Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing
Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelled dataset. In the high-dimensional regime, we derive exact expressions for training and generalis...
| Authors | Valentina Njaradi, Clémentine Dominé, Rachel Swanson et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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