Fixed networks build and self-replicate stored threshold networks exactly
Universal Construction and Exact Self-Reproduction in Ternary McCulloch-Pitts Networks
Logic in Computer ScienceNeural and Evolutionary Computing
Summary
This paper shows how a fixed network made of simple units with limited connections and weights can store and run other network designs inside its own state. The authors demonstrate that such a network can carry out self-reproduction exactly, meaning it can build a copy of itself within its structure and then run the copy, including all its details. They also prove that this scheme scales up to universal computing machines and can protect itself against certain types of noise. This work builds on ideas originally proposed by von Neumann but applies them to a specific model of neural networks called ternary McCulloch-Pitts networks.
What this means in practice
- •For hardware designers: Implement fault-tolerant computing systems that can replicate their designs exactly within fixed neural network architectures.
- •For embedded system engineers: Develop self-replicating control systems for embedded devices using compact ternary threshold networks.
Authors
Charles C. Norton
Abstract
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.