mlsanityData to 7 Oct 2026

Don't Unroll Adjoint: Differentiating SSA-Form Programs

arXiv 1810.07951 ↗First posted 18 Oct 2018cs.PLcited by 44

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Abstract (arXiv)

This paper presents reverse-mode algorithmic differentiation (AD) based on source code transformation, in particular of the Static Single Assignment (SSA) form used by modern compilers. The approach can support control flow, nesting, mutation, recursion, data structures, higher-order functions, and other language constructs, and the output is given to an existing compiler to produce highly efficient differentiated code. Our implementation is a new AD tool for the Julia language, called Zygote, which presents high-level dynamic semantics while transparently compiling adjoint code under the hood. We discuss the benefits of this approach to both the usability and performance of AD tools.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Oct 2018.

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Citing papers per year: 2021: 11; 2022: 10; 2023: 5; 2024: 5; 2025: 7; 2026: 6.

44 papers.

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  1. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  2. 2021Torch.fx: Practical Program Capture and Transformation for Deep Learning in Pythoncited by 38
  3. 2023Interpretable Machine Learning for Science with PySR and SymbolicRegression.jlcited by 36
  4. 2022Automatic Differentiation of Programs with Discrete Randomnesscited by 28
  5. 2021Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristicscited by 26
  6. 2021Discovering Sparse Interpretable Dynamics from Partial Observationscited by 25
  7. 2021Physics-enhanced deep surrogates for partial differential equationscited by 18
  8. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  9. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  10. 2024PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representationscited by 11
  11. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  12. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
32 more
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  2. 2022Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure managementcited by 7
  3. 2023Learned multiphysics inversion with differentiable programming and machine learningcited by 7
  4. 2022DiSECt: A Differentiable Simulator for Parameter Inference and Control in Robotic Cuttingcited by 6
  5. 2024Proximal Oracles for Optimization and Samplingcited by 5
  6. 2024What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learningcited by 5
  7. 2024Provably Scalable Black-Box Variational Inference with Structured Variational Familiescited by 4
  8. 2025Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiationcited by 4
  9. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletionscited by 4
  10. 2021Spline parameterization of neural network controls for deep learningcited by 3
  11. 2021Mapping the Internet: Modelling Entity Interactions in Complex Heterogeneous Networkscited by 3
  12. 2022NeuralFMU: Presenting a workflow for integrating hybrid NeuralODEs into real world applicationscited by 3
  13. 2022Recursive Neural Programs: Variational Learning of Image Grammars and Part-Whole Hierarchiescited by 2
  14. 2021Physics informed machine learning with Smoothed Particle Hydrodynamics: Hierarchy of reduced Lagrangian models of turbulencecited by 1
  15. 2022Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradientcited by 1
  16. 2023RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustnesscited by 1
  17. 2025Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherencecited by 1
  18. 2026Distributionally Robust PAC-Bayesian Controlcited by 1
  19. 2026Investigating Action Encodings in Recurrent Neural Networks in Reinforcement Learningcited by 1
  20. 2021Self-explaining variational posterior distributions for Gaussian Process modelscited by 0
  21. 2021Coarsening Optimization for Differentiable Programmingcited by 0
  22. 2022Combinatory Adjoints and Differentiationcited by 0
  23. 2022Incremental Correction in Dynamic Systems Modelled with Neural Networks for Constraint Satisfactioncited by 0
  24. 2023Chemellia: An Ecosystem for Atomistic Scientific Machine Learningcited by 0
  25. 2025A Common Interface for Automatic Differentiationcited by 0
  26. 2025Universal Differential Equations for Scientific Machine Learning of Node-Wise Battery Dynamics in Smart Gridscited by 0
  27. 2025Residual-Informed Learning of Solutions to Algebraic Loopscited by 0
  28. 2025CODE: A global approach to ODE dynamics learningcited by 0
  29. 2026Loss Landscape Geometry of Partial Differential Equation Emulators: Or, Symmetry Learning via Gradient Alignmentcited by 0
  30. 2026A Differentiable Atari VCS:A Complex, Fully Known Ground Truth for Explainable AIcited by 0
  31. 2026Mosaic: A Benchmark Suite for Differentiable Physics Solverscited by 0
  32. 2026Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learningcited by 0