AI 中文总结
该研究在权重为{-1,0,1}的三元McCulloch-Pitts网络中精确实现冯·诺依曼的通用构造与自复制，构建了可自复制的SUBLEQ计算机，相关结果在Rocq中得到证明。
AI 中文摘要
权重取值为{-1,0,1}的固定McCulloch-Pitts阈值单元网络可在其状态中容纳其他阈值网络并运行它们：该状态是一个由记录组构成的环，每个记录对应一个存储网络的单元，每一步会评估一个记录。我们利用此类网络精确实现冯·诺依曼的通用构造与自复制。如同元胞自动机保持其规则，该固定网络保持其权重，而被复制的是存储的网络。一个包含143个记录的构造器从其磁带上读取网络描述，在下一个存储组中构建该网络，将描述复制到下一个磁带并将控制权交给所构建的网络；当以自身描述启动时，它会在每一代重建自身（包括权重）。该方案可扩展为通用计算机：一个由17598个三元单元构成的SUBLEQ计算机，存储为36080个记录并运行包含27条指令的程序，可构建适配存储组的任意网络，并以相同方式自复制，适用于从8位起的所有字宽；直接运行时，它会输出自身权重、内存和磁带的序列化结果。整数预激活为每个轨道提供1/2的余量，将每个单元复制r倍会使其乘以r，这足以抵御预激活上任意大小的噪声，但对于冯·诺依曼的输出翻转，仅能抵御低于与扇入成反比的阈值的翻转。这些结果在Rocq中得到证明。
英文摘要
A fixed network of McCulloch-Pitts threshold units with weights in {-1,0,1} can hold other threshold networks in its state and run them: the state is a ring of banks of records, each record a unit of a stored network, and each step evaluates one record. We use such a network to carry out von Neumann's universal construction and self-reproduction exactly. As a cellular automaton keeps its rule, the fixed network keeps its weights, and what reproduces is a stored network. A constructor of 143 records reads the description of a network from its tape, builds that network in the next bank, copies the description onto the next tape and hands control to what it built; started on its own description, it rebuilds itself, weights included, in every generation. The scheme scales to a universal computer. A SUBLEQ computer of 17,598 ternary units, stored as 36,080 records and running a program of 27 instructions, builds any network that fits a bank and reproduces itself in the same way, at every word width from eight bits on; run directly, it emits the serialization of its own weights, memory and tape. Integer pre-activations give every orbit a margin of 1/2, and replicating each unit r times multiplies it by r. That suffices against noise of any size on the pre-activations, but against von Neumann's output flips only below a threshold inversely proportional to the fan-in. These results are proved in Rocq.
Comments42 pages, 4 figures, 7 tables. Rocq proofs, code and run records: https://huggingface.co/phanerozoic/threshold-computers
