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1. Systematically Differentiating Parametric Discontinuities

   https://doi.org/10.1145/3450626.3459775  

   Bangaru, Sai Praveen; Michel, Jesse; Mu, Kevin; Bernstein, Gilbert; Li, Tzu-Mao; Ragan-Kelley, Jonathan (August 2021, ACM transactions on graphics)

   Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation. We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs. 

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2. Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients

   Moses, William; Churavy, Valentin (January 2020, Advances in neural information processing systems)

   Applying differentiable programming techniques and machine learning algorithms to foreign programs requires developers to either rewrite their code in a machine learning framework, or otherwise provide derivatives of the foreign code. This paper presents Enzyme, a high-performance automatic differentiation (AD) compiler plugin for the LLVM compiler framework capable of synthesizing gradients of statically analyzable programs expressed in the LLVM intermediate representation (IR). Enzyme synthesizes gradients for programs written in any language whose compiler targets LLVM IR including C, C++, Fortran, Julia, Rust, Swift, MLIR, etc., thereby providing native AD capabilities in these languages. Unlike traditional source-to-source and operator-overloading tools, Enzyme performs AD on optimized IR. On a machine-learning focused benchmark suite including Microsoft's ADBench, AD on optimized IR achieves a geometric mean speedup of 4.2 times over AD on IR before optimization allowing Enzyme to achieve state-of-the-art performance. Packaging Enzyme for PyTorch and TensorFlow provides convenient access to gradients of foreign code with state-of-the-art performance, enabling foreign code to be directly incorporated into existing machine learning workflows. 

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3. Differentiable Quantum Programming with Unbounded Loops

   https://doi.org/10.1145/3617178  

   Fang, Wang; Ying, Mingsheng; Wu, Xiaodi (January 2024, ACM Transactions on Software Engineering and Methodology)

   The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications. 

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4. GPU Accelerated Automatic Differentiation With Clad

   Ifrim, Ioana; Vassilev, Vassil; Lange, David (October 2022, 20th International Workshop on Advanced Computing and Analysis Techniques in Physics Research)

   Automatic Differentiation (AD) is instrumental for science and industry. It is a tool to evaluate the derivative of a function specified through a computer program. The range of AD application domain spans from Machine Learning to Robotics to High Energy Physics. Computing gradients with the help of AD is guaranteed to be more precise than the numerical alternative and have a low, constant factor more arithmetical operations compared to the original function. Moreover, AD applications to domain problems typically are computationally bound. They are often limited by the computational requirements of high-dimensional parameters and thus can benefit from parallel implementations on graphics processing units (GPUs). Clad aims to enable differential analysis for C/C++ and CUDA and is a compiler-assisted AD tool available both as a compiler extension and in ROOT. Moreover, Clad works as a plugin extending the Clang compiler; as a plugin extending the interactive interpreter Cling; and as a Jupyter kernel extension based on xeus-cling. We demonstrate the advantages of parallel gradient computations on GPUs with Clad. We explain how to bring forth a new layer of optimization and a proportional speed up by extending Clad to support CUDA. The gradients of well-behaved C++ functions can be automatically executed on a GPU. The library can be easily integrated into existing frameworks or used interactively. Furthermore, we demonstrate the achieved application performance improvements, including (~10x) in ROOT histogram fitting and corresponding performance gains from offloading to GPUs. 

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5. Automatic Differentiation of Programs with Discrete Randomness

   Arya, Gaurav and (November 2022, Advances in Neural Information Processing Systems)

   Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability p of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters ( p ) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl. 

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