The Flip Side of the Reweighted Coin: Duality of Adaptive Dropout and Regularization
This work provides theoretical insights into sparsification methods for deep learning, potentially aiding researchers in designing more efficient neural networks, though it is incremental as it builds on existing dropout and regularization concepts.
The paper uncovers a duality between adaptive dropout methods for sparsifying deep neural networks and regularization techniques, showing that monotonic dropout strategies correspond to subquadratic penalties leading to sparse solutions, with empirical validation on deep network sparsification tasks.
Among the most successful methods for sparsifying deep (neural) networks are those that adaptively mask the network weights throughout training. By examining this masking, or dropout, in the linear case, we uncover a duality between such adaptive methods and regularization through the so-called "$η$-trick" that casts both as iteratively reweighted optimizations. We show that any dropout strategy that adapts to the weights in a monotonic way corresponds to an effective subquadratic regularization penalty, and therefore leads to sparse solutions. We obtain the effective penalties for several popular sparsification strategies, which are remarkably similar to classical penalties commonly used in sparse optimization. Considering variational dropout as a case study, we demonstrate similar empirical behavior between the adaptive dropout method and classical methods on the task of deep network sparsification, validating our theory.