Throughput-Distortion Computation Of Generic Matrix Multiplication: Toward A Computation Channel For Digital Signal Processing Systems

摘要

The generic matrix multiply (GEMM) function is the core element ofhigh-performance linear algebra libraries used in manycomputationally-demanding digital signal processing (DSP) systems. We proposean acceleration technique for GEMM based on dynamically adjusting theimprecision (distortion) of computation. Our technique employs adaptive scalarcompanding and rounding to input matrix blocks followed by two forms of packingin floating-point that allow for concurrent calculation of multiple results.Since the adaptive companding process controls the increase of concurrency (viapacking), the increase in processing throughput (and the corresponding increasein distortion) depends on the input data statistics. To demonstrate this, wederive the optimal throughput-distortion control framework for GEMM for thebroad class of zero-mean, independent identically distributed, input sources.Our approach converts matrix multiplication in programmable processors into acomputation channel: when increasing the processing throughput, the outputnoise (error) increases due to (i) coarser quantization and (ii) computationalerrors caused by exceeding the machine-precision limitations. We show that,under certain distortion in the GEMM computation, the proposed framework cansignificantly surpass 100% of the peak performance of a given processor. Thepractical benefits of our proposal are shown in a face recognition system and amulti-layer perceptron system trained for metadata learning from a large musicfeature database.