# Differentiable Programming `a la Moreau

arXiv: https://arxiv.org/abs/2012.15458 · HTML: https://mlsanity.com/paper/2012.15458/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2020.

## Built on by (most cited first, 2 of 2)

- [Differentiable Rendering with Perturbed Optimizers](https://mlsanity.com/paper/2110.09107/) (2021)
- [Target Propagation via Regularized Inversion](https://mlsanity.com/paper/2112.01453/) (2021)

## Abstract (arXiv)

The notion of a Moreau envelope is central to the analysis of first-order optimization algorithms for machine learning. Yet, it has not been developed and extended to be applied to a deep network and, more broadly, to a machine learning system with a differentiable programming implementation. We define a compositional calculus adapted to Moreau envelopes and show how to integrate it within differentiable programming. The proposed framework casts in a mathematical optimization framework several variants of gradient back-propagation related to the idea of the propagation of virtual targets.