Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation

• URL: http://arxiv.org/abs/2410.08125v1
• Date: Thu, 10 Oct 2024 17:10:00 GMT
• Title: Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation
• Authors: Felix Petersen, Christian Borgelt, Aashwin Mishra, Stefano Ermon,
• Abstract summary: We deal with the problem of gradient estimation for differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. We develop variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.
• Score: 59.86921150579892
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a non-differentiable function with a differentiable density distribution with full support, smoothing it and enabling gradient estimation. Our theory starts at first principles to derive stochastic smoothing with reduced assumptions, without requiring a differentiable density nor full support, and we present a general framework for relaxation and gradient estimation of non-differentiable black-box functions $f:\mathbb{R}^n\to\mathbb{R}^m$. We develop variance reduction for gradient estimation from 3 orthogonal perspectives. Empirically, we benchmark 6 distributions and up to 24 variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.

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