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：本文报告了一个意外发现：在一种确定性超维计算（HDC）架构中——该架构颠覆了伽罗华域代数的传统角色，将其从追求唯一答案的纠错引擎转变为相对相似性与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，该机制等效于脉冲时序依赖可塑性（STDP），且其幅度可通过闭合形式的表达式由测量值先验预测。为从代数层面解决灾难性遗忘、学习停滞和绑定问题，我们提出了VaCoAl（模糊一致算法）及其在超高维SRAM/DRAM-CAM上的Python实现PyVaCoAl。该方法根植于稀疏分布式记忆，通过伽罗华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——嵌入其架构中，通过路径积分置信度（CR2）对候选方案进行排序，从而达成组合泛化；这种有限理性设计产生的类STDP选择是纠错范式在结构上无法实现的。我们基于Wikidata中约47万个导师-学生关系评估了多跳推理，追溯了多达57代（超过2550万条路径）。通过基于CR去噪的HDC捆绑与解绑操作，量化了有向无环图（DAG）上的概念传播。结果显示了对牛顿-莱布尼茨争议的重新诠释，以及从稀疏收敛到后莱布尼茨“超高速公路”的相变，其结构指标支持库恩范式的转变。VaCoAl由此定义了第三范式——HDC-AI，通过可逆、可审计的多跳推理补充了大语言模型。