arXiv subjects
Publications and source records attributed to Haofeng Zhang.
We answer two questions of Qi [J. Reine Angew. Math. 830 (2026)] on the metric space of saturated filtrations, one affirmatively and one negatively. The main result of this paper was obtained by Chatgpt 5.5 pro, and the Danus system based on the Rethlas system.
Few-Shot Medical Image Segmentation (FSMIS) offers a powerful solution to data scarcity but struggles to generalize across different imaging modalities. This performance collapse stems primarily from the drastic texture discrepancies between domains, which mislead models trained on source-specific intensity distributions. While existing methods attempt to align frequency or local texture features, they often fail to decouple semantic structure from domain-specific appearance. To address this, we identify a critical invariance: despite distinct imaging physics, the position and geometric shape of organs remain robustly consistent across modalities. Therefore, we propose a novel framework that harnesses Position and Shape Priors (PSP) for cross-domain FSMIS. Specifically, PSP first introduces a Position Coordinate Embedding (PCE) module to inject relative spatial coordinates for rapid organ localization. Subsequently, a Shape Prototype Modulation (SPM) module constructs domain-invariant structural prototypes via explicit shape priors, effectively filtering out texture noise. Furthermore, the Hybrid-Prototype Prediction (HPP) module adaptively calibrates the support prototype to the query feature distribution, mitigating feature misalignment. Extensive experiments on two public medical imaging datasets demonstrate that PSP significantly outperforms state-of-the-art methods.
Cross-domain Few-shot Segmentation (CD-FSS) aims to learn generalizable segmentation capability from abundant annotated samples in the source domain, enabling accurate segmentation of novel classes in the target domain with only a few annotated samples. Existing CD-FSS methods mainly focus on mitigating feature distribution shifts caused by style gaps while ignoring significant differences in class semantic granularity and discriminative attributes across domains, leading to two key degradations in support-query matching: semantic over-alignment and attribute over-alignment. To this end, we propose the Dual Hierarchical Aggregation Network (DHANet), which comprises three key modules. First, the Hierarchical Spatial Aggregation (HSA) module performs multi-scale region aggregation of pixel features along the spatial dimension, generating hierarchical semantic-enhanced features to alleviate semantic over-alignment. Additionally, the HCA module conducts multi-scale attribute aggregation along the channel dimension, generating hierarchical attribute-enhanced features to mitigate attribute over-alignment. Finally, we propose the Online Probabilistic Semantic Bank (OPSB), which progressively constructs and updates class probability distributions from query predictions during inference, and samples multiple pseudo-prototypes as additional support information to mitigate insufficient support. Extensive experiments on four target-domain datasets demonstrate that our method achieves state-of-the-art performance.
Cross-domain Few-shot Segmentation (CD-FSS) aims to transfer knowledge learned from source domain to distinct target domains, segmenting unseen target classes with only a few annotated samples. Although existing methods have made significant progress, they still rely on training or fine-tuning processes, which incur high computational costs and risk overfitting. We observe that when powerful and general-purpose vision foundation models are incorporated into these methods, their performance shows only marginal improvement or even degrades due to overfitting. To address this, we eliminate trainable parameters and propose a training-free framework to avoid both training overhead and overfitting. Built upon the self-supervised vision encoder DINOv3, our framework addresses cross-domain challenges through three core modules. First, the Semantic-aware Feature Re-fusion (SAFR) module identifies and re-fuses features that emphasize semantic patterns, generating representations with enhanced semantic discriminability. Additionally, the Adaptive Support Enhancement (ASE) module narrows semantic gaps between support and query through robust query information aggregation. Finally, the Hybrid Prototype Matching (HPM) module integrates matching results from diverse prototypes to adapt to varying semantic complexity across domains. Extensive experiments on four target domain datasets demonstrate that our method achieves state-of-the-art performance in CD-FSS without any training.
Visual evidence selection is a critical component of multimodal retrieval-augmented generation (RAG), yet existing methods typically rely on semantic relevance or surface-level similarity, which are often misaligned with the actual utility of visual evidence for downstream reasoning. We reformulate multimodal evidence selection from an information-theoretic perspective by defining evidence utility as the information gain induced on a model's output distribution. To overcome the intractability of answer-space optimization, we introduce a latent notion of evidence helpfulness and theoretically show that, under mild assumptions, ranking evidence by information gain on this latent variable is equivalent to answer-space utility. We further propose a training-free, surrogate-accelerated framework that efficiently estimates evidence utility using lightweight multimodal models. Experiments on MRAG-Bench and Visual-RAG across multiple model families demonstrate that our method consistently outperforms state-of-the-art RAG baselines while achieving substantial reductions in computational cost.
Cross-domain few-shot medical image segmentation (CD-FSMIS) requires a model to generalise simultaneously to novel anatomical categories and unseen imaging domains from only a handful of annotated examples. Existing prototypical approaches inevitably entangle anatomical structure with domain-specific appearance variations, and thus lack a stable reference for reliable matching under domain shift. We observe that the geometric structure of human anatomy constitutes a reliable, domain-transferable prior that has been overlooked. Building on this insight, we propose GeoProto, a geometry-aware CD-FSMIS framework that enriches prototypical matching with explicit structural priors. The core component, Geometry-Aware Prototype Enrichment (GAPE), augments each local appearance prototype with a learned geometric offset encoding its ordinal position within the organ's interior topology. This offset is derived from an auxiliary Ordinal Shape Branch (OSB) trained under an ordinally consistent objective that enforces monotonic variation of geometric embeddings across interior strata, requiring no annotation beyond standard segmentation masks. Extensive experiments across seven datasets spanning three evaluation settings (cross-modality, cross-sequence, and cross-context) demonstrate that GeoProto achieves state-of-the-art performance.
Conventional few-shot medical image segmentation (FSMIS) approaches face performance bottlenecks that hinder broader clinical applicability. Although the Segment Anything Model (SAM) exhibits strong category-agnostic segmentation capabilities, its direct application to medical images often leads to over-segmentation due to ambiguous anatomical boundaries. In this paper, we reformulate SAM-based FSMIS as a prompt localization task and propose FoB (Focus on Background), a background-centric prompt generator that provides accurate background prompts to constrain SAM's over-segmentation. Specifically, FoB bridges the gap between segmentation and prompt localization by category-agnostic generation of support background prompts and localizing them directly in the query image. To address the challenge of prompt localization for novel categories, FoB models rich contextual information to capture foreground-background spatial dependencies. Moreover, inspired by the inherent structural patterns of background prompts in medical images, FoB models this structure as a constraint to progressively refine background prompt predictions. Experiments on three diverse medical image datasets demonstrate that FoB outperforms other baselines by large margins, achieving state-of-the-art performance on FSMIS, and exhibiting strong cross-domain generalization. Our code is available at https://github.com/primebo1/FoB_SAM.
Existing paradigms for remote sensing change detection are caught in a trade-off: CNNs excel at efficiency but lack global context, while Transformers capture long-range dependencies at a prohibitive computational cost. This paper introduces ChangeRWKV, a new architecture that reconciles this conflict. By building upon the Receptance Weighted Key Value (RWKV) framework, our ChangeRWKV uniquely combines the parallelizable training of Transformers with the linear-time inference of RNNs. Our approach core features two key innovations: a hierarchical RWKV encoder that builds multi-resolution feature representation, and a novel Spatial-Temporal Fusion Module (STFM) engineered to resolve spatial misalignments across scales while distilling fine-grained temporal discrepancies. ChangeRWKV not only achieves state-of-the-art performance on the LEVIR-CD benchmark, with an 85.46% IoU and 92.16% F1 score, but does so while drastically reducing parameters and FLOPs compared to previous leading methods. This work demonstrates a new, efficient, and powerful paradigm for operational-scale change detection. Our code and model are publicly available.
This paper presents a novel approach, Spectral-Interpretable and -Enhanced Transformer (SIEFormer), which leverages spectral analysis to reinterpret the attention mechanism within Vision Transformer (ViT) and enhance feature adaptability, with particular emphasis on challenging Generalized Category Discovery (GCD) tasks. The proposed SIEFormer is composed of two main branches, each corresponding to an implicit and explicit spectral perspective of the ViT, enabling joint optimization. The implicit branch realizes the use of different types of graph Laplacians to model the local structure correlations of tokens, along with a novel Band-adaptive Filter (BaF) layer that can flexibly perform both band-pass and band-reject filtering. The explicit branch, on the other hand, introduces a Maneuverable Filtering Layer (MFL) that learns global dependencies among tokens by applying the Fourier transform to the input ``value" features, modulating the transformed signal with a set of learnable parameters in the frequency domain, and then performing an inverse Fourier transform to obtain the enhanced features. Extensive experiments reveal state-of-the-art performance on multiple image recognition datasets, reaffirming the superiority of our approach through ablation studies and visualizations.
Cross-domain few-shot medical image segmentation (CD-FSMIS) offers a promising and data-efficient solution for medical applications where annotations are severely scarce and multimodal analysis is required. However, existing methods typically filter out domain-specific information to improve generalization, which inadvertently limits cross-domain performance and degrades source-domain accuracy. To address this, we present Contrastive Graph Modeling (C-Graph), a framework that leverages the structural consistency of medical images as a reliable domain-transferable prior. We represent image features as graphs, with pixels as nodes and semantic affinities as edges. A Structural Prior Graph (SPG) layer is proposed to capture and transfer target-category node dependencies and enable global structure modeling through explicit node interactions. Building upon SPG layers, we introduce a Subgraph Matching Decoding (SMD) mechanism that exploits semantic relations among nodes to guide prediction. Furthermore, we design a Confusion-minimizing Node Contrast (CNC) loss to mitigate node ambiguity and subgraph heterogeneity by contrastively enhancing node discriminability in the graph space. Our method significantly outperforms prior CD-FSMIS approaches across multiple cross-domain benchmarks, achieving state-of-the-art performance while simultaneously preserving strong segmentation accuracy on the source domain.
Cross-domain Few-shot Segmentation (CD-FSS) aims to segment novel classes from target domains that are not involved in training and have significantly different data distributions from the source domain, using only a few annotated samples, and recent years have witnessed significant progress on this task. However, existing CD-FSS methods primarily focus on style gaps between source and target domains while ignoring segmentation granularity gaps, resulting in insufficient semantic discriminability for novel classes in target domains. Therefore, we propose a Hierarchical Semantic Learning (HSL) framework to tackle this problem. Specifically, we introduce a Dual Style Randomization (DSR) module and a Hierarchical Semantic Mining (HSM) module to learn hierarchical semantic features, thereby enhancing the model's ability to recognize semantics at varying granularities. DSR simulates target domain data with diverse foreground-background style differences and overall style variations through foreground and global style randomization respectively, while HSM leverages multi-scale superpixels to guide the model to mine intra-class consistency and inter-class distinction at different granularities. Additionally, we also propose a Prototype Confidence-modulated Thresholding (PCMT) module to mitigate segmentation ambiguity when foreground and background are excessively similar. Extensive experiments are conducted on four popular target domain datasets, and the results demonstrate that our method achieves state-of-the-art performance.
Data-driven stochastic optimization is ubiquitous in machine learning and operational decision-making problems. Sample average approximation (SAA) and model-based approaches such as estimate-then-optimize (ETO) or integrated estimation-optimization (IEO) are all popular, with model-based approaches being able to circumvent some of the issues with SAA in complex context-dependent problems. Yet the relative performance of these methods is poorly understood, with most results confined to the dichotomous cases of the model-based approach being either well-specified or misspecified. We develop the first results that allow for a more granular analysis of the relative performance of these methods under a local misspecification setting, which models the scenario where the model-based approach is nearly well-specified. By leveraging tools from contiguity theory in statistics, we show that there is a bias-variance tradeoff between SAA, IEO, and ETO under local misspecification, and that the relative importance of the bias and the variance depends on the degree of local misspecification. Moreover, we derive explicit expressions for the decision bias, which allows us to characterize (un)impactful misspecification directions, and provide further geometric understanding of the variance.
Cross-domain Few-shot Medical Image Segmentation (CD-FSMIS) is a potential solution for segmenting medical images with limited annotation using knowledge from other domains. The significant performance of current CD-FSMIS models relies on the heavily training procedure over other source medical domains, which degrades the universality and ease of model deployment. With the development of large visual models of natural images, we propose a training-free CD-FSMIS model that introduces the Multi-center Adaptive Uncertainty-aware Prompting (MAUP) strategy for adapting the foundation model Segment Anything Model (SAM), which is trained with natural images, into the CD-FSMIS task. To be specific, MAUP consists of three key innovations: (1) K-means clustering based multi-center prompts generation for comprehensive spatial coverage, (2) uncertainty-aware prompts selection that focuses on the challenging regions, and (3) adaptive prompt optimization that can dynamically adjust according to the target region complexity. With the pre-trained DINOv2 feature encoder, MAUP achieves precise segmentation results across three medical datasets without any additional training compared with several conventional CD-FSMIS models and training-free FSMIS model. The source code is available at: https://github.com/YazhouZhu19/MAUP.
Few-Shot Medical Image Segmentation (FSMIS) has been widely used to train a model that can perform segmentation from only a few annotated images. However, most existing prototype-based FSMIS methods generate multiple prototypes from the support image solely by random sampling or local averaging, which can cause particularly severe boundary blurring due to the tendency for normal features accounting for the majority of features of a specific category. Consequently, we propose to focus more attention to those weaker features that are crucial for clear segmentation boundary. Specifically, we design a Support Self-Prediction (SSP) module to identify such weak features by comparing true support mask with one predicted by global support prototype. Then, a Hard Prototypes Generation (HPG) module is employed to generate multiple hard prototypes based on these weak features. Subsequently, a Multiple Similarity Maps Fusion (MSMF) module is devised to generate final segmenting mask in a dual-path fashion to mitigate the imbalance between foreground and background in medical images. Furthermore, we introduce a boundary loss to further constraint the edge of segmentation. Extensive experiments on three publicly available medical image datasets demonstrate that our method achieves state-of-the-art performance. Code is available at https://github.com/jcjiang99/CoW.
The recently proposed Novel Category Discovery (NCD) adapt paradigm of transductive learning hinders its application in more real-world scenarios. In fact, few labeled data in part of new categories can well alleviate this burden, which coincides with the ease that people can label few of new category data. Therefore, this paper presents a new setting in which a trained agent is able to flexibly switch between the tasks of identifying examples of known (labelled) classes and clustering novel (completely unlabeled) classes as the number of query examples increases by leveraging knowledge learned from only a few (handful) support examples. Drawing inspiration from the discovery of novel categories using prior-based clustering algorithms, we introduce a novel framework that further relaxes its assumptions to the real-world open set level by unifying the concept of model adaptability in few-shot learning. We refer to this setting as Few-Shot Novel Category Discovery (FSNCD) and propose Semi-supervised Hierarchical Clustering (SHC) and Uncertainty-aware K-means Clustering (UKC) to examine the model's reasoning capabilities. Extensive experiments and detailed analysis on five commonly used datasets demonstrate that our methods can achieve leading performance levels across different task settings and scenarios.
Data-driven optimization aims to translate a machine learning model into decision-making by optimizing decisions on estimated costs. Such a pipeline can be conducted by fitting a distributional model which is then plugged into the target optimization problem. While this fitting can utilize traditional methods such as maximum likelihood, a more recent approach uses estimation-optimization integration that minimizes decision error instead of estimation error. Although intuitive, the statistical benefit of the latter approach is not well understood yet is important to guide the prescriptive usage of machine learning. In this paper, we dissect the performance comparisons between these approaches in terms of the amount of model misspecification. In particular, we show how the integrated approach offers a ``universal double benefit'' on the top two dominating terms of regret when the underlying model is misspecified, while the traditional approach can be advantageous when the model is nearly well-specified. Our comparison is powered by finite-sample tail regret bounds that are derived via new higher-order expansions of regrets and the leveraging of a recent Berry-Esseen theorem.
Existing few-shot medical image segmentation (FSMIS) models fail to address a practical issue in medical imaging: the domain shift caused by different imaging techniques, which limits the applicability to current FSMIS tasks. To overcome this limitation, we focus on the cross-domain few-shot medical image segmentation (CD-FSMIS) task, aiming to develop a generalized model capable of adapting to a broader range of medical image segmentation scenarios with limited labeled data from the novel target domain. Inspired by the characteristics of frequency domain similarity across different domains, we propose a Frequency-aware Matching Network (FAMNet), which includes two key components: a Frequency-aware Matching (FAM) module and a Multi-Spectral Fusion (MSF) module. The FAM module tackles two problems during the meta-learning phase: 1) intra-domain variance caused by the inherent support-query bias, due to the different appearances of organs and lesions, and 2) inter-domain variance caused by different medical imaging techniques. Additionally, we design an MSF module to integrate the different frequency features decoupled by the FAM module, and further mitigate the impact of inter-domain variance on the model's segmentation performance. Combining these two modules, our FAMNet surpasses existing FSMIS models and Cross-domain Few-shot Semantic Segmentation models on three cross-domain datasets, achieving state-of-the-art performance in the CD-FSMIS task.
We develop a family of new combinatorial models for key polynomials. It is similar to the hybrid pipe dream model for Schubert polynomials defined recently by Knutson and Udell.