Language models as superpositions of natural language programs: why constant-depth transformers won
willcb · x · 2026-10-16
willcb proposes a useful mental model: language models are superpositions of natural language programs, and training compiles the optimal DSL for your data distribution.
Citing one of his favorite modern papers, he explains: in circuit complexity a 'family of circuits' means one circuit CN per input size; constant depth means transformer layers don't grow with input size — only embedding dimension (log scale) and CoT length do, with CoT only needing to match the size of circuit CN. So you can compress the whole circuit family into a single transformer that works for all inputs of length N < exp(embed dim), given sufficient context.
He says the paper 'basically fully explains why transformers won, and why RL emerges as the right algorithm for the architecture.'
Related event: CoT Theory Paper Praised for Explaining Why Transformers Win(2 posts)→
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