Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914969515196416 |
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| author | Petersen, Felix Borgelt, Christian Mishra, Aashwin Ermon, Stefano |
| author_facet | Petersen, Felix Borgelt, Christian Mishra, Aashwin Ermon, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation Petersen, Felix Borgelt, Christian Mishra, Aashwin Ermon, Stefano Machine Learning 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. |
| title | Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.08125 |