arXiv subjects

Bing Xie

Publications and source records attributed to Bing Xie.

At least 19 recordsLinked to original sources

arXiv2026

Bargmann Invariants Are Insufficient for Complete Local-Unitary Orbit Discrimination

Bargmann invariants constructed from a bipartite density operator and its two lifted marginals are polynomial invariants of local-unitary conjugation. We determine the precise information encoded in these invariants. Whenever one subsystem is a qubit, the ordinary marginal-word family determines the full spectrum of the partial transpose and hence decides whether the state has the positive-partial-transpose property. In $2\otimes2$ and $2\otimes3$ systems, this yields complete separability criteria. For the two-qubit system, a finite subfamily additionally separates local-unitary orbits, and a finite extension generates the polynomial invariant ring. These three tasks already diverge for qubit-qutrit states: we exhibit full-rank, locally maximally mixed states that agree on all ordinary marginal-word invariants yet have different operator-Schmidt ranks, together with a quartic correlation invariant that separates them. When both local dimensions are at least three, the analogous collapse on the locally maximally mixed sector produces isospectral pairs consisting of one separable state and one entangled state with negative partial transpose. The ordinary Bargmann algebra therefore coincides with the full local unitary invariant ring if and only if both subsystems are qubits. The missing data are geometric: they encode the placement of global eigenspaces relative to the tensor-product decomposition

quant-ph↗

arXiv2026

Revisiting the invariant ring of two-qubit mixed states

Local unitary equivalence serves as the cornerstone for classifying entanglement in bipartite quantum systems. Mathematically, it reduces to the study of polynomial invariants of the density matrix under the action of local unitary groups. The collection of all such polynomial invariants forms a ring, known as the invariant ring. However, identifying the complete generators of the invariant ring is the central issue. In 2007, for the two-qubit system, King et al fully characterized the structure of the invariant ring and determined its Cohen--Macaulay decomposition. In this paper, we revisit their work, with a focus on the computation of the Molien series and the construction of invariants. On one hand, we rigorously derive the Molien series via explicit contour integration over the maximal torus, filling in all previously omitted computational steps. On the other hand, we systematically construct all invariants using a graphical method, and then reduce the candidate set by applying various identities and algebraic relations, obtaining a generating set consisting of 21 invariants. This paper aims to make this important result more widely accessible to researchers in quantum information and invariant theory through the above discussions.

quant-ph↗

arXiv2026

FeatX: Editing Software by Editing Features for Repository-Level Code Evolution

Large language models (LLMs) are increasingly used for software evolution, yet most interaction paradigms remain code-centric and require manual context management and prompt iteration. We present FeatX, a feature-oriented tool for editing software by editing features. Given an existing repository, FeatX extracts a hierarchical epic-feature structure with explicit feature-to-code mappings, then invokes a three-stage Evolution Agent to translate feature edits into code patches. The workflow is exposed through four coordinated panels. Across a controlled user study and replay experiments on 38 real-world feature-editing commits, FeatX significantly reduces cognitive load and improves usability compared with vanilla ChatGPT. It also achieves a 42.6\% relative improvement in function-level modification localization F1 over strong LLM baselines, at substantially lower cost (\$0.07 in total). The tool and collected dataset are available at https://github.com/a496263365/FeatX/tree/demo, with a demonstration video at https://youtu.be/OZqKZ4Ii-yM.

cs.SE↗

arXiv2026

High-Fidelity 3D Geometric Reconstruction of Pelvic Organs from MRI: A Hybrid Deep Learning and Iterative Optimization Approach

Patient-specific 3D reconstruction of pelvic organ geometry from MRI is important for pelvic floor modeling and downstream patient-specific analysis. However, while previous studies have focused primarily on either image segmentation or downstream use of 3D models, the reconstruction of high-fidelity, high-quality geometries remains labor-intensive and poorly standardized. The study introduced a hybrid deformable shape modeling framework that integrates deep learning prediction with iterative optimization for the reconstruction of the bladder, uterus, and rectum. The framework consists of three core components: a geometry-aware multi-level deep learning architecture that preserves topological consistency of pelvic organs; a two-stage amortized optimization training strategy that balances global shape capture and local surface refinement; and a holistic synergy mechanism--where iterative optimization provides supervision for deep learning during the training phase, and during inference, deep learning rapidly predicts the global organ morphology, followed by iterative optimization to refine local surfaces and mesh quality. This framework demonstrated marked superiority in geometric fidelity than current mainstream deep learning-based organ reconstruction models. For individual anatomical structures, the reconstructed 3D geometries for the bladder, rectum, and uterus achieved significantly lower Chamfer Distance values and higher Dice Similarity Coefficient scores. In addition, while maintaining high computational efficiency, the proposed architecture yielded superior overall volumetric mesh quality. At the patient level, the framework achieved higher mean values for the 10 worst elements for both minSICN and minSIGE compared to traditional geometric post-processing algorithms.

cs.CV↗

arXiv2026

PEEK: Predictive Queue-Informed KV Cache Management for LLM Serving

We present PEEK, a lightweight scheduling and eviction framework for both online (streaming) and offline (batch) LLM serving; this paper focuses on the online regime. PEEK maintains an incremental radix tree over the pending queue, exposing prefix-sharing clusters no existing engine surfaces. A low-overhead dual-walk matches the tree against the engine's prefix cache to yield longest-prefix-match for every waiting request; PEEK then admits cluster pioneers first so siblings inherit the freshly cached prefix, a co-designed eviction hook protects blocks ancestral to queued demand, and a multi-lane stride scheduler bounds starvation. On SGLang and vLLM across five workloads up to 4$\times$H100 (DP=2 over TP=2), PEEK delivers up to 3.0$\times$/2.6$\times$ cache hit, 7.9$\times$/7.1$\times$ TTFT, 6.7$\times$/5.5$\times$ E2E, and 3.6$\times$/4.5$\times$ throughput gains over each engine's strongest stock baseline (SGLang/vLLM), while matching baselines within noise on workloads with no exploitable prefix structure. Wins hold as KV-cache pressure and inference parallelism scale.

cs.DC↗

arXiv2026

Characterization of Maximizers for Sums of the First Two Eigenvalues of Sturm-Liouville Operators

In this paper we study the maximization of the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators with potentials in the noncompact space $L^1$. We prove that there exists a unique potential function achieving the maximum, which is non-negative, piecewise smooth, and symmetric. Using measure differential equations and weak$^*$ convergence, we show that the nonzero part of the maximizer can be determined by the solution to the pendulum equation $\theta'' + \ell \sin\theta = 0 $.

math.DS↗

arXiv2026

Gap Labelling for Almost Periodic Sturm-Liouville Operators

In this paper, we introduce a rotation number for almost periodic Sturm-Liouville operators in the spirit of Johnson and Moser. We then prove the gap labelling theorem in terms of rotation numbers for the operator in question. To do this, we rigorously prove the almost periodicity of Green's functions.

math.SP↗

arXiv2026

Circulant quantum channels and its applications

This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is precisely the set of circulant matrices. This characterization facilitates the analysis of arbitrary $n$-th order Bargmann invariants. Furthermore, we prove that the channel is entanglement-breaking, implying a substantially reduced resource cost for erasing quantum correlations compared to a general mixed-permutation channel. Applications of this channel are also discussed, including the derivation of tighter lower bounds for $\ell_p$-norm coherence and a characterization of its action in bipartite systems.

quant-ph↗

arXiv2026

On Generalized Strong and Norm Resolvent Convergence

We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral projections. In addition, we give some applications to Sturm-Liouville operators.

math.SP↗

arXiv2026

A Survey of Bargmann Invariants: Geometric Foundations and Applications

Bargmann invariants, a class of unitary-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the relative geometry of the projective Hilbert space. This survey offers a comprehensive overview of their theoretical characterization and practical applications, with particular emphasis on recent progress in determining the full structure of their admissible set. The core of this review demonstrates how these invariants serve as a powerful tool for characterizing the intrinsic geometry of the space of quantum states, leading to applications in determining local unitary equivalence and constructing a complete set of polynomial invariants for mixed states. On the operational side, we review the cycle-test quantum circuit for the direct estimation of Bargmann invariants without full state tomography, and demonstrate their utility in witnessing quantum imaginary, discriminating local unitary equivalence, and detecting entanglement via partial-transpose moments---with explicit complete invariant sets provided for two-qubit systems. By connecting fundamental geometric classification with experimentally feasible estimation protocols,this survey establishes Bargmann invariants as indispensable probes of the relational, noncommutative, and geometric structure of quantum states, and identifies key open problems for multipartite high-dimensional systems and for quantum resource theories.

quant-ph↗

arXiv2025

RepoSummary: Feature-Oriented Summarization and Documentation Generation for Code Repositories

Repository summarization is a crucial research question in development and maintenance for software engineering. Existing repository summarization techniques primarily focus on summarizing code according to the directory tree, which is insufficient for tracing high-level features to the methods that collaboratively implement them. To address these limitations, we propose RepoSummary, a feature-oriented code repository summarization approach that simultaneously generates repository documentation automatically. Furthermore, it establishes more accurate traceability links from functional features to the corresponding code elements, enabling developers to rapidly locate relevant methods and files during code comprehension and maintenance. Comprehensive experiments against the state-of-the-art baseline (HGEN) demonstrate that RepoSummary achieves higher feature coverage and more accurate traceability. On average, it increases the rate of completely covered features in manual documentation from 61.2% to 71.1%, improves file-level traceability recall from 29.9% to 53.0%, and generates documentation that is more conceptually consistent, easier to understand, and better formatted than that produced by existing approaches.

cs.SE↗

arXiv2025

Scaling Up Data Parallelism in Decentralized Deep Learning

Although it has been extensively explored in theory, decentralized learning is not yet green-lighted for production use, largely due to a lack of stability, scalability, and generality in large scale DNN training. To shed light on the production use of decentralized learning, this work studies decentralized data parallel training at scale. To this end, we introduce a benchmarking framework, namely DBench, to host both centralized and decentralized DNN training. Building upon DBench, we introduce a benchmarking methodology to uncover the correlations between model accuracy and the variances of parameter tensors by varying communication graphs and training scales. Based on the benchmarking results, we observe that, (1) Similar to centralized learning, decentralized data parallel training also presents the issues of scalability and generality when the training scales up; (2) The model accuracy of decentralized learning is correlated to the number of connections in a communication graph; (3) The model accuracy of decentralized learning is surprisingly sensitive to the variance of parameter tensors across model replicas. Built upon the observations, we propose Ada, a decentralized adaptive approach that performs large scale DNN training following a decentralized SGD method and adapting the communication graph in use dynamically throughout training iterations. We apply Ada on large scale training and observe that Ada can obtain the best convergence rates consistently in decentralized DNN training, and delivers equally or comparably good model accuracy for all sample applications as centralized learning does, even when training ResNet50 for ImageNet-1K on the scale of 1008 GPUs.

cs.LG↗

arXiv2025

Tool-integrated Reinforcement Learning for Repo Deep Search

Issue localization, the process of identifying code locations that need modification to resolve software issues, is a critical yet challenging task in software development. The semantic gap between natural language issue descriptions and faulty code requires complex multi-hop reasoning through code dependencies. Existing LLM-based agents attempt to address this by integrating repository retrieval tools. However, this transforms issue localization into a demanding task we call Repo Deep Search, which requires the LLM to effectively utilize various repository retrieval tools throughout a multi-step reasoning and navigation process. To tackle this challenge, we present ToolTrain, a two-stage tool-integrated training framework combining rejection-sampled supervised fine-tuning and tool-integrated reinforcement learning to enhance LLMs' ability to use retrieval tools for issue localization. Experimental results show that ToolTrain-trained models achieve state-of-the-art performance, with our 32B model even surpassing Claude-3.7 on function-level localization. The results also show that improved localization performance translates to better end-to-end issue resolution performance. This further demonstrates that training for issue localization is a viable and effective strategy for improving automated software development.

cs.SE↗

arXiv2025

One application of Duistermaat-Heckman measure in quantum information theory

While the exact separability probability of 8/33 for two-qubit states under the Hilbert-Schmidt measure has been reported by Huong and Khoi [\href{https://doi.org/10.1088/1751-8121/ad8493}{J.Phys.A:Math.Theor.{\bf57}, 445304(2024)}], detailed derivations remain inaccessible for general audiences. This paper provides a comprehensive, self-contained derivation of this result, elucidating the underlying geometric and probabilistic structures. We achieve this by developing a framework centered on the computation of Hilbert-Schmidt volumes for key components: the quantum state space, relevant flag manifolds, and regular (co)adjoint orbits. Crucially, we establish and leverage the connection between these Hilbert-Schmidt volumes and the symplectic volumes of the corresponding regular co-adjoint orbits, formalized through the Duistermaat-Heckman measure. By meticulously synthesizing these volume computations -- specifically, the ratios defining the relevant probability measures -- we reconstruct and rigorously verify the 8/33 separability probability. Our approach offers a transparent pathway to this fundamental constant, detailing the interplay between symplectic geometry, representation theory, and quantum probability.

quant-ph↗

arXiv2025

Islanding Strategy for Smart Grids Oriented to Resilience Enhancement and Its Power Supply Range Optimization

With the increasing prevalence of distributed generators, islanded operation based on distributed generation is considered a vital means to enhance the reliability and resilience of smart grids. This paper investigates the main factors in islanding partition of smart grids and establishes a mathematical model for islanding division. A method to determine the maximum power supply range of distributed energy resources (DERs) based on the reachability matrix and power circle algorithm is proposed to improve computational efficiency. A dynamic programming method based on breadth-first search (BFS) is used to solve the islanding partition scheme, and a region correction method is applied to modify the maximum power supply area by considering controllable loads and prioritizing critical load restoration, thereby enhancing system resilience. Finally, simulation results verify the effectiveness of the proposed algorithm in improving smart grid resilience.

eess.SY↗

arXiv2025

Issue Retrieval and Verification Enhanced Supplementary Code Comment Generation

Issue reports have been recognized to contain rich information for retrieval-augmented code comment generation. However, how to minimize hallucinations in the generated comments remains significant challenges. In this paper, we propose IsComment, an issue-based LLM retrieval and verification approach for generating method's design rationale, usage directives, and so on as supplementary code comments. We first identify five main types of code supplementary information that issue reports can provide through code-comment-issue analysis. Next, we retrieve issue sentences containing these types of supplementary information and generate candidate code comments. To reduce hallucinations, we filter out those candidate comments that are irrelevant to the code or unverifiable by the issue report, making the code comment generation results more reliable. Our experiments indicate that compared with LLMs, IsComment increases the coverage of manual supplementary comments from 33.6% to 72.2% for ChatGPT, from 35.8% to 88.4% for GPT-4o, and from 35.0% to 86.2% for DeepSeek-V3. Compared with existing work, IsComment can generate richer and more useful supplementary code comments for programming understanding, which is quantitatively evaluated through the MESIA metric on both methods with and without manual code comments.

cs.SE↗

arXiv2025

SoRFT: Issue Resolving with Subtask-oriented Reinforced Fine-Tuning

Mainstream issue-resolving frameworks predominantly rely on commercial models, leading to high costs and privacy concerns. Existing training approaches for issue resolving struggle with poor generalization and fail to fully leverage open-source development resources. We propose Subtask-oriented Reinforced Fine-Tuning (SoRFT), a novel training approach to enhance the issue resolving capability of LLMs. We decomposes issue resolving into structured subtasks: file localization, function localization, line localization, and code edit generation. SoRFT consists of two training stages: (1) rejection-sampled supervised fine-tuning, Chain of Thought (CoT) data is filtered using ground-truth before fine-tuning the LLM, and (2) rule-based reinforcement learning, which leverages PPO with ground-truth based rewards. We evaluate the SoRFT-trained model on SWE-Bench Verified and SWE-Bench Lite, achieving state-of-the-art (SOTA) performance among open-source models (e.g., resolve 21.4% issues on SWE-Bench Verified with SoRFT-Qwen-7B). The experimental results demonstrate that SoRFT significantly enhances issue-resolving performance, improves model generalization, and provides a cost-efficient alternative to commercial models.

cs.SE↗

arXiv2024

Repository Structure-Aware Training Makes SLMs Better Issue Resolver

Language models have been applied to various software development tasks, but the performance varies according to the scale of the models. Large Language Models (LLMs) outperform Small Language Models (SLMs) in complex tasks like repository-level issue resolving, but raise concerns about privacy and cost. In contrast, SLMs are more accessible but under-perform in complex tasks. In this paper, we introduce ReSAT (Repository Structure-Aware Training), construct training data based on a large number of issues and corresponding pull requests from open-source communities to enhance the model's understanding of repository structure and issue resolving ability. We construct two types of training data: (1) localization training data, a multi-level progressive localization data to improve code understanding and localization capability; (2) code edit training data, which improves context-based code editing capability. The evaluation results on SWE-Bench-verified and RepoQA demonstrate that ReSAT effectively enhances SLMs' issue-resolving and repository-level long-context understanding capabilities.

cs.SE↗