jacobian sensitivity modeling

This study addresses the limited interpretability of existing automated diabetic retinopathy (DR) grading methods, which often overlook the spatial relationships between lesions and retinal vasculature as well as their associations with biomarkers. To overcome this, the authors propose a bilateral spatial Jacobian image graph model that jointly captures lesion–vessel geometric relationships and embedding–biomarker sensitivity for the first time. The model integrates vascular structure, lesion evidence maps, contrastive embeddings, and morphometric biomarkers, enhanced by a lightweight dual-label attention mechanism for effective multi-source information fusion. Evaluated on the APTOS dataset (2,910 images), the method achieves an accuracy of 0.8076, weighted Kappa of 0.8312, macro F1-score of 0.5915, and adjacent-level accuracy of 0.9330. For referable DR detection, it attains 0.9055 accuracy and 0.9711 AUROC, substantially improving both diagnostic performance and model interpretability.

This work addresses the lack of a unified theoretical framework for assessing the reliability of nonlinear dimensionality reduction embeddings. It proposes a cohesive perspective grounded in differential and integral geometry, systematically analyzing the geometric properties of differentiable embeddings through both local differential structure and global path integrals. The study reveals, for the first time, that multiple existing diagnostic methods fundamentally arise from a common geometric object and demonstrates that their global characteristics cannot be fully captured by derivatives of any finite order, necessitating an irreducible integral viewpoint. Leveraging tools such as curvature analysis, path-dependence detection, and mapping continuity evaluation, the framework validates its theoretical predictions on both synthetic and real-world datasets—including single-cell data—enabling precise estimation of embedding reliability and effective discrimination between single-valued and path-dependent embeddings.

Biological pathway graphs exhibit high topological complexity and suffer from severe distortion when embedded in Euclidean space. To address this, we propose MC-GCN—the first non-Euclidean graph neural network that learns pathway node embeddings on a product manifold endowed with mixed curvature. Methodologically, MC-GCN integrates multi-curvature geometric modeling with product manifold optimization, designs a curvature-aware graph convolution tailored for highly distorted structures, and employs a supervised edge-prediction framework. Its key contribution lies in pioneering the incorporation of mixed-curvature geometry and product manifold representation into pathway embedding learning, effectively mitigating embedding distortion caused by global curvature inconsistency. Experiments demonstrate that MC-GCN significantly reduces embedding distortion and achieves substantial improvements in accuracy on in-distribution protein–protein interaction prediction. The source code and pathway analysis toolkit are publicly available.

In high-dimensional data dimensionality reduction, the initial similarity graph is unreliable due to the “curse of dimensionality” and information sparsity, impeding cluster separation—especially as dataset size increases. To address this, we propose LocalMAP, a novel algorithm that introduces a dynamic local subgraph extraction and online update mechanism. LocalMAP achieves fine-grained, adaptive refinement of the adjacency graph via embedding-driven subgraph sampling, local neighborhood-aware adaptive reweighting, and iterative graph optimization. Compared with conventional methods (e.g., t-SNE, UMAP), LocalMAP significantly improves clustering structure recovery accuracy. On large-scale transcriptomic datasets, it successfully disentangles biologically meaningful but previously confounded subpopulations, accurately identifying critical cell types that were either missed or erroneously merged in prior analyses. LocalMAP thus establishes a new paradigm for interpretable, scalable dimensionality reduction of high-dimensional biological data.

This study systematically evaluates the robustness of graph embedding methods for community detection under edge deletion perturbations. Addressing the lack of cross-method comparisons and principled perturbation analysis in prior work, we conduct the first unified robustness evaluation of two major classes of models—matrix factorization (LE, LLE, HOPE, M-NMF) and random-walk-based approaches (DeepWalk, LINE, node2vec)—on both synthetic and real-world heterogeneous networks. Experiments quantify how network scale, community strength, and perturbation type affect detection performance. Results reveal that node2vec and LLE consistently achieve top robustness across diverse perturbation regimes, particularly maintaining stability in networks with skewed degree distributions and highly imbalanced community sizes. This work establishes an empirical benchmark for robust graph representation learning and provides actionable design insights for developing perturbation-resilient embedding methods.

本文针对图异常检测中的特征适应性、细粒度信息丢失及标签利用不足问题，提出了一种结合特征变换与自适应Jacobi多项式图滤波的新方法。

Traditional linear dimensionality reduction methods often fail to effectively uncover the intrinsic low-dimensional manifold structure embedded in high-dimensional data. This work systematically traces the historical development of manifold fitting and, for the first time, categorizes it into three distinct phases: nonparametric statistics, mathematically inspired analysis, and modern practical statistics. It clarifies manifold fitting’s role as an independent geometric data analysis tool and delineates its conceptual boundaries from related techniques such as manifold embedding and denoising. By integrating nonparametric methods, differential geometry, and contemporary statistical learning approaches, the paper explores cutting-edge applications of manifold fitting in neural networks and bioinformatics, offering a comprehensive reference framework that elucidates both its theoretical limits and practical utility.

This work proposes a randomized, unbiased vector-Jacobian product (VJP) approximation method with minimal variance to replace exact computations in backpropagation, aiming to reduce the computational and memory costs of training deep neural networks. The approach achieves theoretically optimal estimation under sparsity constraints and establishes a principled trade-off between approximation accuracy and per-iteration training cost. Empirical evaluations on multilayer perceptrons, BagNets, and Vision Transformers demonstrate that the method substantially lowers training overhead while preserving model accuracy almost entirely.

本文针对高维或非欧几里得数据中传统统计方法失效的问题，提出Cursive方法，通过保留关系信息来改进数据分析。

This study addresses the underexplored challenge of effectively visualizing bivariate distributions on graph edges under the spatial constraints of adjacency matrix layouts. The work proposes a novel approach that encodes edge-wise bivariate distributions using two statistical summaries: central tendency and dispersion. Through a preregistered crowdsourced experiment, the authors systematically evaluate four compact encoding designs—bivariate color mapping, embedded bar charts, and two superimposed mark types combining area or angle with color. Results demonstrate that the area-based superimposed marks and embedded bar charts yield the best overall performance, while angle-based encodings show moderate but inconsistent accuracy, and bivariate color mappings perform significantly worse. This research provides empirical evidence and practical guidance for designing visualizations of bivariate edge data in graph structures.