Learning From Filtration Sketches

Methods from computational topology are widely used in machine learning to extract topological and geometric information from data. Their use, however, often involves several computational stages before a representation suitable for learning is obtained. We investigate whether the underlying mathematical object, a filtration of a simplicial complex built on the data, can itself serve as the basis of a learning representation. We introduce *filtration sketches*, which combine estimated spectral summaries at selected filtration levels with approximate persistent ranks between them. Both components are computed through sparse boundary-operator applications and randomized trace estimation, without explicit eigendecomposition or persistence-barcode computation. The resulting fixed-width sequence is processed by a sequence model for downstream learning. On molecular property prediction and point-cloud benchmarks, filtration sketches outperform topology-based baselines and match or outperform point-cloud-specific neural networks.