$$s = f(\theta,\ e,\ \mathcal{P},\ \mathcal{H},\ \mathcal{S},\ t)$$

Equation 31 · Foundation Models

OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Collect the moving parts and the measurement problem becomes plain. An observed score s is produced by $s = f(\theta,\ e,\ \mathcal{P},\ \mathcal{H},\ \mathcal{S},\ t)$. with weights $\theta$ , reasoning effort e , prompt and decoding configuration $\mathcal{P}$ , evaluation harness $\mathcal{H}$ , serving stack $\mathcal{S}$ , and date t . A published number fixes s and usually reports only part of $\theta$ and t . The system is underdetermined : many configurations produce the same score, and the same configuration produces different scores on different dates.

Meanings in this article

• $s$: the observed score.
• $\theta$: the weights.
• $e$: the reasoning effort.
• $\mathcal{P}$: the prompt and decoding configuration.
• $\mathcal{H}$: the evaluation harness.
• $\mathcal{S}$: the serving stack.
• $t$: the date.

Equation guide → · Article →