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

TL;DR

This paper introduces a novel approach to accelerate GEMM operations in DSP systems by adaptively controlling computation distortion, effectively transforming matrix multiplication into a computation channel that balances throughput and error.

Contribution

It proposes an adaptive scalar companding and packing method for GEMM, deriving an optimal throughput-distortion control framework for broad input data classes.

Findings

Can surpass 100% of peak processor performance under certain distortion levels.

Demonstrated benefits in face recognition and music metadata learning systems.

Provides a new perspective on matrix multiplication as a computation channel.

Abstract

The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based on dynamically adjusting the imprecision (distortion) of computation. Our technique employs adaptive scalar companding and rounding to input matrix blocks followed by two forms of packing in floating-point that allow for concurrent calculation of multiple results. Since the adaptive companding process controls the increase of concurrency (via packing), the increase in processing throughput (and the corresponding increase in distortion) depends on the input data statistics. To demonstrate this, we derive the optimal throughput-distortion control framework for GEMM for the broad class of zero-mean, independent identically distributed, input sources. Our approach converts matrix multiplication in programmable processors into a computation channel: when increasing the processing throughput, the output noise (error) increases due to (i) coarser quantization and (ii) computational errors caused by exceeding the machine-precision limitations. We show that, under certain distortion in the GEMM computation, the proposed framework can significantly surpass 100% of the peak performance of a given processor. The practical benefits of our proposal are shown in a face recognition system and a multi-layer perceptron system trained for metadata learning from a large music feature database.