024

Hypergeometric $\mathcal D$-modules and exponential sums for reductive groups

We define the hypergeometric exponential sum associated to a family of representations of a reductive group over a finite field. We introduce the hypergeometric $\ell$-adic sheaf to describe the hypergeometric exponential sum. Motivated by the definition of the hypergeometric sheaf, we introduce the hypergeometric $\mathcal D$-module, prove it is holonomic and estimate its rank. Using the theory of the Fourier transform for vector bundles over a general base developed by Wang, we show how the hypergeometric $\mathcal D$-module controls the general behavior of the hypergeometric sheaf. We apply our results to the estimation of the hypergeometric exponential sum.

math.AG↗
arXiv2024

Unambiguous identification of the indirect band nature of atomically thin hexagonal boron nitride

Atomically thin hexagonal boron nitride (h-BN), especially monolayer, has garnered increasing attention due to its intriguing optical and light-matter-interaction properties. However, its intrinsic optical properties and electronic band structure, have long remained elusive. In this study, near-resonance excited deep-UV photoluminescence/Raman spectroscopy and deep-UV reflectance contrast spectroscopy are utilized to experimentally investigate the optical properties of atomically thin h-BN across various layer numbers. It is revealed that the absence of luminescence in 1-3 layers h-BN is indicative of their indirect band gap nature, rectifying previously adopted identification of a direct band gap in monolayer BN. Notably, band-edge luminescence signals and indirect bandgap absorption start to appear in 4-layer, and the luminescence intensity increases with the number of layers, suggesting that interlayer interactions and periodicity along the z-axis enhance phonon-assisted indirect bandgap transition, even in the 4-layer case, and furthermore indicating the formation process of flat bands at the K and M valleys as the periodicity along the z direction increases. Additionally, the prominent resonance Raman signals in atomically thin h-BN underscore strong electron-phonon coupling in this material.

cond-mat.mtrl-sci↗
arXiv2024

DataGpt-SQL-7B: An Open-Source Language Model for Text-to-SQL

In addressing the pivotal role of translating natural language queries into SQL commands, we propose a suite of compact, fine-tuned models and self-refine mechanisms to democratize data access and analysis for non-expert users, mitigating risks associated with closed-source Large Language Models. Specifically, we constructed a dataset of over 20K sample for Text-to-SQL as well as the preference dateset, to improve the efficiency in the domain of SQL generation. To further ensure code validity, a code corrector was integrated into the model. Our system, DataGpt-sql, achieved 87.2\% accuracy on the spider-dev, respectively, showcasing the effectiveness of our solution in text-to-SQL conversion tasks. Our code, data, and models are available at \url{https://github.com/CainiaoTechAi/datagpt-sql-7b}

cs.AI↗
arXiv2024

The exotic inverted Kloosterman sum

Let $B$ be a product of finitely many finite fields containing $\mathbb F_q$, $\psi:\mathbb F_q\to \overline{\mathbb Q}_\ell^*$ a nontrivial additive character, and $\chi: B^*\to \overline{\mathbb Q}_\ell^*$ a multiplicative character. Katz introduced the so-called exotic inverted Kloosterman sum \begin{eqnarray*} \mathrm{EIK}(\mathbb F_q, a):=\sum_{\substack{x\in B^* \\ \mathrm{Tr}_{B/\mathbb F_q}(x)\not =0\\ \mathrm{N}_{B/\mathbb F_q}(x)=a}} \chi(x)\psi\Big(\frac{1}{\mathrm{Tr}_{B/\mathbb F_q}(x)}\Big), \ \ a\in \mathbb F_q^*. \end{eqnarray*} We estimate this sum using $\ell$-adic cohomology theory. Our main result is that, up to a trivial term, the associated exotic inverted Kloosterman sheaf is lisse of rank at most $2(n+1)$ and mixed of weight at most $n$, where $n+1 = \dim_{\mathbb F_q}B$. Up to a trivial main term, this gives the expected square root cancellation.

math.NT↗
arXiv2024

Equidistribution of Kloosterman sums over function fields

We prove the Sato--Tate distribution of Kloosterman sums over function fields with explicit error terms, when the places vary in arithmetic progressions or short intervals. A joint Sato--Tate distribution of two ``different" exponential sums is also proved.

math.NT↗