This paper reports an unexpected finding: in a deterministic hyperdimensional computing (HDC) architecture **that inverts the conventional role of Galois-field algebra -- employing it not for error correction toward a unique answer but as an engine for relative similarity and path-quality ranking -- **a path-dependent semantic selection mechanism emerges, equivalent to spike-timing-dependent plasticity (STDP), with magnitude predictable a priori from a closed-form expression matching measured values. Addressing catastrophic forgetting, learning stagnation, and the Binding Problem at an algebraic level, we propose VaCoAl (Vague Coincident Algorithm) and its Python implementation PyVaCoAl on ultra-high-dimensional SRAM/DRAM-CAM. Rooted in Sparse Distributed Memory, it resolves orthogonalisation and retrieval in high-dimensional binary spaces via Galois-field diffusion, enabling low-load deployment. Crucially, VaCoAl embeds a cognitive bound -- the Frontier Size -- into its architecture, ranking candidates by path-integral confidence (CR2) to achieve compositional generalisation; this bounded-rationality design produces STDP-like selection that error-correction paradigms structurally cannot attain. We evaluated multi-hop reasoning on about 470k mentor-student relations from Wikidata, tracing up to 57 generations (over 25.5M paths). HDC bundling and unbinding with CR-based denoising quantify concept propagation over DAGs. Results show a reinterpretation of the Newton-Leibniz dispute and a phase transition from sparse convergence to a post-Leibniz "superhighway", with structural indicators supporting a Kuhnian paradigm shift. VaCoAl thus defines a third paradigm, HDC-AI, complementing LLMs with reversible, auditable multi-hop reasoning.

翻译：本文报道一项意外发现：在一种确定性超维计算架构中——该架构反转了伽罗瓦域代数的传统角色，将其从纠错以获得唯一答案转变为用于相对相似性和路径质量排序的引擎——一种路径依赖的语义选择机制由此涌现，其特性等同于脉冲时序依赖可塑性，且其量级可通过闭合形式表达式预先计算，与实测值完美匹配。为从代数层面解决灾难性遗忘、学习停滞和绑定问题，我们提出VaCoAl算法及其Python实现PyVaCoAl，该算法运行于超高维SRAM/DRAM-CAM平台。基于稀疏分布式记忆，该算法通过伽罗瓦域扩散实现高维二值空间中的正交化与检索，支持低负载部署。关键在于，VaCoAl将认知边界——“前沿尺寸”——内嵌于架构中，通过路径积分置信度对候选方案进行排序，从而实现组合泛化；这种受限理性设计产生了结构性超越纠错范式的STDP式选择机制。我们基于维基数据中约47万条师生关系记录开展多跳推理评估，追溯至第57代（超过2550万条路径）。采用超维计算捆绑与解绑技术，结合基于置信度的去噪方法，量化有向无环图上的概念传播。结果表明，该框架不仅重新诠释了牛顿-莱布尼茨之争，更揭示了从稀疏收敛到后莱布尼茨时代“超高速公路”的相变过程，其结构指标支持库恩式范式转换。VaCoAl由此定义了第三种范式——高维计算人工智能，以可逆、可审计的多跳推理能力补充大语言模型。