Bayesian Neural Scaling Law Extrapolation with Prior-Data Fitted Networks
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912431472640000 |
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| author | Lee, Dongwoo Lee, Dong Bok Adriaensen, Steven Lee, Juho Hwang, Sung Ju Hutter, Frank Kim, Seon Joo Lee, Hae Beom |
| author_facet | Lee, Dongwoo Lee, Dong Bok Adriaensen, Steven Lee, Juho Hwang, Sung Ju Hutter, Frank Kim, Seon Joo Lee, Hae Beom |
| contents | Scaling has been a major driver of recent advancements in deep learning. Numerous empirical studies have found that scaling laws often follow the power-law and proposed several variants of power-law functions to predict the scaling behavior at larger scales. However, existing methods mostly rely on point estimation and do not quantify uncertainty, which is crucial for real-world applications involving decision-making problems such as determining the expected performance improvements achievable by investing additional computational resources. In this work, we explore a Bayesian framework based on Prior-data Fitted Networks (PFNs) for neural scaling law extrapolation. Specifically, we design a prior distribution that enables the sampling of infinitely many synthetic functions resembling real-world neural scaling laws, allowing our PFN to meta-learn the extrapolation. We validate the effectiveness of our approach on real-world neural scaling laws, comparing it against both the existing point estimation methods and Bayesian approaches. Our method demonstrates superior performance, particularly in data-limited scenarios such as Bayesian active learning, underscoring its potential for reliable, uncertainty-aware extrapolation in practical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Neural Scaling Law Extrapolation with Prior-Data Fitted Networks Lee, Dongwoo Lee, Dong Bok Adriaensen, Steven Lee, Juho Hwang, Sung Ju Hutter, Frank Kim, Seon Joo Lee, Hae Beom Machine Learning Artificial Intelligence Scaling has been a major driver of recent advancements in deep learning. Numerous empirical studies have found that scaling laws often follow the power-law and proposed several variants of power-law functions to predict the scaling behavior at larger scales. However, existing methods mostly rely on point estimation and do not quantify uncertainty, which is crucial for real-world applications involving decision-making problems such as determining the expected performance improvements achievable by investing additional computational resources. In this work, we explore a Bayesian framework based on Prior-data Fitted Networks (PFNs) for neural scaling law extrapolation. Specifically, we design a prior distribution that enables the sampling of infinitely many synthetic functions resembling real-world neural scaling laws, allowing our PFN to meta-learn the extrapolation. We validate the effectiveness of our approach on real-world neural scaling laws, comparing it against both the existing point estimation methods and Bayesian approaches. Our method demonstrates superior performance, particularly in data-limited scenarios such as Bayesian active learning, underscoring its potential for reliable, uncertainty-aware extrapolation in practical applications. |
| title | Bayesian Neural Scaling Law Extrapolation with Prior-Data Fitted Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2505.23032 |