Topological Descriptors in Graph Representation Learning: From Persistent Homology to Scalable Embeddings

The intersection of algebraic topology and machine learning has opened new avenues for understanding the multi-scale structural properties of complex data. While Graph Neural Networks (GNNs) excel at capturing local neighborhood information, they often fail to account for higher-order topological features, such as cycles and voids, which are critical for structural robustness. In this talk, I will discuss how to mathematically formalize these features using Topological Data Analysis (TDA) and integrate them into modern learning architectures.
First, I will introduce TopoFormer (ICLR 2026), a scalable framework that integrates topological structure into attention-based architectures. TopoFormer uses a novel Topo-Scan module to convert graphs into ordered sequences of topological tokens, enabling the use of Transformers for graph-level representation learning. This approach preserves multi-scale structural information, provides theoretical stability guarantees, and achieves state-of-the-art results in graph classification and molecular property prediction, while remaining computationally efficient and parallelizable.
Next, I will present TopER – Topological Evolution Rate (NeurIPS 2025), which introduces a low-dimensional, interpretable graph embedding derived from a simplified persistent homology pipeline. By quantifying the evolution rate of graph substructures across filtrations, TopER produces intuitive representations that enable visualization and interpretability while achieving competitive or state-of-the-art performance on molecular, biological, and social network benchmarks. The method is also available as an open-source Python package on PyPI.
Together, these works illustrate a broader research direction: embedding topological inductive biases into modern deep learning architectures to achieve interpretability, scalability, and strong predictive performance.