LogHD: Robust Compression of Hyperdimensional Classifiers via Logarithmic Class-Axis Reduction

Hyperdimensional computing (HDC) suits memory, energy, and reliability-constrained systems, yet the standard "one prototype per class" design requires O(CD) memory (with C classes and dimensionality D). Prior compaction reduces D (feature axis), improving storage/compute but weakening robustness. We introduce LogHD, a logarithmic class-axis reduction that replaces the C per-class prototypes with n!≈!lceillogk Crceil bundle hypervectors (alphabet size k) and decodes in an n-dimensional activation space, cutting memory to O(Dlogk C) while preserving D. LogHD uses a capacity-aware codebook and profile-based decoding, and composes with feature-axis sparsification. Across datasets and injected bit flips, LogHD attains competitive accuracy with smaller models and higher resilience at matched memory. Under equal memory, it sustains target accuracy at roughly 2.5-3.0× higher bit-flip rates than feature-axis compression; an ASIC instantiation delivers 498× energy efficiency and 62.6× speedup over an AMD Ryzen 9 9950X and 24.3×/6.58× over an NVIDIA RTX 4090, and is 4.06× more energy-efficient and 2.19× faster than a feature-axis HDC ASIC baseline.