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AutoHOOT: Automatic High-Order Optimization for Tensors

Ma, Linjian ; Ye, Jiayu ; Solomonik, Edgar

Proceedings of the ACM International Conference on Parallel Architectures and Compilation Techniques, 2020, p.125-137

New York, NY, USA: ACM

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  • Título:
    AutoHOOT: Automatic High-Order Optimization for Tensors
  • Autor: Ma, Linjian ; Ye, Jiayu ; Solomonik, Edgar
  • Assuntos: Mathematics of computing -- Mathematical analysis -- Mathematical optimization -- Continuous optimization -- Nonconvex optimization ; Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Automatic differentiation ; Mathematics of computing -- Mathematical software -- Mathematical software performance
  • É parte de: Proceedings of the ACM International Conference on Parallel Architectures and Compilation Techniques, 2020, p.125-137
  • Descrição: High-order optimization methods, including Newton's method and its variants as well as alternating minimization methods, dominate the optimization algorithms for tensor decompositions and tensor networks. These tensor methods are used for data analysis and simulation of quantum systems. In this work, we introduce AutoHOOT, the first automatic differentiation (AD) framework targeting at high-order optimization for tensor computations. AutoHOOT takes input tensor computation expressions and generates optimized derivative expressions. In particular, AutoHOOT contains a new explicit Jacobian / Hessian expression generation kernel whose outputs maintain the input tensors' granularity and are easy to optimize. The expressions are then optimized by both the traditional compiler optimization techniques and specific tensor algebra transformations. Experimental results show that AutoHOOT achieves competitive CPU and GPU performance for both tensor decomposition and tensor network applications compared to existing AD software and other tensor computation libraries with manually written kernels. The tensor methods generated by AutoHOOT are also well-parallelizable, and we demonstrate good scalability on a distributed memory supercomputer.
  • Editor: New York, NY, USA: ACM
  • Idioma: Inglês
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