Compute Optimal Scaling of Skills: Knowledge vs Reasoning

Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, alongside a more recent growing list of other crucial decisions. In this work, we ask whether compute-optimal scaling behaviour can be skill-dependent. In particular, we examine knowledge and reasoning-based skills such as knowledge-based QA and code generation, and we answer this question in the affirmative: $\textbf{scaling laws are skill-dependent}$. Next, to understand whether skill-dependent scaling is an artefact of the pretraining datamix, we conduct an extensive ablation of different datamixes and find that, also when correcting for datamix differences, $\textbf{knowledge and code exhibit fundamental differences in scaling behaviour}$. We conclude with an analysis of how our findings relate to standard compute-optimal scaling using a validation set, and find that \textbf{a misspecified validation set can impact compute-optimal parameter count by nearly 50%,} depending on its skill composition.