A Simple Model of Inference Scaling Laws
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910732429295616 |
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| author | Levi, Noam |
| author_facet | Levi, Noam |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple Model of Inference Scaling Laws Levi, Noam Machine Learning Artificial Intelligence Information Theory 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 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. |
| title | A Simple Model of Inference Scaling Laws |
| topic | Machine Learning Artificial Intelligence Information Theory |
| url | https://arxiv.org/abs/2410.16377 |