arXiv:2605.16785cs.CVcs.AI2026-05

用拓扑结构提升高维计算的抗干扰能力,让模型在旋转、噪声下仍保持高精度。

Encoding Robust Topological Signatures for Hyperdimensional Computing

论文配图:Encoding Robust Topological Signatures for Hyperdimensional Computing
图 1 · 摘自论文原文
  • 从二值图像中提取孔洞等拓扑特征,结合不变性描述符构建稳定表征
  • 在多种扰动下准确率显著优于传统高维编码方法,轻量在线训练效果好
  • 适合边缘设备上的鲁棒学习,尤其对旋转、噪声等像素级干扰敏感场景

高维(HD)计算因其简单性、快速原型推理和在线更新兼容性,成为边缘学习的有力替代方案。然而,标准像素编码器易受微小分布偏移影响,如旋转、噪声或遮挡会大幅降低准确率。本文从二值化形状中提取离散拓扑基元(尤其是孔洞),并结合旋转/平移/缩放(RTS)不变形状签名。方法通过空间金字塔变体的Zernike矩构建外轮廓的稳定描述符,用径向签名的内在傅里叶描述符与RTS规范相对几何表示每个孔洞。每个基元经随机投影和角色绑定映射为双极超向量,可变数量的孔洞集通过置换不变捆绑聚合为单一图像超向量。为避免某类线索过强,基于验证集学习非负可靠性权重,通过余弦相似度晚期融合实现。在MNIST和EMNIST上针对旋转、高斯噪声、椒盐噪声、裁剪、缩放等控制扰动的实验表明,拓扑引导的HD计算相比朴素基线显著提升鲁棒性,在多类扰动下维持高准确率,并支持轻量在线训练。与仅在干净数据上训练的紧凑卷积网络相比,本方法在干净数据上达到相当准确率,同时对多种像素级扰动表现出更强鲁棒性,证明显式拓扑结构是构建鲁棒高维表示的可行路径。代码已公开于https://github.com/arpan-kusari/Topological-HDC。

原文摘要 · Abstract (English)

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.

高维计算拓扑特征鲁棒性边缘学习

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