用异或移位机制实现高速低功耗记忆，自动排序推理路径。
Beyond LLMs, Sparse Distributed Memory, and Neuromorphics <A Hyper-Dimensional SRAM-CAM "VaCoAl" for Ultra-High Speed, Ultra-Low Power, and Low Cost>
- 基于伽罗瓦域的异或移位操作，构建可逆绑定的记忆结构。
- 在64位导师-学生图中，56代后路径可靠性仍保持0.905以上。
- 无需修复冲突，碰撞容忍反成路径质量评估的关键机制。
VaCoAl（Python: PyVaCoAl）以代数方式解决绑定问题，而非统计方法：采用SRAM/DRAM-CAM架构，围绕一个基本操作——基于本原多项式LFSR的GF(2)上异或与移位。该设计源自Kanerva的稀疏分布式记忆，在百万维二进制空间中通过伽罗瓦域扩散实现检索；绑定与解绑在O(L)时间内完全可逆，支持组合泛化并具备事后可审计性。意外发现一种路径依赖的语义选择机制，功能等同于尖峰时间依赖可塑性（STDP），且可由数十万条记录的闭式匹配测量预先预测。其核心是‘不关心’（碰撞容忍）规则：非需消除的缺陷，而是路径质量排序的来源。可逆绑定结合碰撞容忍生成路径积分置信度量（CR2），用于候选路径的累积可靠性排名，这是哈希搜索所不具备的能力。若完全修复碰撞，排名即消失；永不失败的记忆无法记录路径的难易程度。我们并非超越大语言模型，而是提供其缺失的可审计路径排序层。基于约47万条WIKIDATA学者的导师-学生本体，从全部64位菲尔兹奖得主回溯至深度57，生成超过2550万条路径，对大规模有向无环图上的多跳推理进行压力测试。消融实验表明，‘不关心’规则施加深度相关的指数惩罚，剔除迂回路径而保留直接路径，体现奥卡姆剃刀原理。每代CR1维持在0.995–0.999之间，但累计CR2随代数单调衰减至第56代约0.905，与闭式公式0.997^56=0.846在观测波动范围内一致。所有测量均来自软件实现的PyVaCoAl DRAM-CAM；速度与功耗为投影值。
原文摘要 · Abstract (English)
VaCoAl (Python: PyVaCoAl) attacks the Binding Problem algebraically rather than statistically: an SRAM/DRAM-CAM organised end-to-end around one primitive, XOR-and-shift over GF(2) via primitive-polynomial LFSRs. Rooted in Kanerva's Sparse Distributed Memory, it retrieves in a million-dimensional binary space by Galois-field diffusion; Binding and Unbinding are exactly reversible at O(L), giving compositional generalisation with post-hoc auditability. Unexpectedly, a path-dependent semantic selection mechanism emerges undesigned, functionally equivalent to Spike-Timing-Dependent Plasticity (STDP) and predictable a priori from a closed form matching measurement on tens of millions of records. It is the Don't Care (collision-tolerance) rule: not a defect to engineer away, but the source of its ability to rank paths by quality. Capability: reversible binding plus tolerated collisions yields a path-integral confidence measure (CR2) ranking candidates by accumulated reliability, absent from hash-based search. Necessity: repair the collisions fully and the ranking vanishes; a memory that never fails has no record of which paths were difficult. Position: we do not surpass large language models; the substrate is orthogonal, supplying the auditable path-ranking layer they lack. A mentor-student ontology of ~470,000 WIKIDATA scholars, traversed backwards from all 64 Fields Medalists to depth 57 and >25.5M paths, stress-tests multi-hop reasoning over a large DAG. Ablation shows Don't Care imposing a depth-dependent exponential penalty that prunes circuitous routes and preserves direct ones: an Occam's razor. Per-generation CR1 stays within 0.995-0.999, yet cumulative CR2 decays monotonically to ~0.905 by generation 56, matching the closed form 0.997^56 = 0.846 within observed variation. All measurements are from PyVaCoAl, a software DRAM-CAM; speed and power figures are projections.
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