arXiv subjects

Zhipeng Deng

Publications and source records attributed to Zhipeng Deng.

17 recordsLinked to original sources

arXiv2026

Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover

Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle \[ T=\text{conv}\{(-c,0),(c,0),(0,s)\},\qquad s=\frac{766}{\sqrt{625565}},\qquad c=\frac{197}{\sqrt{625565}}. \] The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected $\Lambda$-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy $\|R\|<27131/25000$. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally \[ E(T)\ge D:=\frac{82074390584}{84861020075} =0.9671624323094728\ldots \] Hence, the convex universal cover of Moser's worm \[ \frac{\text{area}(T)}{D^2} =\frac{11511821678274125}{44639604443512928} =0.257883595112076188\ldots. \]

math.MG↗

arXiv2026

Test-Time Adaptation for ECG Classification via SQI-Gated Self-Training and Beat-Rhythm Consistency

Deep learning models for electrocardiogram (ECG) classification often suffer from significant performance degradation when deployed in unseen domains due to shifts in acquisition devices and patient populations. Test-time adaptation (TTA) offers a practical solution by adapting models using only unlabeled data at inference time. However, existing TTA methods often underperform on ECG tasks, since naive online updates ignore the hierarchical beat-rhythm structure of cardiac cycles and are vulnerable to signal artifacts, which leads to unstable adaptation and model drift. We propose BeatRhythm-TTA, an ECG-tailored TTA framework that explicitly accounts for ECG's noisy observations and structured beat-rhythm semantics under domain shift. First, to handle pervasive ECG artifacts, we introduce a Signal Quality Index (SQI)-gated adaptation scheme that selectively filters out low-quality signals to prevent harmful updates. Second, to leverage ECG's beat-rhythm semantics, we enforce dual-level consistency so the model preserves beat morphology and rhythm dynamics while adapting to shifted acquisition conditions. Extensive experiments on multi-label ECG diagnosis across three adaptation protocols, using PTB-XL as the source domain and CPSC2018/Georgia as two target domains, demonstrate the effectiveness of our method, yielding an average +2.70% relative improvement in Macro-F1 over the best competing method.

cs.LG↗

arXiv2026

Universal Triangle Covering Curve and Polygonal Chain: Escaping Forest and Fitting Worm

In this paper, we present a general formulation to address the problems of covering curves and polygonal chains with triangle, and fitting these curves into triangle. These problems can be formulated as special cases of Bellman's lost-in-a-forest problem (escaping triangular forest) and Moser's worm problem (covered by triangle). We model and reformulate the problem by keeping the curve stationary while allowing the triangle to translate and rotate. Subsequently, we derive the functional minimization formulation with support function constraints to solve. We also prove the equivalence and convergence of the formulas. Finally, we employ numerical methods and present results for covering curves with arbitrary triangles of various angles. We also present some corollaries and variant results, including closed curves and closed polygonal chains.

math.OC↗

arXiv2026

Revisit escape path for infinite unit strip forest and unit broadworm

Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escape path for the infinite unit-strip forest and unit broadworm by Zalgaller. Earlier studies addressed these problems exclusively through geometric methods. We reformulated the problem as an interval-cover problem and then formulated it as a constrained functional minimization problem. This constrained functional minimization can be directly discretized and subsequently solved as a convex optimization. Furthermore, we extend the analysis of various line segment. Finally, we show that, in the case of a closed escape path for the unit strip, the optimal solution is a curve of constant unit width.

math.OC↗

arXiv2026

Proof and More Variations of Bellman's Lost-in-a-forest Problem

In this paper, based on our previous general formulation and computational solution to Bellman's Lost-in-a-forest Problem, we provide the proof of general solution and obtained more variations and results related to this problem. This paper provides generalized formalized method connecting curve covering, lost-in-the-forest problem, and traveling salesman problem with neighborhoods. We prove the equivalence and convergence. We also provide more results of searching for two lines, connection to Wetzel's unit arc covering problem, variations with closed path, variations in three dimensions, etc. The results include general calculation equations, partial analytical results, and numerical results.

math.OC↗

arXiv2026

VoxShield: Protecting 3D Medical Datasets from Unauthorized Training via Frequency-Aware Inter-Slice Disruption

The release of public 3D medical image segmentation (MIS) datasets accelerates clinical research but simultaneously heightens risks of unauthorized AI model training. While Unlearnable Examples (UE) offer protection by injecting imperceptible perturbations to prevent effective model learning, existing methods primarily target 2D scenarios. They neglect the volumetric spatial correlations and inter-slice anatomical consistency inherent in 3D medical volumes, which serve as critical learning priors for 3D segmentation networks. To bridge this gap, we propose VoxShield, a UE framework that explicitly targets the volumetric inductive biases of 3D networks. Our core insight is that by systematically dismantling the cross-slice continuity that 3D architectures rely on, we can fundamentally impair their spatial aggregation process. Specifically, we introduce an Inter-Slice Frequency Consistency Disruption mechanism that maximizes the spectral divergence between adjacent slices, injecting structural incoherence along the $z$-axis. Complementing this structural attack, a Semantic Prediction Disruption module is incorporated. By maximizing the $\ell_1$ divergence between clean and perturbed logits, it forces the injected noise to penetrate the entire network and corrupt the final semantic mapping. Experiments on BraTS19 and FLARE21 demonstrate that VoxShield successfully degrades 3D segmentation performance, reducing the DSC from 80.0% to near 0.0% and from 88.6% to 6.8%, respectively. All protections are achieved with minimal perturbation ($\epsilon=4/255$) to preserve high visual fidelity. The code is available at https://github.com/KK266299/VoxShield.

cs.CV↗

arXiv2026

VISTA: Variance-Gated Inter-Sequence Test-Time Adaptation for Multi-Sequence MRI Segmentation

Deploying multi-sequence magnetic resonance imaging (MRI) segmentation models to new clinical environments is challenging due to variations in scanners and acquisition protocols. Although existing TTA methods handle basic per-modality shifts, they often fail under a fundamental dual-shift problem, as their adaptation signals fail to capture modality-interaction shifts that disrupt inter-sequence consistency. To address this, we propose Variance-gated Inter-Sequence Test-time Adaptation (VISTA), a source-free framework that tackles modality-interaction shifts. First, we design an Inter-Sequence Intervention Generator (ISIG) that generates a set of consistency probes by swapping low-frequency spectra and entropy-localized patches across sequences, preserving anatomical semantics while challenging inter-sequence dependencies. Second, we introduce Cross-View Disagreement-Aware Pseudo Labeling (CDPL), which establishes a voxel-wise reliability metric using cross-view disagreement variance to dynamically gate self-training and enforce interventional consistency, encouraging the network to rely on robust anatomical semantics. Extensive experiments adapting from standard adult MRI (BraTS-GLI-Pre) to African low-field (BraTS-SSA) and pediatric (BraTS-PED) cohorts show improved performance over competing methods under clinical shifts, achieving absolute Dice improvements of +1.89% (SSA) and +2.82% (PED) over the source model. The code is available at https://github.com/dzp2095/VISTA.

cs.CV↗

arXiv2026

The Rise of Quantum Computing -- Take a BITE for Built Environment and Urban Microclimate Research

Quantum computing is a new approach to computation that utilizes superposition, entanglement, interference, and tunneling to solve problems too complex for classical computers. This paper discusses the basic concepts and development of quantum computing, exploring its potential applications in the built environment and urban microclimate research. In buildings, quantum computing may help optimize energy management, control HVAC systems, and plan electric vehicle charging networks more efficiently. For urban microclimates, it could accelerate renewable energy planning and support multi-objective design, making it easier to balance urban building performance with climate conditions. Since current quantum hardware is still in the Noisy Intermediate-Scale Quantum (NISQ) stage, we propose the "BITE" principle to guide researchers in choosing suitable problems for quantum acceleration: B (Big search), I (Input-light), T (Tiny computation), and E (Evaluation polish). Although quantum computing still faces challenges such as noise and hardware limits, it offers great potential for developing more climate-resilient, sustainable, and energy-efficient cities of the future.

physics.pop-ph↗

arXiv2026

Step-CoT: Stepwise Visual Chain-of-Thought for Medical Visual Question Answering

Chain-of-thought (CoT) reasoning has advanced medical visual question answering (VQA), yet most existing CoT rationales are free-form and fail to capture the structured reasoning process clinicians actually follow. This work asks: Can traceable, multi-step reasoning supervision improve reasoning accuracy and the interpretability of Medical VQA? To this end, we introduce Step-CoT, a large-scale medical reasoning dataset with expert-curated, structured multi-step CoT aligned to clinical diagnostic workflows, implicitly grounding the model's reasoning in radiographic evidence. Step-CoT comprises more than 10K real clinical cases and 70K VQA pairs organized around diagnostic workflows, providing supervised intermediate steps that guide models to follow valid reasoning trajectories. To effectively learn from Step-CoT, we further introduce a teacher-student framework with a dynamic graph-structured focusing mechanism that prioritizes diagnostically informative steps while filtering out less relevant contexts. Our experiments show that using Step-CoT can improve reasoning accuracy and interpretability. Benchmark: github.com/hahaha111111/Step-CoT. Dataset Card: huggingface.co/datasets/fl-15o/Step-CoT

cs.CV↗

arXiv2026

Evolving Medical Imaging Agents via Experience-driven Self-skill Discovery

Clinical image interpretation is inherently multi-step and tool-centric: clinicians iteratively combine visual evidence with patient context, quantify findings, and refine their decisions through a sequence of specialized procedures. While LLM-based agents promise to orchestrate such heterogeneous medical tools, existing systems treat tool sets and invocation strategies as static after deployment. This design is brittle under real-world domain shifts, across tasks, and evolving diagnostic requirements, where predefined tool chains frequently degrade and demand costly manual re-design. We propose MACRO, a self-evolving, experience-augmented medical agent that shifts from static tool composition to experience-driven tool discovery. From verified execution trajectories, the agent autonomously identifies recurring effective multi-step tool sequences, synthesizes them into reusable composite tools, and registers these as new high-level primitives that continuously expand its behavioral repertoire. A lightweight image-feature memory grounds tool selection in a visual-clinical context, while a GRPO-like training loop reinforces reliable invocation of discovered composites, enabling closed-loop self-improvement with minimal supervision. Extensive experiments across diverse medical imaging datasets and tasks demonstrate that autonomous composite tool discovery consistently improves multi-step orchestration accuracy and cross-domain generalization over strong baselines and recent state-of-the-art agentic methods, bridging the gap between brittle static tool use and adaptive, context-aware clinical AI assistance. Code will be available upon acceptance.

cs.AI↗

arXiv2025

CADIC: Continual Anomaly Detection Based on Incremental Coreset

The primary objective of Continual Anomaly Detection (CAD) is to learn the normal patterns of new tasks under dynamic data distribution assumptions while mitigating catastrophic forgetting. Existing embedding-based CAD approaches continuously update a memory bank with new embeddings to adapt to sequential tasks. However, these methods require constructing class-specific sub-memory banks for each task, which restricts their flexibility and scalability. To address this limitation, we propose a novel CAD framework where all tasks share a unified memory bank. During training, the method incrementally updates embeddings within a fixed-size coreset, enabling continuous knowledge acquisition from sequential tasks without task-specific memory fragmentation. In the inference phase, anomaly scores are computed via a nearest-neighbor matching mechanism, achieving state-of-the-art detection accuracy. We validate the method through comprehensive experiments on MVTec AD and Visa datasets. Results show that our approach outperforms existing baselines, achieving average image-level AUROC scores of 0.972 (MVTec AD) and 0.891 (Visa). Notably, on a real-world electronic paper dataset, it demonstrates 100% accuracy in anomaly sample detection, confirming its robustness in practical scenarios. The implementation will be open-sourced on GitHub.

cs.CV↗

arXiv2025

FedSemiDG: Domain Generalized Federated Semi-supervised Medical Image Segmentation

Medical image segmentation is challenging due to the diversity of medical images and the lack of labeled data, which motivates recent developments in federated semi-supervised learning (FSSL) to leverage a large amount of unlabeled data from multiple centers for model training without sharing raw data. However, what remains under-explored in FSSL is the domain shift problem which may cause suboptimal model aggregation and low effectivity of the utilization of unlabeled data, eventually leading to unsatisfactory performance in unseen domains. In this paper, we explore this previously ignored scenario, namely domain generalized federated semi-supervised learning (FedSemiDG), which aims to learn a model in a distributed manner from multiple domains with limited labeled data and abundant unlabeled data such that the model can generalize well to unseen domains. We present a novel framework, Federated Generalization-Aware SemiSupervised Learning (FGASL), to address the challenges in FedSemiDG by effectively tackling critical issues at both global and local levels. Globally, we introduce Generalization-Aware Aggregation (GAA), assigning adaptive weights to local models based on their generalization performance. Locally, we use a Dual-Teacher Adaptive Pseudo Label Refinement (DR) strategy to combine global and domain-specific knowledge, generating more reliable pseudo labels. Additionally, Perturbation-Invariant Alignment (PIA) enforces feature consistency under perturbations, promoting domain-invariant learning. Extensive experiments on four medical segmentation tasks (cardiac MRI, spine MRI, bladder cancer MRI and colorectal polyp) demonstrate that our method significantly outperforms state-of-the-art FSSL and domain generalization approaches, achieving robust generalization on unseen domains.

cs.CV↗

arXiv2024

A General Solution to Bellman's Lost-in-a-forest Problem

We present a general solution and formulation framework to Bellman's lost-in-a-forest problem. The forest boundary is known and may take any shape. The starting point and the orientation are unspecified. We convert the problem into translation and rotation of the forest boundary. This transformation allows us to formulate this problem as a constrained minimization problem. Upon discretization, the problem becomes a variation of the traveling salesman problem or the Hamiltonian path problem. We leverage discrete optimization and derive several nontrivial results consistent with those from previous papers. This method is general, and we also extend the approach to related problems, including Moser's worm problem and the shortest opaque set problem.

math.OC↗

arXiv2024

Enable the Right to be Forgotten with Federated Client Unlearning in Medical Imaging

The right to be forgotten, as stated in most data regulations, poses an underexplored challenge in federated learning (FL), leading to the development of federated unlearning (FU). However, current FU approaches often face trade-offs between efficiency, model performance, forgetting efficacy, and privacy preservation. In this paper, we delve into the paradigm of Federated Client Unlearning (FCU) to guarantee a client the right to erase the contribution or the influence, introducing the first FU framework in medical imaging. In the unlearning process of a client, the proposed model-contrastive unlearning marks a pioneering step towards feature-level unlearning, and frequency-guided memory preservation ensures smooth forgetting of local knowledge while maintaining the generalizability of the trained global model, thus avoiding performance compromises and guaranteeing rapid post-training. We evaluated our FCU framework on two public medical image datasets, including Intracranial hemorrhage diagnosis and skin lesion diagnosis, demonstrating that our framework outperformed other state-of-the-art FU frameworks, with an expected speed-up of 10-15 times compared with retraining from scratch. The code and the organized datasets can be found at: https://github.com/dzp2095/FCU.

eess.IV↗

arXiv2024

Solving Moving Sofa Problem Using Calculus of Variations

In 1966, Leo Moser introduced the "moving sofa problem," which seeks to determine the largest area of a shape that can be maneuvered through a 90-degree hallway of unit-width. This problem remains unsolved and open yet. In this paper, we employ calculus of variations method to solve this problem. Assuming the trajectories and envelopes are convex, the sofa's area is formulated as an integral functional on a set of parametric equations for curves. The final shape is determined by solving the Euler-Lagrange equations. Utilizing numerical methods, we obtain the non-trivial area of 2.2195316, consistent with the previously well-known Gerver's constant since 1992. We prove that both the results of Gerver's sofa and Romik's car satisfy the Euler-Lagrange equations for the necessary condition of maximal area. We also explore additional cases and asymmetric conditions, and discuss other variant problems.

math.CA↗

arXiv2024

Federated Active Learning Framework for Efficient Annotation Strategy in Skin-lesion Classification

Federated Learning (FL) enables multiple institutes to train models collaboratively without sharing private data. Current FL research focuses on communication efficiency, privacy protection, and personalization and assumes that the data of FL have already been ideally collected. In medical scenarios, however, data annotation demands both expertise and intensive labor, which is a critical problem in FL. Active learning (AL), has shown promising performance in reducing the number of data annotations in medical image analysis. We propose a federated AL (FedAL) framework in which AL is executed periodically and interactively under FL. We exploit a local model in each hospital and a global model acquired from FL to construct an ensemble. We use ensemble-entropy-based AL as an efficient data-annotation strategy in FL. Therefore, our FedAL framework can decrease the amount of annotated data and preserve patient privacy while maintaining the performance of FL. To our knowledge, this is the first FedAL framework applied to medical images. We validated our framework on real-world dermoscopic datasets. Using only 50% of samples, our framework was able to achieve state-of-the-art performance on a skin-lesion classification task. Our framework performed better than several state-of-the-art AL methods under FL and achieved comparable performance to full-data FL.

cs.CV↗

arXiv2023

Scale Federated Learning for Label Set Mismatch in Medical Image Classification

Federated learning (FL) has been introduced to the healthcare domain as a decentralized learning paradigm that allows multiple parties to train a model collaboratively without privacy leakage. However, most previous studies have assumed that every client holds an identical label set. In reality, medical specialists tend to annotate only diseases within their area of expertise or interest. This implies that label sets in each client can be different and even disjoint. In this paper, we propose the framework FedLSM to solve the problem of Label Set Mismatch. FedLSM adopts different training strategies on data with different uncertainty levels to efficiently utilize unlabeled or partially labeled data as well as class-wise adaptive aggregation in the classification layer to avoid inaccurate aggregation when clients have missing labels. We evaluated FedLSM on two public real-world medical image datasets, including chest X-ray (CXR) diagnosis with 112,120 CXR images and skin lesion diagnosis with 10,015 dermoscopy images, and showed that it significantly outperformed other state-of-the-art FL algorithms. The code can be found at https://github.com/dzp2095/FedLSM.

cs.CV↗