Encoding Robust Topological Signatures for Hyperdimensional Computing

2026-05-15

AI Summary

Standard hyperdimensional (HD) computing lacks robustness against distribution shifts such as image rotation, noise, and occlusion. To address this limitation, this work proposes a novel HD representation that integrates explicit topological structures with rotation-, translation-, and scale- (RTS-) invariant shape features. The method extracts topological primitives—such as holes—from binary shapes and combines them with a Zernike moment spatial pyramid and hole-based radial Fourier descriptors to construct stable features. A permutation-invariant aggregation mechanism over hole sets, together with a channel reliability weighting strategy, maps these features into robust hyperdimensional vectors. Evaluated on MNIST and EMNIST under various perturbations, the approach significantly outperforms existing HD baselines, achieves clean-data accuracy comparable to lightweight CNNs, and maintains high robustness under severe deformations and occlusions, while supporting efficient online learning.

Abstract

Hyperdimensional (HD) computing offers an attractive alternative to deep networks for edge learning due to its simplicity, fast prototype-based inference, and compatibility with online updates. However, standard pixel-based HD encoders are brittle: small distribution shifts such as rotation, noise, or occlusion can drastically reduce accuracy. We extract discrete topological primitives-most notably holes-from binarized shapes and pair them with rotation/translation/scale (RTS)-invariant shape signatures. Our method constructs RTS-stable descriptors for (i) the outer shape using a spatial-pyramid variant of Zernike moments and (ii) each hole using an intrinsic Fourier descriptor of its radial signature together with RTS-canonical relative geometry. Each primitive is mapped to a bipolar hypervector via randomized projection and role binding, and variable-cardinality hole sets are aggregated by permutation-invariant bundling to form a single image hypervector. To avoid over-weighting any cue, we learn nonnegative reliability weights for the Zernike and hole channels on a validation set via late fusion of cosine similarities. Experiments on MNIST and EMNIST under controlled corruptions (rotation, Gaussian noise, salt-and-pepper, cutout, zoom) show that Topology-guided HD computing substantially improves robustness compared with a naive HD baseline, maintaining high accuracy across multiple corruption families and benefiting from lightweight online training. Compared with a compact CNN trained on clean data, our method achieves competitive clean accuracy while offering markedly stronger robustness to several pixel-level corruptions, demonstrating that explicit topological structure is a practical route to robust HD representations. The code is provided at https://github.com/arpan-kusari/Topological-HDC.

Problem

• hyperdimensional computing
• robustness
• distribution shift
• topological representation
• image corruption

Innovation

• Topological Representation
• Hyperdimensional Computing
• RTS-Invariant Descriptors
• Permutation-Invariant Bundling
• Robust Edge Learning