Bridging Discrete and Backpropagation: Straight-Through and Beyond

• URL: http://arxiv.org/abs/2304.08612v3
• Date: Mon, 16 Oct 2023 16:27:02 GMT
• Title: Bridging Discrete and Backpropagation: Straight-Through and Beyond
• Authors: Liyuan Liu, Chengyu Dong, Xiaodong Liu, Bin Yu, Jianfeng Gao
• Abstract summary: We propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. We propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs.
• Score: 62.46558842476455
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Backpropagation, the cornerstone of deep learning, is limited to computing gradients for continuous variables. This limitation poses challenges for problems involving discrete latent variables. To address this issue, we propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. First, we examine the widely used Straight-Through (ST) heuristic and demonstrate that it works as a first-order approximation of the gradient. Guided by our findings, we propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs. ReinMax does not require Hessian or other second-order derivatives, thus having negligible computation overheads. Extensive experimental results on various tasks demonstrate the superiority of ReinMax over the state of the art. Implementations are released at https://github.com/microsoft/ReinMax.

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