There are papers written about this. https://openreview.net/pdf/0c9a0f445d430a4d2bf9a08078c43509199adf4d.pdf https://openreview.net/pdf/0c9a0f445d430a4d2bf9a08

There are papers written about this. https://openreview.net/pdf/0c9a0f445d430a4d2bf9a08078c43509199adf4d.pdf https://openreview.net/pdf/0c9a0f445d430a4d2bf9a08078c435091... Without a loop - an LLM takes a fixed set of tokens and produces a fixed set of tokens. It has some internal state. So without a loop an LLM cannot be a general purpose computer (Turing machine). Turing machines are simple. They need 3 things - infinitely long tape, ability to have internal state, and conditionally write and move tape based on what is on tape. So if an LLM had access to infinite memory, all it needs is to implement a subleq instruction which is quite simple, and run itself in a loop. See https://en.m.wikipedia.org/wiki/One-instruction_set_computer https://en.m.wikipedia.org/wiki/One-instruction_set_computer One instruction set computer See this paper from DeepMind which talks about compiling existing code into transformer primitives https://arxiv.org/pdf/2301.05062.pdf https://arxiv.org/pdf/2301.05062.pdf So the smallest ML model that can do arbitrary math with () * / + - operators and floating/int numbers is not that complex. Perhaps few 1000s of params. One can compile existing code into transformer weights. Now that you mention, I’ve been nerdsniped to building it.