Title: TopoCore: Unifying Topology Manifolds and Persistent Homology for Data Pruning
Primary area: learning on graphs and other geometries & topologies
Keywords: Coreset Selection, Topological Data Analysis, Persistent Homology, Architectural Transferability, Data-Efficient Learning, Manifold Learning, Pretrained Models

Abstract: Geometric coreset selection methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometric metrics makes them highly sensitive to variations in feature embeddings, leading to poor performance when transferring across different network architectures or when dealing with noisy features. We introduce TopoCore, a novel framework that resolves this challenge by leveraging the principles of topology to capture the intrinsic, stable structure of data. TopoCore operates in two stages, (1) utilizing a _topology-aware manifold approximation_ to establish a global low-dimensional embedding of the dataset. Subsequently, (2) it employs _differentiable persistent homology_ to perform a local topological optimization on the manifold embeddings, scoring samples based on their structural complexity. We show that at high pruning rates (e.g., 90\%), our _dual-scale topological approach_ yields a coreset selection method that boosts accuracy with up to 4$\times$ better precision than existing methods. Furthermore, through the inherent stability properties of topology, TopoCore is (a) exceptionally robust to noise perturbations of the feature embeddings and (b) demonstrates superior architecture transferability, improving both accuracy and stability across diverse network architectures. This study demonstrates a promising avenue towards stable and principled topology-based frameworks for robust data-efficient learning.