Tokens-per-Parameter Coverage Is Critical for Robust LLM Scaling Law Extrapolation
Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio $k$ and set $D = kN$. We show that this collinear design, combined with the empirically common near-equality of the exponents governing $N$ and $D$, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the $N$ and $D$-exponents. The scale coefficients become practically unidentifiable, with confidence intervals i...
| Authors | Joshua Shay Kricheli, Alexander Lawrence Reid, Soumajyoti Sarkar et al. |
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| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 12 May 2026 |
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