Encoding Robust Topological Signatures for Hyperdimensional Computing

• URL: http://arxiv.org/abs/2605.16785v1
• Date: Sat, 16 May 2026 03:36:40 GMT
• Title: Encoding Robust Topological Signatures for Hyperdimensional Computing
• Abstract summary: We show that Topology-guided HD computing substantially improves robustness compared with a naive HD baseline.<n>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.
• Score: 1.370633147306388
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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