arXiv:2601.08149v1 Announce Type: new 
Abstract: Geometric Representation Learning (GRL) aims to approximate the non-Euclidean topology of high-dimensional data through discrete graph structures, grounded in the manifold hypothesis. However, traditional static graph construction methods based on Euclidean distance often fail to capture the intrinsic curvature characteristics of the data manifold. Although Ollivier-Ricci Curvature Flow (OCF) has proven to be a powerful tool for dynamic topological optimization, its core reliance on Optimal Transport (Wasserstein distance) leads to prohibitive computational complexity, severely limiting its application in large-scale datasets and deep learning frameworks. To break this bottleneck, this paper proposes a novel geometric evolution framework: Resistance Curvature Flow (RCF). Leveraging the concept of effective resistance from circuit physics, RCF transforms expensive curvature optimization into efficient matrix operations. This approach achieves over 100x computational acceleration while maintaining geometric optimization capabilities comparable to OCF. We provide an in-depth exploration of the theoretical foundations and dynamical principles of RCF, elucidating how it guides the redistribution of edge weights via curvature gradients to eliminate topological noise and strengthen local cluster structures. Furthermore, we provide a mechanistic explanation of RCF's role in manifold enhancement and noise suppression, as well as its compatibility with deep learning models. We design a graph optimization algorithm, DGSL-RCF, based on this framework. Experimental results across deep metric learning, manifold learning, and graph structure learning demonstrate that DGSL-RCF significantly improves representation quality and downstream task performance.

تقدم دراسة جديدة تدفق مقاومة الانحناء (RCF)، وهو إطار تطور هندسي مصمم لتحسين تعلم هيكل الرسوم البيانية الديناميكي من خلال تحسين حسابات الانحناء عبر عمليات المصفوفة الفعالة. تعالج هذه الابتكار القيود المفروضة على طرق تدفق الانحناء أوليفييه-ريشي التقليدية، التي تواجه صعوبات في التعقيد الحسابي في مجموعات البيانات الكبيرة.

Un nuevo estudio presenta el Resistance Curvature Flow (RCF), un marco de evolución geométrica diseñado para mejorar el aprendizaje dinámico de estructuras gráficas mediante la optimización de cálculos de curvatura a través de operaciones matriciales eficientes. Esta innovación aborda las limitaciones de los métodos tradicionales de Ollivier-Ricci Curvature Flow, que enfrentan dificultades de complejidad computacional en grandes conjuntos de datos.

Une nouvelle étude présente le Resistance Curvature Flow (RCF), un cadre d'évolution géométrique conçu pour améliorer l'apprentissage dynamique des structures graphiques en optimisant les calculs de courbure par des opérations matricielles efficaces. Cette innovation répond aux limitations des méthodes traditionnelles d'Ollivier-Ricci Curvature Flow, qui rencontrent des difficultés de complexité computationnelle dans de grands ensembles de données.

A new study introduces Resistance Curvature Flow (RCF), a geometric evolution framework designed to enhance dynamic graph structure learning by optimizing curvature calculations through efficient matrix operations. This innovation addresses the limitations of traditional Ollivier-Ricci Curvature Flow methods, which struggle with computational complexity in large datasets.

Dynamic Graph Structure Learning via Resistance Curvature Flow

arXiv:2601.08122v1 Announce Type: new 
Abstract: Deep learning (DL) has driven broad advances across scientific and engineering domains. Despite its success, DL models often exhibit limited interpretability and generalization, which can undermine trust, especially in safety-critical deployments. As a result, there is growing interest in (i) analyzing interpretability and generalization and (ii) developing models that perform robustly under data distributions different from those seen during training (i.e. domain generalization). However, the theoretical analysis of DL remains incomplete. For example, many generalization analyses assume independent samples, which is violated in sequential data with temporal correlations. Motivated by these limitations, this paper proposes a method to analyze interpretability and out-of-domain (OOD) generalization for a family of recurrent neural networks (RNNs). Specifically, the evolution of a trained RNN's states is modeled as an unknown, discrete-time, nonlinear closed-loop feedback system. Using Koopman operator theory, these nonlinear dynamics are approximated with a linear operator, enabling interpretability. Spectral analysis is then used to quantify the worst-case impact of domain shifts on the generalization error. Building on this analysis, a domain generalization method is proposed that reduces the OOD generalization error and improves the robustness to distribution shifts. Finally, the proposed analysis and domain generalization approach are validated on practical temporal pattern-learning tasks.

تم إصدار ورقة جديدة تقترح طريقة لتحليل القابلية للتفسير والتعميم خارج النطاق في الشبكات العصبية المتكررة (RNN)، حيث تتناول القيود التي تواجه نماذج التعلم العميق التي غالبًا ما تكافح مع التعميم في البيانات التسلسلية. تسلط الدراسة الضوء على أهمية فهم تطور حالات RNN كعملية زمنية منفصلة.

Se ha publicado un nuevo artículo que propone un método para analizar la interpretabilidad y la generalización fuera de dominio en redes neuronales recurrentes (RNN), abordando las limitaciones de los modelos de aprendizaje profundo que a menudo luchan con la generalización en datos secuenciales. El estudio destaca la importancia de entender la evolución de los estados de las RNN como un proceso de tiempo discreto.

Un nouvel article a été publié proposant une méthode pour analyser l'interprétabilité et la généralisation hors domaine dans les réseaux de neurones récurrents (RNN), abordant les limitations des modèles d'apprentissage profond qui ont souvent du mal à généraliser dans les données séquentielles. L'étude souligne l'importance de comprendre l'évolution des états des RNN comme un processus en temps discret.

A new paper has been released that proposes a method for analyzing interpretability and out-of-domain generalization in recurrent neural networks (RNNs), addressing the limitations of existing deep learning models which often struggle with generalization in sequential data. The study highlights the importance of understanding the evolution of RNN states as a discrete-time process.

Dynamic Graph Structure Learning via Resistance Curvature Flow

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