Relevant math, said the Bear
“That's a lot of math, I think,” said the Bear, very confused. “But it looks like relevant math.”Internal monologue // upon encountering the diagram
Why it is
relevant
The diagram gives the compact, general story: gather inputs, multiply them by learned weights, add a bias, pass the result through a nonlinear curve, and adjust parameters during training so the network makes smaller errors.
That is relevant to the Mesocosm work because our “landings” inspect post-nonlinearity MLP activations. We ask which neuron reaches the largest observed activation for a given string, then preserve and replay the strings selected by that criterion.
It is not, however, a literal diagram of a GPT-2 MLP neuron. GPT-2 projects a high-dimensional residual-stream vector into its MLP, applies GELU rather than the sigmoid drawn here, and projects the result back into the residual stream. Bear's visual suspicion was sound: GELU is not this bounded S-curve. It resembles a softened hockey stick, with a slight negative dip before rising almost linearly on the positive side. The image is a friendly account of the family resemblance, not the exact local machinery.
There is indeed a lot of math. It is indeed relevant. Total comprehension is not required before recording the encounter.