arXiv Machine Learning
Aug 4
Differentiable Lifting for Topological Neural Networks
arXiv:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.
Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
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arXiv Machine Learning
4d ago
TopoEmbedX: A General Framework for Representation Learning on Topological Domains
arXiv:2609.37884v1 Announce Type: new Abstract: Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationship...
arXiv AI
Jul 23
A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv Machine Learning
Jul 31
TopoFormer: Topology Meets Attention for Graph Learning
arXiv:2607. 28259v1 Announce Type: new Abstract: We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences.
arXiv Machine Learning
4d ago
Exploring Learning Models for Topological Relationship Recognition from Image Data
arXiv:2609.36172v1 Announce Type: cross Abstract: Figuring out how objects relate to each other, like whether they touch, overlap, stay completely separate or one sits inside another, matters a lot i...
arXiv Machine Learning
Jun 5
HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
arXiv:2505. 15405v3 Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems.
arXiv Machine Learning
Jun 5
Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
arXiv:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations.
arXiv AI
Jun 30
TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
arXiv AI
Jun 9
Topological Neural Operators
arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv Computer Vision
Sep 1
TopoAgent: A Structure-Aware Perception-to-Reasoning Framework for Diagram-to-Graph Topology Extraction with Large Vision-Language Models
The paper introduces TopoBench-180, a human‑verified benchmark of 180 structural diagrams with canonical graph annotations, and TopoAgent, a perception‑to‑reasoning framework that extracts graph topology from diagrams using large vision‑language models. TopoAgent combines grounded perception, global structural priors, node inventory construction, local‑to‑global relation reasoning, and consistency enforcement to progressively build the target graph. Experiments demonstrate that TopoAgent surpasses strong baselines, particularly in edge extraction, thereby advancing multimodal structured understanding for diagram‑to‑graph tasks.
arXiv Machine Learning
Jun 18
Unreduced Persistence Diagrams for Topological Machine Learning
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
arXiv Computer Vision
Sep 21
Graph-Augmented Topological Internalization with Dual-Stream Classifiers for Medical Report Generation
The paper introduces GDMRG, a Graph-Augmented Dual-Stream Medical Report Generation framework that incorporates a Topological Knowledge Internalization module using a Graph Convolutional Network to encode disease co-occurrence priors. It employs a dual-stream classifier—one branch generating diagnostic prompts under topological constraints and an auxiliary branch dynamically calibrating decision boundaries for imbalanced samples—alongside a Diagnosis-Guided Spatial Attention mechanism to align visual features with clinical semantics. Experiments on MIMIC-CXR show competitive clinical efficacy and natural language fluency, with strong zero-shot performance on IU X-Ray.