Make Haste Slowly: A Theory of Emergent Structured Mixed Selectivity in Feature Learning ReLU Networks
This work addresses a foundational gap in understanding feature learning in practical deep learning models, though it is incremental as it builds on existing theories and focuses on specific tasks.
The paper tackles the lack of a theory for feature learning in finite-dimensional ReLU neural networks by establishing an equivalence with Gated Deep Linear Networks and analyzing learning dynamics on multi-task-like tasks, showing that ReLU networks develop structured, reusable latent representations rather than strictly modular ones, with this effect enhanced by more contexts and hidden layers.
In spite of finite dimension ReLU neural networks being a consistent factor behind recent deep learning successes, a theory of feature learning in these models remains elusive. Currently, insightful theories still rely on assumptions including the linearity of the network computations, unstructured input data and architectural constraints such as infinite width or a single hidden layer. To begin to address this gap we establish an equivalence between ReLU networks and Gated Deep Linear Networks, and use their greater tractability to derive dynamics of learning. We then consider multiple variants of a core task reminiscent of multi-task learning or contextual control which requires both feature learning and nonlinearity. We make explicit that, for these tasks, the ReLU networks possess an inductive bias towards latent representations which are not strictly modular or disentangled but are still highly structured and reusable between contexts. This effect is amplified with the addition of more contexts and hidden layers. Thus, we take a step towards a theory of feature learning in finite ReLU networks and shed light on how structured mixed-selective latent representations can emerge due to a bias for node-reuse and learning speed.