alt Hacker NewsI was under the impression that intermediate tokens (“chain of thought”) are _not_ a representation of a model’s logical path, with one study observing that you can replace intermediate tokens with single character chains and still get the increased precision…
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How can they do that? Does state propagate between each token output?
That is, I were under the impression LLMs were just f(context), so chain of thought was f(...f(f(f(initial)+initial)+f(initial)+initial), i.e. y_n+1 = f(y_n+f(y_n-1)), where y_n is the nth output and f() the transformer inference function. Do they carry state across?
Yes dots increases precision, but not nearly the same increase in precision as having actual useful reasoning in the CoT
The tokens inside the transformer are only projected into token space to train them. In reality they ought to be treated as their own thing. What's really gone on is you've trained the final projection to be sensible rather than trained the llm to think using words. This seems to escape a lot of people. You can throw random empty tokens into transformers to get them to think more. More tokens means more attention mixing which means a larger dimensional space in which to think essentially.
CoT is both correlated and causal of the model's real computations, it's just imperfect. If you manually add "Let's wrap it up" in the CoT during generation, most LLMs will actually wrap it up (this is a commonly used trick in local LLM circles to get long-winded LLMs to stop reasoning). This wouldn't work if CoT text didn't affect the actual internal model logic.