This is ultimately a basic adaptation of the pigeonhole principle and is not surprising. A finite system of matrix multiplications cannot be turing complete. Yo

This is ultimately a basic adaptation of the pigeonhole principle and is not surprising. A finite system of matrix multiplications cannot be turing complete. You cannot expect one trip through a series of matrix multiplications and bias additions and a final sampling at the end which commits it to a certain answer to ever produce a correct answer. It's a mathematical impossibility. No talk of quantum woo, emergent phenomenen, or whatever other pseudo-science has arisen to explain AI intelligence can get around this simple truth of mathematics. However, chain of thought reasoning where token streams can continue ad infinitum could potentially solve large swaths of problems whose ordinary solutions require turing machines. It could also solve problems that cannot generally be solved by turing machines, but where you only need solutions for a few classes of problems. Either way, even with chain of thought, you would expect that... in some instances, the model output diverges and does not complete. And unsurprisingly... this is exactly what you see with the DeepSeek models (and other CoT models) when you pose it difficult questions. It will never emit the </think> tag.