A Simple Model of Inference Scaling Laws
Track: long paper (up to 8 pages)
Keywords: Scaling Laws, Inference Scaling, Maths, Coding, LLMs.
TL;DR: We provide a simple predictive model for the functional behavior of inference scaling with increasing number of attempts.
Abstract: Neural scaling laws have garnered significant interest due to their ability to predict model performance as a function of increasing parameters, data, and compute. In this work, we propose a simple statistical ansatz based on memorization to study scaling laws in the context of inference. Specifically, how performance improves with multiple inference attempts. We explore the coverage, or pass@k metric, which measures the chance of success over repeated attempts and provide a motivation for the observed functional form of the inference scaling behavior of the coverage in large language models (LLMs) on reasoning tasks.
We then define an "inference loss", which exhibits a power-law decay as the number of trials increases, and connect this result with prompting costs. We further test the universality of our construction by conducting experiments on a simple generative model, and find that our predictions are in agreement with the empirical coverage curves in a controlled setting. Our simple framework sets the ground for incorporating inference scaling with other known scaling laws.
Submission Number: 86
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