去随机化稠密二值超向量码本用于量化标量
Derandomizing Dense Binary Hypervector Codebooks for Quantized Scalars
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中文总结 AI 辅助
针对超维计算中稠密二值标量码本因有限维度误差偏离目标相似度的问题，提出基于转换的去随机化框架，分离目标定律、变体和生成器构造，推导精确误差表达式，模拟验证各约束消除特定不匹配来源，为硬件约束下选择码本生成器提供指导。
中文摘要 AI 辅助
超维计算和向量符号架构通常使用稠密二值码本来表示量化的标量级别，其级别间的相似度旨在遵循标量间隔的预定函数。在有限维度下，随机标量码本构造会因采样噪声、随机起始不平衡、更新计数波动、分量依赖性和有限容量效应而偏离此目标。我们开发了一种基于转换的去随机化框架，用于两类目标相似度族中的稠密二值标量码本，其中相似度随级别间隔呈指数或线性衰减。该框架将目标相似度定律、去随机化变体和具体生成器构造分开，明确说明了初始化、选择、更新和容量处理机制如何塑造诱导的相似度分布。我们形式化了去随机化变体，这些变体分别约束初始汉明权重、更新计数变异性和更新平衡，从而控制有限维度误差的不同来源。对于每个族和变体，我们推导了诱导的平均相似度，识别了实现级和均值目标匹配机制，并推导了偏差、方差和均方根误差的精确有限维度表达式。跨维度、量化范围、参考标量级别和生成器构造的模拟验证了理论，并展示了每个约束如何消除或减少特定来源的相似度不匹配。结果为在有限维度和硬件相关约束下选择更接近期望相似度定律的标量码本生成器提供了实用指导。
英文摘要
Hyperdimensional computing and vector symbolic architectures often represent quantized scalar levels by dense binary codebooks whose level-to-level similarity is intended to follow a prescribed function of scalar separation. At finite dimensionality, randomized scalar codebook constructions deviate from this target because of sampling noise, random-start imbalance, update-count fluctuations, component dependence, and finite-capacity effects. We develop a transition-based derandomization framework for dense binary scalar codebooks across two target-similarity families, with similarity decaying exponentially or linearly with level separation. The framework separates the target similarity law, the derandomization variant, and the concrete generator construction, making explicit how initialization, selection, update, and capacity-handling mechanisms shape the induced similarity profile. We formalize derandomization variants that separately constrain initial Hamming weight, update-count variability, and update balance, thereby controlling distinct sources of finite-dimensional error. For each family and variant, we derive the induced mean similarity, identify realization-wise and mean target-matching regimes, and derive exact finite-dimensional expressions for bias, variance, and root-mean-square error. Simulations across dimensions, quantization ranges, reference scalar levels, and generator constructions validate the theory and show how each constraint removes or reduces a specific source of similarity mismatch. The results provide practical guidance for choosing scalar codebook generators that more closely match a desired similarity law under finite-dimensional and hardware-relevant constraints.
发表机构
- Luleå University of Technology（吕勒奥理工大学）
- Institute of Information Technologies and Systems（信息技术与系统研究所）
- Örebro University（厄勒布鲁大学）
- Research Institutes of Sweden（瑞典研究院）
- VSB - Technical University of Ostrava（VSB-俄斯特拉发技术大学）
机构由 AI 辅助整理，请以论文原文为准。
