Generalization Bounds for Few-Shot Transfer Learning with Pretrained Classifiers

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. We offer a theoretical explanation for this behavior based on the recently discovered phenomenon of class-feature-variability collapse, that is, that during the training of deep classification networks the feature embeddings of samples belonging to the same class tend to concentrate around their class means. More specifically, we show that the few-shot error of the learned feature map on new classes (defined as the classification error of the nearest class-center classifier using centers learned from a small number of random samples from each new class) is small in case of class-feature-variability collapse, under the assumption that the classes are selected independently from a fixed distribution. This suggests that foundation models can provide feature maps that are transferable to new downstream tasks, even with very few samples; to our knowledge, this is the first performance bound for transfer-learning that is non-vacuous in the few-shot setting.