Taisuke Yasuda, Kyriakos Axiotis, Gang Fu, MohammadHossein Bateni, Vahab Mirrokni
Neural network pruning is a key technique towards engineering large yet scalable, interpretable, and generalizable models. Prior work on the subject has developed largely along two orthogonal directions: (1) differentiable pruning for efficiently and accurately scoring the importance of parameters, and (2) combinatorial optimization for efficiently searching over the space of sparse models. We unite the two approaches, both theoretically and empirically, to produce a coherent framework for structured neural network pruning in which differentiable pruning guides combinatorial optimization algorithms to select the most important sparse set of parameters. Theoretically, we show how many existing differentiable pruning techniques can be understood as nonconvex regularization for group sparse optimization, and prove that for a wide class of nonconvex regularizers, the global optimum is unique, group-sparse, and provably yields an approximate solution to a sparse convex optimization problem. The resulting algorithm that we propose, SequentialAttention++, advances the state of the art in large-scale neural network block-wise pruning tasks on the ImageNet and Criteo datasets.
Taisuke Yasuda, MohammadHossein Bateni, Lin Chen, Matthew Fahrbach, Gang Fu, Vahab Mirrokni
Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on $\ell_1$ regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest.