This paper reports an unexpected finding: in a deterministic hyperdimensional computing (HDC) architecture based on Galois-field algebra, a path-dependent semantic selection mechanism emerges, equivalent to spike-timing-dependent plasticity (STDP), with magnitude predictable a priori by a closed-form expression matching large-scale measurements. This addresses limitations of modern AI including catastrophic forgetting, learning stagnation, and the Binding Problem at an algebraic level. We propose VaCoAl (Vague Coincident Algorithm) and its Python implementation PyVaCoAl, combining ultra-high-dimensional memory with deterministic logic. Rooted in Sparse Distributed Memory, it resolves orthogonalisation and retrieval in high-dimensional binary spaces via Galois-field diffusion, enabling low-load deployment. VaCoAl is a memory-centric architecture prioritising retrieval and association, enabling reversible composition while preserving element independence and supporting compositional generalisation with a transparent reliability metric (CR score). We evaluated multi-hop reasoning on about 470k mentor-student relations from Wikidata, tracing up to 57 generations (over 25.5M paths). Using HDC bundling and unbinding with CR-based denoising, we 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", from which structural indicators emerge supporting a Kuhnian paradigm shift. Collision-tolerance mechanisms further induce path-based pruning that favors direct paths, yielding emergent semantic selection equivalent to STDP. VaCoAl thus defines a third paradigm, HDC-AI, complementing LLMs with reversible multi-hop reasoning.

翻译：本文报告一项意外发现：在基于伽罗瓦域代数的确定性超维计算架构中，涌现出一种与脉冲时序依赖可塑性等效、且幅值可通过封闭公式预测（与大尺度测量结果吻合）的路径依赖语义选择机制。该机制在代数层面解决了现代人工智能的局限性，包括灾难性遗忘、学习停滞以及绑定问题。我们提出VaCoAl（模糊重合算法）及其Python实现PyVaCoAl，将超高维记忆与确定性逻辑相结合。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元空间的正交化与检索问题，支持低负载部署。VaCoAl是一种以记忆为中心的架构，优先实现检索与关联，在保持元素独立性的同时支持可逆组合，并通过透明可信度指标实现组合泛化。我们基于Wikidata中约47万组导师-学生关系（追踪至第57代，超过2550万条路径）评估了多跳推理能力。利用基于超维计算绑定/解绑与CR去噪的方法，我们量化了有向无环图中的概念传播机制。结果表明：牛顿-莱布尼茨争议获得全新诠释，并出现从稀疏收敛到后莱布尼茨“超级高速路”的相变，由此涌现支持库恩范式转移的结构性指标。碰撞容忍机制进一步诱导出偏好直接路径的路径剪枝，产生等效于脉冲时序依赖可塑性的涌现语义选择。VaCoAl由此定义了第三种范式——HDC-AI，以可逆多跳推理补充大语言模型。