# Demystifying Differentiable Programming: Shift/Reset the Penultimate Backpropagator

arXiv: https://arxiv.org/abs/1803.10228 · HTML: https://mlsanity.com/paper/1803.10228/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2018.

## Built on by (most cited first, 14 of 14)

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- [Learning to Optimize by Differentiable Programming](https://mlsanity.com/paper/2601.16510/) (2026)
- [Automatic Differentiation via Effects and Handlers: An Implementation in Frank](https://mlsanity.com/paper/2101.08095/) (2021)
- [Coarsening Optimization for Differentiable Programming](https://mlsanity.com/paper/2110.02307/) (2021)
- [Differentiable programming: Generalization, characterization and limitations of deep learning](https://mlsanity.com/paper/2205.06898/) (2022)
- [Combinatory Adjoints and Differentiation](https://mlsanity.com/paper/2207.00847/) (2022)
- [Differentiable Quantum Programming with Unbounded Loops](https://mlsanity.com/paper/2211.04507/) (2022)
- [Efficient and Sound Differentiable Programming in a Functional Array-Processing Language](https://mlsanity.com/paper/2212.10307/) (2022)
- [nablaSD: Differentiable Programming for Sparse Tensors](https://mlsanity.com/paper/2303.07030/) (2023)
- [Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning](https://mlsanity.com/paper/2607.03574/) (2026)

## Abstract (arXiv)

Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests in crucial ways on gradient-descent optimization and the ability to learn parameters of a neural network by backpropagating observed errors. However, neural network architectures are growing increasingly sophisticated and diverse, which motivates an emerging quest for even more general forms of differentiable programming, where arbitrary parameterized computations can be trained by gradient descent. In this paper, we take a fresh look at automatic differentiation (AD) techniques, and especially aim to demystify the reverse-mode form of AD that generalizes backpropagation in neural networks. We uncover a tight connection between reverse-mode AD and delimited continuations, which permits implementing reverse-mode AD purely via operator overloading and without any auxiliary data structures. We further show how this formulation of AD can be fruitfully combined with multi-stage programming (staging), leading to a highly efficient implementation that combines the performance benefits of deep learning frameworks based on explicit reified computation graphs (e.g., TensorFlow) with the expressiveness of pure library approaches (e.g., PyTorch).