Implicit regularization of multi-task learning and finetuning in overparameterized neural networks

It is common in deep learning to train networks on auxiliary tasks with the expectation that the learning will transfer, at least partially, to another task of interest. In this work, we investigate the inductive biases that result from learning auxiliary tasks, either simultaneously (multi-task learning, MTL) or sequentially (pretraining and subsequent finetuning, PT+FT). In the simplified setting of two-layer diagonal linear networks trained with gradient descent, we identify implicit regularization penalties associated with MTL and PT+FT, both of which incentivize feature sharing between tasks and sparsity in learned task-specific features. Notably, our results imply that during finetuning, networks operate in a hybrid of the kernel (or "lazy") regime and the feature learning ("rich") regime identified in prior work. Moreover, PT+FT can exhibit a novel "nested feature learning" behavior not captured by either regime, which biases it to extract a sparse subset of the features learned during pretraining. In ReLU networks, we reproduce all of these qualitative behaviors. We also observe that PT+FT (but not MTL) is biased to learn features that are correlated with (but distinct from) those needed for the auxiliary task, while MTL is biased toward using identical features for both tasks. As a result, we find that in realistic settings, MTL generalizes better when comparatively little data is available for the task of interest, while PT+FT outperforms it with more data available. We show that our findings hold qualitatively for a deep architecture trained on image classification tasks. Our characterization of the nested feature learning regime also motivates a modification to PT+FT that we find empirically improves performance. Overall, our results shed light on the impact of auxiliary task learning and suggest ways to leverage it more effectively.