用对数方式压缩高维分类器，大幅省内存还更抗干扰。
LogHD: Robust Compression of Hyperdimensional Classifiers via Logarithmic Class-Axis Reduction
- 用少量基向量替代每类一个原型，按对数规模减少类别轴
- 相同内存下比传统压缩多承受2.5到3倍的位翻转错误
- 适合资源受限场景，如嵌入式设备或低功耗系统
高维计算（HDC）适用于内存、能耗和可靠性受限的系统，但标准的‘每类一个原型’设计需占用O(CD)内存（C为类别数，D为维度）。以往压缩方法虽降低特征维度D，提升存储与计算效率，却削弱了鲁棒性。本文提出LogHD，采用对数类轴压缩：将C个类原型替换为n≈⌈log_k C⌉个基向量组（字母表大小为k），在n维激活空间中解码，使内存降至O(D log_k C)，同时保持原维度D。LogHD结合容量感知码本与基于特征的解码策略，并可与特征轴稀疏化协同使用。在多个数据集及注入位翻转测试中，其精度表现优异，模型更小且更抗干扰。在相同内存条件下，其能维持目标精度的位翻转率比特征轴压缩高出2.5至3.0倍；硬件实现显示，相比AMD Ryzen 9 9950X，能效提升498倍，速度提升62.6倍；对比NVIDIA RTX 4090，能效提升24.3倍/6.58倍，且比现有特征轴HDC ASIC更节能4.06倍、更快2.19倍。
原文摘要 · Abstract (English)
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 $n\!\approx\!\lceil\log_k C\rceil$ bundle hypervectors (alphabet size $k$) and decodes in an $n$-dimensional activation space, cutting memory to $O(D\log_k C)$ 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 $2.5$-$3.0\times$ higher bit-flip rates than feature-axis compression; an ASIC instantiation delivers $498\times$ energy efficiency and $62.6\times$ speedup over an AMD Ryzen 9 9950X and $24.3\times$/$6.58\times$ over an NVIDIA RTX 4090, and is $4.06\times$ more energy-efficient and $2.19\times$ faster than a feature-axis HDC ASIC baseline.
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