Google Research

Efficient Convolution Optimisation by Composing Microkernels

  • Nicolas Tollenaere
  • Auguste Olivry
  • Guillaume Iooss
  • Hugo Brunie
  • Albert Cohen
  • P Sadayappan
  • Fabrice Rastello
INRIA (2021)

Abstract

Optimizing the implementation of tensor computations is essential to exploiting the full capacity of a given processor architecture on a wide range of scientific and machine learning applications. However, the complexity of the microarchitectural features that come into play when approaching the peak performance of the processor makes it very hard. Focusing on 2D convolutions, we observe a common weakness in all tensor compilers and libraries related to efficiently covering the wide variety of problem sizes occurring in real-world applications. We propose TTile, a domain-specific code generator and autotuner for implementing efficient convolutions. Similarly to BLIS, TTile nests multiple levels of tiling above a vectorized tensor contraction microkernel. But unlike traditional approaches, we explore of a variety of microkernels and compose them to fit exactly the tensor shapes of a convolution. While this helps achieving consistently high performance on virtually all possible tensor sizes, our method also introduces more degrees of freedom in the optimization space, which makes it challenging for autotuning strategies. To address this, we leverage an analytical model of data movement, and combine it with feedback-directed autotuning. We evaluate TTile as a stand-alone compiler and also as a complement to TVM on recent Intel x86 microarchitectures.

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