arXiv subjects

Hao Shen

Publications and source records attributed to Hao Shen.

At least 37 records · Page 2Linked to original sources

arXiv2026

In-Situ Polarimetry in Collimated Magneto-Infrared Spectroscopy System

Magneto-infrared spectroscopy under strong magnetic fields provides a powerful probe of Landau quantization and field-induced collective excitations, yet its full potential has long been constrained by the lack of in-situ polarization control, because the highly divergent infrared beam propagating through narrow light tubes undergoes multiple wall reflections, leading to severe polarization degradation. Here we report a collimated magneto-infrared spectroscopy system that integrates continuous in-situ polarimetry. The system employs incident and exit collimation chambers forming a Kepler type optical architecture, which converts the large-aperture FTIR output into a low-divergence beam and strongly suppresses multi-reflection trajectories inside long gold-plated light tubes, thereby enhancing both optical throughput and polarization fidelity. A remotely controlled polarization module, consisting of an automated linear polarizer and a switchable Fresnel rhomb positioned entirely outside the high-field region, enables continuous in-situ tuning between linear, circular, and arbitrary elliptical polarization states without thermal cycling, manual realignment, or breaking vacuum. Interchangeable compact focusing modules further support Faraday and Voigt geometries in both transmission and reflection experiments within a 50 mm magnet bore, providing efficient beam focusing and signal collection while maintaining polarization fidelity. The setup achieves a minimum root-mean-square noise of 0.0033%, an average noise of 0.0082%, and a linear polarization extinction ratio up to 40:1. We demonstrate the capability through continuous in-situ linear polarimetry and broadband circular polarimetry in the magneto-infrared spectroscopy of various single crystals. This platform establishes a robust experimental framework for in-situ polarization-resolved magneto-infrared spectroscopy.

physics.ins-det↗

arXiv2026

Geometry-Aware Fisheye-LiDAR Fusion for Robust 3D Object Detection in Low-Overlap Setups

As autonomous systems expand from capital-intensive robotaxis to cost-sensitive logistics, sensor configurations are increasingly optimized for coverage-per-cost. A prevalent sparse-view setup utilizes dual-fisheye cameras with a roof-mounted LiDAR, introducing severe geometric challenges: extreme radial distortion, minimal overlap, and misalignment between spherical projections and rectilinear grids. BEV fusion algorithms typically force image and point cloud modalities into unified Cartesian grids early in the pipeline, causing significant feature distortion and information loss for wide-view fisheye cameras. To address this, we propose a Geometry-Aware Hybrid Fusion (GA-HF) framework that explicitly accounts for fisheye geometry and BEV feature distortion, where fisheye features are lifted into a polar BEV grid via a Distortion-Aware Lift-Splat-Shoot (LSS) module to preserve native angular density, while LiDAR features are processed in native Cartesian space for metric fidelity of bounding box regression. To bridge these heterogeneous streams, we introduce a Dual-Attention Warping Correction module that applies spatial and channel attention to the warped camera features before fusion, explicitly suppressing artifacts in low-quality peripheral regions while enhancing high-quality semantic cues. GA-HF is evaluated on three benchmarks: KITTI-360, Dur360BEV, and Fisheye3DOD datasets. To the best of our knowledge, it is the first approach to explore LiDAR-fisheye camera fusion. On KITTI-360, GA-HF improves NDS by 4.2% over Cartesian baselines; on Dur360BEV, it surpasses both LiDAR-only and BEVFusion, while significantly reducing orientation error despite the geometric distortions; on Fisheye3DOD, it attains the highest detection score among all fusion methods.

cs.CV↗

arXiv2026

Are Large Language Models Reliable Reviewers? A Benchmark for Error Detection in Financial Documents

Ensuring the accuracy of financial documents is critical for economic analysis, regulatory compliance, and corporate decision-making. Several studies have shown that Large Language Models (LLMs) perform well in many financial tasks, such as stock price movements and financial analytics. However, a critical task remains unexplored: the ability of LLMs to identify errors in financial documents. In this paper, we introduce \textbf{FinED-Bench}, the first publicly \textbf{Bench}mark for \textbf{Fin}ancial \textbf{E}rror \textbf{D}etection across three levels of cognitive complexity. FinED-Bench covers nine real-world financial scenarios, and includes over 900 documents reported in 2025 that are unseen by existing language models. We detail the benchmark construction process and evaluate several advanced LLMs (e.g., GPT-4o, Qwen3-14B) on this tasks, which requires both financial domain knowledge and reasoning capabilities. Experimental results show that current LLMs still struggle with this task, especially in high-complexity cases. Besides, supervised fine-tuning can significantly improve the performance of weaker LLMs on this task. Our data and code are available at https://github.com/hedyHe/FinED-Bench.

cs.CL↗

arXiv2026

Mechanistic Independence: A Principle for Identifiable Disentangled Representations

Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through mechanistic independence, which characterizes latent factors by how they act on observed variables rather than by their latent distribution. This perspective is invariant to changes of the latent density, even when such changes induce statistical dependencies among factors. Within this framework, we propose several related independence criteria -- ranging from support-based and sparsity-based to higher-order conditions -- and show that each yields identifiability of latent subspaces, even under nonlinear, non-invertible mixing. We further establish a hierarchy among these criteria and provide a graph-theoretic characterization of latent subspaces as connected components. Together, these results clarify the conditions under which disentangled representations can be identified without relying on statistical assumptions.

cs.LG↗

arXiv2026

GenericAgent: A Token-Efficient Self-Evolving LLM Agent via Contextual Information Density Maximization (V1.0)

Long-horizon large language model (LLM) agents are fundamentally limited by context. As interactions become longer, tool descriptions, retrieved memories, and raw environmental feedback accumulate and push out the information needed for decision-making. At the same time, useful experience gained from tasks is often lost across episodes. We argue that long-horizon performance is determined not by context length, but by how much decision-relevant information is maintained within a finite context budget. We present GenericAgent (GA), a general-purpose, self-evolving LLM agent system built around a single principle: context information density maximization. GA implements this through four closely connected components: a minimal atomic tool set that keeps the interface simple, a hierarchical on-demand memory that only shows a small high-level view by default, a self-evolution mechanism that turns verified past trajectories into reusable SOPs and executable code, and a context truncation and compression layer that maintains information density during long executions. Across task completion, tool use efficiency, memory effectiveness, self-evolution, and web browsing, GA consistently outperforms leading agent systems while using significantly fewer tokens and interactions, and it continues to evolve over time. Project: https://github.com/lsdefine/GenericAgent

cs.CL↗

arXiv2026

Formalizing Wu-Ritt Method in Lean 4

We formalize the Wu-Ritt characteristic set method for the triangular decomposition of polynomial systems in the Lean 4 theorem prover. Our development includes the core algebraic notions of the method, such as polynomial initials, orders, pseudo-division, pseudo-remainders with respect to a polynomial or a triangular set, and standard and weak ascending sets. On this basis, we formalize algorithms for computing basic sets, characteristic sets, and zero decompositions, and prove their termination and correctness. In particular, we formalize the well-ordering principle relating a polynomial system to its characteristic set and verify that zero decomposition expresses the zero set of the original system as a union of zero sets of triangular sets away from the zeros of the corresponding initials. This work provides a machine-checked verification of Wu-Ritt's method in Lean 4 and establishes a foundation for certified polynomial system solving and geometric theorem proving.

math.AC↗

arXiv2026

Automated Tactics for Polynomial Reasoning in Lean 4

Applying Gröbner basis theory to concrete problems in Lean 4 remains difficult since the current formalization of multivariate polynomials is based on a non-computable representation and is therefore not suitable for efficient symbolic computation. As a result, computing Gröbner bases directly inside Lean is impractical for realistic examples. To address this issue, we propose a certificate-based approach that combines external computer algebra systems, such as SageMath or SymPy, with formal verification in Lean 4. Our approach uses a computable representation of multivariate polynomials in Lean to import and verify externally generated Gröbner basis computations. The external solver carries out the main algebraic computations, while the returned results are verified inside Lean. Based on this method, we develop automated tactics that transfer polynomial data between Lean and the external system and certify the returned results. These tactics support tasks such as remainder verification, Gröbner basis checking, ideal equality, and ideal or radical membership. This work provides a practical way to integrate external symbolic computation into Lean 4 while preserving the reliability of formal proof.

cs.LO↗

arXiv2026

Invariant measure and universality of the 2D Yang-Mills Langevin dynamic

We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge-fixing, and Bourgain's method for invariant measures. Several corollaries are presented including a gauge-fixed decomposition of the YM measure into a Gaussian free field and an almost Lipschitz remainder, and a proof of universality for the YM measure that we derive from a universality for the Langevin dynamic for a wide class of discrete approximations. The latter includes standard lattice gauge theories associated to Wilson, Villain, and Manton actions. An important step in the argument, which is of independent interest, is a proof of uniqueness for the mass renormalisation of the gauge-covariant continuum Langevin dynamic, which allows us to identify the limit of discrete approximations. This latter result relies on Euler estimates for singular SPDEs and for Young ODEs arising from Wilson loops.

math.PR↗

arXiv2026

Benchmarking Multi-View BEV Object Detection with Mixed Pinhole and Fisheye Cameras

Modern autonomous driving systems increasingly rely on mixed camera configurations with pinhole and fisheye cameras for full view perception. However, Bird's-Eye View (BEV) 3D object detection models are predominantly designed for pinhole cameras, leading to performance degradation under fisheye distortion. To bridge this gap, we introduce a multi-view BEV detection benchmark with mixed cameras by converting KITTI-360 into nuScenes format. Our study encompasses three adaptations: rectification for zero-shot evaluation and fine-tuning of nuScenes-trained models, distortion-aware view transformation modules (VTMs) via the MEI camera model, and polar coordinate representations to better align with radial distortion. We systematically evaluate three representative BEV architectures, BEVFormer, BEVDet and PETR, across these strategies. We demonstrate that projection-free architectures are inherently more robust and effective against fisheye distortion than other VTMs. This work establishes the first real-data 3D detection benchmark with fisheye and pinhole images and provides systematic adaptation and practical guidelines for designing robust and cost-effective 3D perception systems. The code is available at https://github.com/CesarLiu/FishBEVOD.git.

cs.CV↗

arXiv2026

PII-Bench: Evaluating Query-Aware Privacy Protection Systems

The widespread adoption of Large Language Models (LLMs) has raised significant privacy concerns regarding the exposure of personally identifiable information (PII) in user prompts. To address this challenge, we propose a query-unrelated PII masking strategy and introduce PII-Bench, the first comprehensive evaluation framework for assessing privacy protection systems. PII-Bench comprises 2,842 test samples across 55 fine-grained PII categories, featuring diverse scenarios from single-subject descriptions to complex multi-party interactions. Each sample is carefully crafted with a user query, context description, and standard answer indicating query-relevant PII. Our empirical evaluation reveals that while current models perform adequately in basic PII detection, they show significant limitations in determining PII query relevance. Even state-of-the-art LLMs struggle with this task, particularly in handling complex multi-subject scenarios, indicating substantial room for improvement in achieving intelligent PII masking.

cs.CR↗

arXiv2026

ScholarGym: Benchmarking Large Language Model Capabilities in the Information-Gathering Stage of Deep Research

Large language models have advanced from single-turn question answering to deep research systems that iteratively decompose research questions, invoke retrieval tools, and synthesize information across multiple rounds. Evaluating such systems typically involves scoring their final research reports holistically, but this end-to-end paradigm tightly couples the language model's decision-making, workflow design, and environmental feedback, precluding decomposable analysis of individual components. We introduce ScholarGym, an evaluation environment that isolates the information-gathering stage of deep research on academic literature. Under a unified workflow, ScholarGym decomposes the research process into three explicit stages -- Query Planning, Tool Invocation, and Relevance Assessment -- and evaluates each against 2,536 expert-annotated queries over a static corpus of 570K papers with deterministic retrieval. Systematic experiments reveal that iterative query decomposition yields 2.9--3.3$\times$ F1 gains over single-query retrieval, models with extended thinking trade recall for precision, and Query Planning quality together with Relevance Assessment constitute dual bottlenecks that separate proprietary from open-source model performance.

cs.AI↗

arXiv2026

Formalizing Gröbner Basis Theory in Lean

We present a formalization of Gröbner basis theory in Lean 4, built on top of Mathlib's infrastructure for multivariate polynomials and monomial orders. Our development covers the core foundations of Gröbner basis theory, including polynomial division with remainder, Buchberger's criterion, and the existence and uniqueness of reduced Gröbner bases. We develop the theory uniformly for polynomial rings indexed by arbitrary types, enabling the treatment of Gröbner bases in rings with infinitely many variables. Furthermore, we connect the finite and infinite settings by showing that infinite-variable reduced Gröbner bases can be characterized via reduced Gröbner bases on finite-variable subrings through monomial-order embeddings and filter-based limit constructions.

math.AC↗

arXiv2026

Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold

We study the sine-Gordon measure defined on each homotopy class. The energy space decomposes into infinitely many such classes indexed by the topological degree $Q \in \mathbf{Z}$. Even though the sine-Gordon action admits no minimizer in homotopy classes with $|Q| \ge 2$, we prove that the Gibbs measure on each class nevertheless concentrates and exhibits Ornstein-Uhlenbeck fluctuations near the multi-soliton manifold in the joint low-temperature and infinite-volume limit. Moreover, we show that soliton collisions are unlikely events, so that typical states consist of solitons separated at an appropriate scale. Finally, we identify the joint distribution of the multi-soliton centers as the ordered statistics of independent uniform random variables, so that each soliton's location follows a Beta distribution.

math.PR↗

arXiv2026

Human-AI Co-Embodied Intelligence for Scientific Experimentation and Manufacturing

Scientific experimentation and manufacturing rely on prolonged protocol development and complex, multi-step implementation, which require continuous human expertise for precise execution and decision-making, limiting interpretability and scalability. Here, we introduce human-artificial intelligence (AI) co-embodied intelligence, a new form of physical AI that unites human researchers, agentic AI, and wearable hardware. In this paradigm, humans provide precise execution, while agentic AI contributes contextual reasoning, adaptive planning, and analysis. The wearable interface continuously captures experimentation and manufacturing, facilitating seamless communication between humans and AI. We instantiate this paradigm in a microfabrication cleanroom, leading to the agentic-physical experimentation (APEX) system which understands fabrication procedure with accuracy 51% higher than state-of-the-art multimodal large language models/vision language models (LLMs/VLMs), detects and corrects fabrication errors in real-time, and transfers procedural expertise to novice users. Critically, APEX system enables the co-development of fabrication protocols in cleanrooms, overcoming the incompatibility of elastomeric materials in standard microfabrication processes and enabling previously unattainable fabrication outcomes, as demonstrated by the wafer-scale realization of brain-level soft neural probe capable of single-unit-resolution neural recording. These results establish the human-AI co-embodied intelligence that extends agentic reasoning beyond computation into the physical domain, transforming scientific experimentation and manufacturing into autonomous, traceable, interpretable and scalable processes.

cs.AI↗

arXiv2026

An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we present a unifying framework with topics in causal inference to make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce bias in causal effect estimation arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for mitigating confounding bias and improving predictive performance across interventions even when certain IV properties are relaxed. Finally, we cast parameterized DA as an IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.

cs.LG↗

arXiv2026

Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem

Weight Space Learning (WSL), which frames neural network weights as a data modality, is an emerging field with potential for tasks like meta-learning or transfer learning. Particularly, Implicit Neural Representations (INRs) provide a convenient testbed, where each set of weights determines the corresponding individual data sample as a mapping from coordinates to contextual values. So far, a precise theoretical explanation for the mechanism of encoding semantics of data into network weights is still missing. In this work, we deploy the Implicit Function Theorem (IFT) to establish a rigorous mapping between the data space and its latent weight representation space. We analyze a framework that maps instance-specific embeddings to INR weights via a shared hypernetwork, achieving performance competitive with existing baselines on downstream classification tasks across 2D and 3D datasets. These findings offer a theoretical lens for future investigations into network weights.

cs.LG↗

arXiv2026

Cross-Level Sensor Fusion with Object Lists via Transformer for 3D Object Detection

In automotive sensor fusion systems, smart sensors and Vehicle-to-Everything (V2X) modules are commonly utilized. Sensor data from these systems are typically available only as processed object lists rather than raw sensor data from traditional sensors. Instead of processing other raw data separately and then fusing them at the object level, we propose an end-to-end cross-level fusion concept with Transformer, which integrates highly abstract object list information with raw camera images for 3D object detection. Object lists are fed into a Transformer as denoising queries and propagated together with learnable queries through the latter feature aggregation process. Additionally, a deformable Gaussian mask, derived from the positional and size dimensional priors from the object lists, is explicitly integrated into the Transformer decoder. This directs attention toward the target area of interest and accelerates model training convergence. Furthermore, as there is no public dataset containing object lists as a standalone modality, we propose an approach to generate pseudo object lists from ground-truth bounding boxes by simulating state noise and false positives and negatives. As the first work to conduct cross-level fusion, our approach shows substantial performance improvements over the vision-based baseline on the nuScenes dataset. It demonstrates its generalization capability over diverse noise levels of simulated object lists and real detectors.

cs.CV↗

arXiv2026

Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs

Local solutions to the 3D stochastic quantisation equations of Yang-Mills-Higgs were constructed in (arXiv:2201.03487), and it was shown that, in the limit of smooth mollifications, there exists a mass renormalisation of the Yang-Mills field such that the solution is gauge covariant. In this paper we prove uniqueness of the mass renormalisation that leads to gauge covariant solutions. This strengthens the main result of (arXiv:2201.03487), and is potentially important for the identification of the limit of other approximations, such as lattice dynamics. Our proof relies on systematic short-time expansions of singular stochastic PDEs and of regularised Wilson loops. We also strengthen the recently introduced state spaces to allow finer control on line integrals appearing in expansions of Wilson loops.

math.PR↗