Equation 1 · Claude, From First Principles: Training, Constitutional Methods, and What Actually Shapes a Response
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Symbol C_pre
re is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol D
the number of training tokens, the factor of six accounting for the forward and backward pass together.
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The architecture underneath a Claude model, like nearly every other frontier language system, is a decoder-only transformer trained to predict the next token over a very large corpus [ 12 ] . What that training actually produces is not knowledge in any curated sense but a prior — a broad distribution over plausible continuations that encodes an enormous amount about language, code, and the structure of arguments, and comparatively little about what any particular operator wants done with it. Two variables set the price of that prior. Pretraining compute for a dense transformer is well approximated by . where N is the parameter count and D is the number of training tokens,…
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The architecture underneath a Claude model, like nearly every other frontier language system, is a decoder-only transformer trained to predict the next token over a very large corpus [ 12 ] . What that training actually produces is not knowledge in any curated sense but a prior — a broad distribution over plausible continuations that encodes an enormous amount about language, code, and the structure of arguments, and comparatively little about what any particular operator wants done with it. Two variables set the price of that prior. Pretraining compute for a dense transformer is well approximated by . where N is the parameter count and D is the number of training tokens, the factor of six accounting for the forward and backward pass together. Kaplan and colleagues showed empirically that test loss falls as a power law in each of N , D , and compute across many orders of magnitude, with a functional form that includes an irreducible floor: doubling the parameter count buys a fixed decrement in loss, not a fixed multiple of capability [ 12 ] . That single empirical regularity is a large part of why frontier pretraining runs keep growing and why each one produces diminishing, rather than accelerating, returns.
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