spred: Solving $L_1$ Penalty with SGD

• URL: http://arxiv.org/abs/2210.01212v5
• Date: Wed, 12 Jul 2023 15:09:24 GMT
• Title: spred: Solving $L_1$ Penalty with SGD
• Authors: Liu Ziyin, Zihao Wang
• Abstract summary: We propose to minimize a differentiable objective with $L_$ using a simple reparametrization. We prove that the reparametrization trick is completely benign" with an exactiable non function.
• Score: 6.2255027793924285
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, \textit{spred}, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely ``benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.

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