Papers › The Elements of Differentiable Programming

The Elements of Differentiable Programming

21 Mar 2024arXiv:2403.14606archive 2025-07-28

Mathieu Blondel, Vincent Roulet

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming paradigm enables end-to-end differentiation of complex computer programs (including those with control flows and data structures), making gradient-based optimization of program parameters possible. As an emerging paradigm, differentiable programming builds upon several areas of computer science and applied mathematics, including automatic differentiation, graphical models, optimization and statistics. This book presents a comprehensive review of the fundamental concepts useful for differentiable programming. We adopt two main perspectives, that of optimization and that of probability, with clear analogies between the two. Differentiable programming is not merely the differentiation of programs, but also the thoughtful design of programs intended for differentiation. By making programs differentiable, we inherently introduce probability distributions over their execution, providing a means to quantify the uncertainty associated with program outputs.

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argmax diffprog/code/control_flows/plot_soft_thresholding.py official repository ran fingerprinted Apache-2.0 (permissive) · 802c2203920ee74b · report
chain_log_sum diffprog/code/graphical_models/inference_chain.py official repository ran Apache-2.0 (permissive) · f2d5d8a5fd1be3c9 · report
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chain_product diffprog/code/graphical_models/inference_chain.py official repository ran Apache-2.0 (permissive) · 46817697c062b78f · report
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fun diffprog/code/control_flows/plot_global_vs_local_smoothing.py official repository ran fingerprinted Apache-2.0 (permissive) · 13c7a0f0304259eb · report
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or_op diffprog/code/control_flows/plot_logical_ops_3d.py official repository ran fingerprinted Apache-2.0 (permissive) · 0cf69f025a2232ed · report
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