Sparse linear algebra is an important kernel in many different applications. Among various sparse general matrix-matrix multiplication (SpGEMM) algorithms, Gustavson’s column-wise SpGEMM has good locality when reading input matrix and can be easily parallelized by distributing the computation of different columns of an output matrix to different processors. However, the sparse accumulation (SPA) step in column-wise SpGEMM, which merges partial sums from each of the multiplications by the row indices, is still a performance bottleneck. The state-of-the-art software implementation uses a hash table for partial sum search in the SPA, which makes SPA the largest contributor to the execution time of SpGEMM. There are three reasons that cause the SPA to become the bottleneck: (1) hash probing requires data-dependent branches that are difficult for a branch predictor to predict correctly; (2) the accumulation of partial sum is dependent on the results of the hash probing, which makes it difficult to hide the hash probing latency; and (3) hash collision requires time-consuming linear search and optimizations to reduce these collisions require an accurate estimation of the number of non-zeros in each column of the output matrix. This work proposes ASA architecture to accelerate the SPA. ASA overcomes the challenges of SPA by (1) executing the partial sum search and accumulate with a single instruction through ISA extension to eliminate data-dependent branches in hash probing, (2) using a dedicated on-chip cache to perform the search and accumulation in a pipelined fashion, (3) relying on the parallel search capability of a set-associative cache to reduce search latency, and (4) delaying the merging of overflowed entries. As a result, ASA achieves an average of 2.25× and 5.05× speedup as compared to the state-of-the-art software implementation of a Markov clustering application and its SpGEMM kernel, respectively. As compared to a state-of-the-art hashing accelerator design, ASA achieves an average of 1.95× speedup in the SpGEMM kernel.
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NESTA: Hamming Weight Compression-Based Neural Proc. EngineAli Mirzaeian
In this paper, we present NESTA, a specialized Neural engine that significantly accelerates the computation of convolution layers in a deep convolutional neural network, while reducing the computational energy. NESTA reformats Convolutions into 3 × 3 batches and uses a hierarchy of Hamming Weight Compressors to process each batch. Besides, when processing the convolution across multiple channels, NESTA, rather than computing the precise result of a convolution per channel, quickly computes an approximation of its partial sum, and a residual value such that if added to the approximate partial sum, generates the accurate output. Then, instead of immediately adding the residual, it uses (consumes) the residual when processing the next batch in the hamming weight compressors with available capacity. This mechanism shortens the critical path by avoiding the need to propagate carry signals during each round of computation and speeds up the convolution of each channel. In the last stage of computation, when the partial sum of the last channel is computed, NESTA terminates by adding the residual bits to the approximate output to generate a correct result.
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- NSF-PAR ID:
- 10182706
- Date Published:
- Journal Name:
- ASP-DAC
- Page Range / eLocation ID:
- 530 to 537
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ASP-DAC47756.2020.9045135
