用代数确定性内存架构模拟海马体记忆，实现可复现的向量联想与因果推理。
Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM
- 基于伽罗瓦域的确定性扩散机制替代随机投影，确保记忆复现精确
- 路径积分置信度比模型解释多跳回放衰减呈乘积关系，符合实测数据
- 打通神经科学与超维计算桥梁，适合研究记忆机制与因果推理的学者
向量-哈希（Vector-HaSH）与托尔曼-艾亨堡机器（TEM）提出海马-内嗅皮层回路通过网格细胞骨架对记忆进行组合性重播。与此同时，人类颅内脑电图（iEEG）显示，尖波涟漪调控回忆，多跳回放保真度按乘积方式衰减。然而，这两个领域缺乏共同的代数基础。本文提出VaCoAl——一种基于伽罗瓦域线性反馈移位寄存器的代数确定性超维内存架构。其确定性的伽罗瓦域扩散提供了向量-哈希中随机投影的底层替代方案，在保持准正交性的同时确保比特级精确复现。此外，路径积分置信度比CR2为经验观察到的乘积式回放衰减提供了代数可处理模型。生物上，VaCoAl的双运行模式与内嗅皮层-CA3直接通路及内嗅皮层-齿状回-CA3三突触通路一致，解释了其5.2亿年的保守性。独立细胞证据表明，齿状回-CA3通路实现了伽罗瓦域算术的生物物理同源。我们还将该框架与朱迪亚·珀尔的因果之梯关联：可逆的GF(2)绑定提供反事实操作（第2层）的代数手术工具，而双正交化器架构则为反事实推理（第3层）提供了并行底座。最终，我们证明了这些形式对应关系，并推导出可验证的iEEG预测，统一了计算神经科学、电生理学与超维计算。
原文摘要 · Abstract (English)
Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520-Myr conservation. Independent cellular evidence supports that the DG-CA3 pathway implements a biophysical homologue of Galois-field arithmetic. We also link this framework to Judea Pearl's Ladder of Causation. Reversible GF(2) binding provides the surgical algebra for the do-operator (Rung 2), and VaCoAl's dual-orthogonalizer architecture supplies the parallel substrate required for counterfactual reasoning (Rung 3). Ultimately, we prove these formal correspondences and derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.
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