Equation 4 · Claude, From First Principles: Training, Constitutional Methods, and What Actually Shapes a Response
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the parameter count. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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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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