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：本文报告一项意外发现：在一种确定性超维度计算（HDC）架构中——该架构颠覆了伽罗瓦域代数的传统角色，将其从纠错以获得唯一答案的用途转变为相对相似性和路径质量排序的引擎——涌现出一种路径依赖的语义选择机制，其等效于脉冲时序依赖可塑性（STDP），且该机制的量级可通过闭合表达式准确预测，并与实测值吻合。针对代数层面的灾难性遗忘、学习停滞与绑定问题，我们提出VaCoAl（模糊一致性算法）及其Python实现PyVaCoAl，并部署于超高维度SRAM/DRAM-CAM架构。该方法根植于稀疏分布式记忆，通过伽罗瓦域扩散解决高维二值空间中的正交化与检索问题，实现低负载部署。关键在于，VaCoAl将认知边界——前沿大小——嵌入架构，通过路径积分置信度（CR2）对候选路径进行排序，从而实现组合泛化；这种有限理性设计产生的STDP式选择，是纠错范式在结构上无法实现的。我们基于Wikidata中约47万条师徒关系数据评估了多跳推理能力，追踪至多57代（超过2550万条路径）。通过结合基于置信度降噪的HDC捆绑与解绑操作，量化了有向无环图上的概念传播。结果表明，该模型不仅重新诠释了牛顿-莱布尼茨之争，还揭示了从稀疏收敛到后莱布尼茨“超高速通道”的相变过程，其结构指标支持库恩范式转换的观点。因此，VaCoAl定义了第三范式——HDC-AI，以可逆、可审计的多跳推理能力补充大语言模型。