Principled and Efficient Transfer Learning of Deep Models via Neural Collapse

With the ever-growing model size and the limited availability of labeled training data, transfer learning has become an increasingly popular approach in many science and engineering domains. For classification problems, this work delves into the mystery of transfer learning through an intriguing phenomenon termed neural collapse (NC), where the last-layer features and classifiers of learned deep networks satisfy: (i) the within-class variability of the features collapses to zero, and (ii) the between-class feature means are maximally and equally separated. Through the lens of NC, our findings for transfer learning are the following: (i) when pre-training models, preventing intra-class variability collapse (to a certain extent) better preserves the intrinsic structures of the input data, so that it leads to better model transferability; (ii) when fine-tuning models on downstream tasks, obtaining features with more NC on downstream data results in better test accuracy on the given task. The above results not only demystify many widely used heuristics in model pre-training (e.g., data augmentation, projection head, self-supervised learning), but also leads to more efficient and principled fine-tuning method on downstream tasks that we demonstrate through extensive experimental results.