Collinear tokens-per-parameter designs in scaling law fits induce ill-conditioning when N and D exponents are similar, inflating uncertainty and degrading off-ray extrapolations; non-collinear designs are required for robust estimation.
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Tokens-per-Parameter Coverage Is Critical for Robust LLM Scaling Law Extrapolation
Collinear tokens-per-parameter designs in scaling law fits induce ill-conditioning when N and D exponents are similar, inflating uncertainty and degrading off-ray extrapolations; non-collinear designs are required for robust estimation.