Communication Lower Bounds of Convolutions in CNNs

Abstract

Convolution is the most time-consuming part in the computation of convolutional neural networks (CNNs), which have achieved great successes in numerous practical applications. Due to the complex data dependency and the increase in the amount of model samples, the convolution suffers from high overhead on data movement (i.e., memory access). This work provides comprehensive analysis and methodologies to minimize the communication for the convolution in CNNs. With an in-depth analysis of the recent I/O complexity theory under the red-blue game model, we develop a general I/O lower bound theory for a composite algorithm which consists of several different sub-computations. Based on the proposed theory, we establish the data movement lower bound results for two main convolution algorithms in CNNs, namely the direct convolution and Winograd algorithm, which represents the direct and indirect implementations of a convolution respectively. Next, derived from I/O lower bound results, we design the near I/O-optimal dataflow strategies for the two main convolution algorithms by fully exploiting the data reuse. Furthermore, in order to push the envelope of performance of the near I/O-optimal dataflow strategies further, an aggressive design of auto-tuning based on I/O lower bounds, is proposed to search an optimal parameter configuration for the direct convolution and Winograd algorithm on GPU, such as the number of threads and the size of shared memory used in each thread block. Finally, experiment evaluation results on the direct convolution and Winograd algorithm show that our dataflow strategies with the auto-tuning approach can achieve about 3.32× performance speedup on average over cuDNN. In addition, compared with TVM, which represents the state-of-the-art technique for auto-tuning, not only our auto-tuning method based on I/O lower bounds can find the optimal parameter configuration faster, but also our solution has higher performance than the optimal solution provided by TVM.

I/O lower bounds for auto-tuning of convolutions in CNNs

“…As the recent methodology mainly focuses on the workflow's specific properties which do not translate across different computational patterns, the recent lower bound theory seems hard to be applied to arbitrary computations such as convolutions, in which different sub-computations involve different computational patterns. How to establish a systematic I/O lower bound theory for convolutions based on the red-blue pebble game model is a big challenge [32]. Even if the lower bounds could be obtained, the theoretical minimum of I/O complexity is not easy to directly yield an efficient dataflow strategy.…”