arXiv subjects

Peng Lu

Publications and source records attributed to Peng Lu.

At least 55 records · Page 3Linked to original sources

arXiv2025

Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients

It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations with temperature-dependent coefficients in the whole space. When the initial density and the initial temperature are linearly equivalent to some large constant states, we establish the first result on the global existence of large strong solution. Moreover, the optimal decay rates of the solution to its associated equilibrium are established when the initial data belong to $L^{p_0}(\mathbb{R}^3)$ for some $p_0\in[1,2]$.

math.AP↗

arXiv2025

Mamba Modulation: On the Length Generalization of Mamba

The quadratic complexity of the attention mechanism in Transformer models has motivated the development of alternative architectures with sub-quadratic scaling, such as state-space models. Among these, Mamba has emerged as a leading architecture, achieving state-of-the-art results across a range of language modeling tasks. However, Mamba's performance significantly deteriorates when applied to contexts longer than those seen during pre-training, revealing a sharp sensitivity to context length extension. Through detailed analysis, we attribute this limitation to the out-of-distribution behaviour of its state-space dynamics, particularly within the parameterization of the state transition matrix $\mathbf{A}$. Unlike recent works which attribute this sensitivity to the vanished accumulation of discretization time steps, $\exp(-\sum_{t=1}^NΔ_t)$, we establish a connection between state convergence behavior as the input length approaches infinity and the spectrum of the transition matrix $\mathbf{A}$, offering a well-founded explanation of its role in length extension. Next, to overcome this challenge, we propose an approach that applies spectrum scaling to pre-trained Mamba models to enable robust long-context generalization by selectively modulating the spectrum of $\mathbf{A}$ matrices in each layer. We show that this can significantly improve performance in settings where simply modulating $Δ_t$ fails, validating our insights and providing avenues for better length generalization of state-space models with structured transition matrices.

cs.LG↗

arXiv2025

Flow-Aided Flight Through Dynamic Clutters From Point To Motion

Challenges in traversing dynamic clutters lie mainly in the efficient perception of the environmental dynamics and the generation of evasive behaviors considering obstacle movement. Previous solutions have made progress in explicitly modeling the dynamic obstacle motion for avoidance, but this key dependency of decision-making is time-consuming and unreliable in highly dynamic scenarios with occlusions. On the contrary, without introducing object detection, tracking, and prediction, we empower the reinforcement learning (RL) with single LiDAR sensing to realize an autonomous flight system directly from point to motion. For exteroception, a depth sensing distance map achieving fixed-shape, low-resolution, and detail-safe is encoded from raw point clouds, and an environment change sensing point flow is adopted as motion features extracted from multi-frame observations. These two are integrated into a lightweight and easy-to-learn representation of complex dynamic environments. For action generation, the behavior of avoiding dynamic threats in advance is implicitly driven by the proposed change-aware sensing representation, where the policy optimization is indicated by the relative motion modulated distance field. With the deployment-friendly sensing simulation and dynamics model-free acceleration control, the proposed system shows a superior success rate and adaptability to alternatives, and the policy derived from the simulator can drive a real-world quadrotor with safe maneuvers.

cs.RO↗

arXiv2025

PolarGuide-GSDR: 3D Gaussian Splatting Driven by Polarization Priors and Deferred Reflection for Real-World Reflective Scenes

Polarization-aware Neural Radiance Fields (NeRF) enable novel view synthesis of specular-reflection scenes but face challenges in slow training, inefficient rendering, and strong dependencies on material/viewpoint assumptions. However, 3D Gaussian Splatting (3DGS) enables real-time rendering yet struggles with accurate reflection reconstruction from reflection-geometry entanglement, adding a deferred reflection module introduces environment map dependence. We address these limitations by proposing PolarGuide-GSDR, a polarization-forward-guided paradigm establishing a bidirectional coupling mechanism between polarization and 3DGS: first 3DGS's geometric priors are leveraged to resolve polarization ambiguity, and then the refined polarization information cues are used to guide 3DGS's normal and spherical harmonic representation. This process achieves high-fidelity reflection separation and full-scene reconstruction without requiring environment maps or restrictive material assumptions. We demonstrate on public and self-collected datasets that PolarGuide-GSDR achieves state-of-the-art performance in specular reconstruction, normal estimation, and novel view synthesis, all while maintaining real-time rendering capabilities. To our knowledge, this is the first framework embedding polarization priors directly into 3DGS optimization, yielding superior interpretability and real-time performance for modeling complex reflective scenes.

cs.CV↗

arXiv2025

$\text{R}^2\text{R}$: A Route-to-Rerank Post-Training Framework for Multi-Domain Decoder-Only Rerankers

Decoder-only rerankers are central to Retrieval-Augmented Generation (RAG). However, generalist models miss domain-specific nuances in high-stakes fields like finance and law, and naive fine-tuning causes surface-form overfitting and catastrophic forgetting. To address this challenge, we introduce R2R, a domain-aware framework that combines dynamic expert routing with a two-stage training strategy, Entity Abstraction for Generalization (EAG). EAG introduces a counter-shortcut mechanism by masking the most predictive surface cues, forcing the reranker to learn domain-invariant relevance patterns rather than memorizing dataset-specific entities. To efficiently activate domain experts, R2R employs a lightweight Latent Semantic Router that probes internal representations from the frozen backbone decoder to select the optimal LoRA expert per query. Extensive experiments across different reranker backbones and diverse domains (legal, medical, and financial) demonstrate that R2R consistently surpasses generalist and single-domain fine-tuned baselines. Our results confirm that R2R is a model-agnostic and modular approach to domain specialization with strong cross-domain robustness.

cs.CL↗

arXiv2025

Null controllability of damped nonlinear wave equation

In this paper, we investigate the null controllability of nonlinear wave systems. Initially, we employ a combination of the Galerkin method and a fixed point theorem to establish the null controllability for semi-linear wave equations with nonlinear functions that are dependent on velocities, under the geometric control condition. Subsequently, utilizing a novel iterative method, we demonstrate the null controllability for a class of quasi-linear wave systems in a constructive manner. Lastly, we present a control result for a class of fully nonlinear wave systems, serving as an application.

math.AP↗

arXiv2025

When Agents Trade: Live Multi-Market Trading Benchmark for LLM Agents

Although Large Language Model (LLM)-based agents are increasingly used in financial trading, it remains unclear whether they can reason and adapt in live markets, as most studies test models instead of agents, cover limited periods and assets, and rely on unverified data. To address these gaps, we introduce Agent Market Arena (AMA), the first lifelong, real-time benchmark for evaluating LLM-based trading agents across multiple markets. AMA integrates verified trading data, expert-checked news, and diverse agent architectures within a unified trading framework, enabling fair and continuous comparison under real conditions. It implements four agents, including InvestorAgent as a single-agent baseline, TradeAgent and HedgeFundAgent with different risk styles, and DeepFundAgent with memory-based reasoning, and evaluates them across GPT-4o, GPT-4.1, Claude-3.5-haiku, Claude-sonnet-4, and Gemini-2.0-flash. Live experiments on both cryptocurrency and stock markets demonstrate that agent frameworks display markedly distinct behavioral patterns, spanning from aggressive risk-taking to conservative decision-making, whereas model backbones contribute less to outcome variation. AMA thus establishes a foundation for rigorous, reproducible, and continuously evolving evaluation of financial reasoning and trading intelligence in LLM-based agents.

cs.CL↗

arXiv2025

Calibrated Language Models and How to Find Them with Label Smoothing

Recent advances in natural language processing (NLP) have opened up greater opportunities to enable fine-tuned large language models (LLMs) to behave as more powerful interactive agents through improved instruction-following ability. However, understanding how this impacts confidence calibration for reliable model output has not been researched in full. In this work, we examine various open-sourced LLMs, identifying significant calibration degradation after instruction tuning in each. Seeking a practical solution, we look towards label smoothing, which has been shown as an effective method to regularize for overconfident predictions but has yet to be widely adopted in the supervised fine-tuning (SFT) of LLMs. We first provide insight as to why label smoothing is sufficient to maintain calibration throughout the SFT process. However, settings remain where the effectiveness of smoothing is severely diminished, in particular the case of large vocabulary LLMs (LV-LLMs). We posit the cause to stem from the ability to become over-confident, which has a direct relationship with the hidden size and vocabulary size, and justify this theoretically and experimentally. Finally, we address an outstanding issue regarding the memory footprint of the cross-entropy loss computation in the label smoothed loss setting, designing a customized kernel to dramatically reduce memory consumption without sacrificing speed or performance in comparison to existing solutions for non-smoothed losses.

cs.LG↗

arXiv2025

VeritasFi: An Adaptable, Multi-tiered RAG Framework for Multi-modal Financial Question Answering

Retrieval-Augmented Generation (RAG) is becoming increasingly essential for Question Answering (QA) in the financial sector, where accurate and contextually grounded insights from complex public disclosures are crucial. However, existing financial RAG systems face two significant challenges: (1) they struggle to process heterogeneous data formats, such as text, tables, and figures; and (2) they encounter difficulties in balancing general-domain applicability with company-specific adaptation. To overcome these challenges, we present VeritasFi, an innovative hybrid RAG framework that incorporates a multi-modal preprocessing pipeline alongside a cutting-edge two-stage training strategy for its re-ranking component. VeritasFi enhances financial QA through three key innovations: (1) A multi-modal preprocessing pipeline that seamlessly transforms heterogeneous data into a coherent, machine-readable format. (2) A tripartite hybrid retrieval engine that operates in parallel, combining deep multi-path retrieval over a semantically indexed document corpus, real-time data acquisition through tool utilization, and an expert-curated memory bank for high-frequency questions, ensuring comprehensive scope, accuracy, and efficiency. (3) A two-stage training strategy for the document re-ranker, which initially constructs a general, domain-specific model using anonymized data, followed by rapid fine-tuning on company-specific data for targeted applications. By integrating our proposed designs, VeritasFi presents a groundbreaking framework that greatly enhances the adaptability and robustness of financial RAG systems, providing a scalable solution for both general-domain and company-specific QA tasks. Code accompanying this work is available at https://github.com/simplew4y/VeritasFi.git.

cs.IR↗

arXiv2025

MultiFinBen: Benchmarking Large Language Models for Multilingual and Multimodal Financial Application

Real-world financial analysis involves information across multiple languages and modalities, from reports and news to scanned filings and meeting recordings. Yet most existing evaluations of LLMs in finance remain text-only, monolingual, and largely saturated by current models. To bridge these gaps, we present MultiFinBen, the first expert-annotated multilingual (five languages) and multimodal (text, vision, audio) benchmark for evaluating LLMs in realistic financial contexts. MultiFinBen introduces two new task families: multilingual financial reasoning, which tests cross-lingual evidence integration from filings and news, and financial OCR, which extracts structured text from scanned documents containing tables and charts. Rather than aggregating all available datasets, we apply a structured, difficulty-aware selection based on advanced model performance, ensuring balanced challenge and removing redundant tasks. Evaluating 21 leading LLMs shows that even frontier multimodal models like GPT-4o achieve only 46.01% overall, stronger on vision and audio but dropping sharply in multilingual settings. These findings expose persistent limitations in multilingual, multimodal, and expert-level financial reasoning. All datasets, evaluation scripts, and leaderboards are publicly released.

cs.CL↗

arXiv2025

Like Playing a Video Game: Spatial-Temporal Optimization of Foot Trajectories for Controlled Football Kicking in Bipedal Robots

Humanoid robot soccer presents several challenges, particularly in maintaining system stability during aggressive kicking motions while achieving precise ball trajectory control. Current solutions, whether traditional position-based control methods or reinforcement learning (RL) approaches, exhibit significant limitations. Model predictive control (MPC) is a prevalent approach for ordinary quadruped and biped robots. While MPC has demonstrated advantages in legged robots, existing studies often oversimplify the leg swing progress, relying merely on simple trajectory interpolation methods. This severely constrains the foot's environmental interaction capability, hindering tasks such as ball kicking. This study innovatively adapts the spatial-temporal trajectory planning method, which has been successful in drone applications, to bipedal robotic systems. The proposed approach autonomously generates foot trajectories that satisfy constraints on target kicking position, velocity, and acceleration while simultaneously optimizing swing phase duration. Experimental results demonstrate that the optimized trajectories closely mimic human kicking behavior, featuring a backswing motion. Simulation and hardware experiments confirm the algorithm's efficiency, with trajectory planning times under 1 ms, and its reliability, achieving nearly 100 % task completion accuracy when the soccer goal is within the range of -90° to 90°.

cs.RO↗

arXiv2025

MARG: MAstering Risky Gap Terrains for Legged Robots with Elevation Mapping

Deep Reinforcement Learning (DRL) controllers for quadrupedal locomotion have demonstrated impressive performance on challenging terrains, allowing robots to execute complex skills such as climbing, running, and jumping. However, existing blind locomotion controllers often struggle to ensure safety and efficient traversal through risky gap terrains, which are typically highly complex, requiring robots to perceive terrain information and select appropriate footholds during locomotion accurately. Meanwhile, existing perception-based controllers still present several practical limitations, including a complex multi-sensor deployment system and expensive computing resource requirements. This paper proposes a DRL controller named MAstering Risky Gap Terrains (MARG), which integrates terrain maps and proprioception to dynamically adjust the action and enhance the robot's stability in these tasks. During the training phase, our controller accelerates policy optimization by selectively incorporating privileged information (e.g., center of mass, friction coefficients) that are available in simulation but unmeasurable directly in real-world deployments due to sensor limitations. We also designed three foot-related rewards to encourage the robot to explore safe footholds. More importantly, a terrain map generation (TMG) model is proposed to reduce the drift existing in mapping and provide accurate terrain maps using only one LiDAR, providing a foundation for zero-shot transfer of the learned policy. The experimental results indicate that MARG maintains stability in various risky terrain tasks.

cs.RO↗

arXiv2025

Global well-posedness and large-time behavior for three-dimensional magneto-micropolar equations with horizontal dissipation

This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its vertical derivatives required to be sufficiently small in $L^2$ space. Moreover, we obtain the optimal decay rates for the $H^1$-norm of the solution. The proofs of our main results rely on the special structure of the equations and anisotropic Sobolev-type inequalities.

math.AP↗

arXiv2025

Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotion

Reinforcement learning has produced remarkable advances in humanoid locomotion, yet a fundamental dilemma persists for real-world deployment: policies must choose between the robustness of reactive proprioceptive control or the proactivity of complex, fragile perception-driven systems. This paper resolves this dilemma by introducing a paradigm that imbues a purely proprioceptive policy with proactive capabilities, achieving the foresight of perception without its deployment-time costs. Our core contribution is a contrastive learning framework that compels the actor's latent state to encode privileged environmental information from simulation. Crucially, this ``distilled awareness" empowers an adaptive gait clock, allowing the policy to proactively adjust its rhythm based on an inferred understanding of the terrain. This synergy resolves the classic trade-off between rigid, clocked gaits and unstable clock-free policies. We validate our approach with zero-shot sim-to-real transfer to a full-sized humanoid, demonstrating highly robust locomotion over challenging terrains, including 30 cm high steps and 26.5° slopes, proving the effectiveness of our method. Website: https://lu-yidan.github.io/cra-loco.

cs.RO↗

arXiv2025

FR-Net: Learning Robust Quadrupedal Fall Recovery on Challenging Terrains through Mass-Contact Prediction

Fall recovery for legged robots remains challenging, particularly on complex terrains where traditional controllers fail due to incomplete terrain perception and uncertain interactions. We present \textbf{FR-Net}, a learning-based framework that enables quadrupedal robots to recover from arbitrary fall poses across diverse environments. Central to our approach is a Mass-Contact Predictor network that estimates the robot's mass distribution and contact states from limited sensory inputs, facilitating effective recovery strategies. Our carefully designed reward functions ensure safe recovery even on steep stairs without dangerous rolling motions common to existing methods. Trained entirely in simulation using privileged learning, our framework guides policy learning without requiring explicit terrain data during deployment. We demonstrate the generalization capabilities of \textbf{FR-Net} across different quadrupedal platforms in simulation and validate its performance through extensive real-world experiments on the Go2 robot in 10 challenging scenarios. Our results indicate that explicit mass-contact prediction is key to robust fall recovery, offering a promising direction for generalizable quadrupedal skills.

cs.RO↗

arXiv2025

FinSage: A Multi-aspect RAG System for Financial Filings Question Answering

Leveraging large language models in real-world settings often entails a need to utilize domain-specific data and tools in order to follow the complex regulations that need to be followed for acceptable use. Within financial sectors, modern enterprises increasingly rely on Retrieval-Augmented Generation (RAG) systems to address complex compliance requirements in financial document workflows. However, existing solutions struggle to account for the inherent heterogeneity of data (e.g., text, tables, diagrams) and evolving nature of regulatory standards used in financial filings, leading to compromised accuracy in critical information extraction. We propose the FinSage framework as a solution, utilizing a multi-aspect RAG framework tailored for regulatory compliance analysis in multi-modal financial documents. FinSage introduces three innovative components: (1) a multi-modal pre-processing pipeline that unifies diverse data formats and generates chunk-level metadata summaries, (2) a multi-path sparse-dense retrieval system augmented with query expansion (HyDE) and metadata-aware semantic search, and (3) a domain-specialized re-ranking module fine-tuned via Direct Preference Optimization (DPO) to prioritize compliance-critical content. Extensive experiments demonstrate that FinSage achieves an impressive recall of 92.51% on 75 expert-curated questions derived from surpasses the best baseline method on the FinanceBench question answering datasets by 24.06% in accuracy. Moreover, FinSage has been successfully deployed as financial question-answering agent in online meetings, where it has already served more than 1,200 people.

cs.IR↗

arXiv2025

In-between Motion Generation Based Multi-Style Quadruped Robot Locomotion

Quadruped robots face persistent challenges in achieving versatile locomotion due to limitations in reference motion data diversity. To address these challenges, we introduce an in-between motion generation based multi-style quadruped robot locomotion framework. We propose a CVAE based motion generator, synthesizing multi-style dynamically feasible locomotion sequences between arbitrary start and end states. By embedding physical constraints and leveraging joint poses based phase manifold continuity, this component produces physically plausible motions spanning multiple gait modalities while ensuring kinematic compatibility with robotic morphologies. We train the imitation policy based on generated data, which validates the effectiveness of generated motion data in enhancing controller stability and improving velocity tracking performance. The proposed framework demonstrates significant improvements in velocity tracking and deployment stability. We successfully deploy the framework on a real-world quadruped robot, and the experimental validation confirms the framework's capability to generate and execute complex motion profiles, including gallop, tripod, trotting and pacing.

cs.RO↗

arXiv2025

ReGLA: Refining Gated Linear Attention

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage requirements, primarily due to the quadratic computation complexity of softmax attention. To mitigate this issue, linear attention has been designed to reduce the quadratic space-time complexity that is inherent in standard transformers. In this work, we embarked on a comprehensive exploration of three key components that substantially impact the performance of the Gated Linear Attention module: feature maps, normalization, and the gating mechanism. We developed a feature mapping function to address some crucial issues that previous suggestions overlooked. Then we offered further rationale for the integration of normalization layers to stabilize the training process. Moreover, we explored the saturation phenomenon of the gating mechanism and augmented it with a refining module. We conducted extensive experiments and showed our architecture outperforms previous Gated Linear Attention mechanisms in extensive tasks including training from scratch and post-linearization with continual pre-training.

cs.CL↗