High-level static optimizations for efficient differentiable programming in MLIR

Automatic differentiation (AD) is ubiquitous in the training of deep neural networks and other machine learning tasks.The emerging field of differentiable programming has recently found success in generalizing deep learning by applying gradient-based optimization via AD to increasingly sophisticated applications in a diverse array of fields [1][2][3][4][5].However, the most popular tools for AD are hyper-specialized to deep learning workloads.The performance of both the AD process itself and the resulting differentiated code suffer as applications veer further away from deep neural networks.The most popular AD tools also perform differentiation at runtime, which incurs runtime overhead with each of the potential millions of gradient descent steps.Some of these issues can be mitigated through performing ahead-of-time AD in a compiler.However, existing compiler-based methods predominantly operate on low-level compiler intermediate representations (IRs) that lose context and information after being lowered from the original program.Additionally, the most common form of AD incurs an asymptotically large memory cost relative to the original program, regardless of if the AD procedure is done at compile time or run time.To address these challenges, this thesis introduces LAGrad, a reverse-mode, compile time AD system that leverages high-level information in MLIR to produce efficient differentiated code.LAGrad employs a collection of novel static optimizations that benefit from the semantics of high-level MLIR dialects to exploit the sparsity and structured control flow of generated code.Using these, LAGrad is able to achieve speedups of up to 2.8 and use 35 less memory relative to state of the art AD systems on real-world machine learning and computer vision benchmarks.LAGrad is the first tool to the authors' knowledge to exploit the structure and sparsity inherent in AD through static optimizations in a compiler.I would like to extend my deepest gratitude to my advisor, Professor Christophe Dubach, for his wisdom and continued support throughout my Master's degree.His guidance was instrumental in shaping me into the researcher that I am today,

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