Precision-energy-throughput scaling of generic matrix multiplication and discrete convolution kernels via linear projections

Abstract

Generic matrix multiplication (GEMM) and onedimensional discrete convolution/cross-correlation (CONV) kernels perform the bulk of the compute-and memory-intensive processing within image/audio recognition and matching systems. We propose a novel method to scale the energy and processing throughput of GEMM and CONV kernels for such errortolerant multimedia applications by adjusting the precision of computation. Our technique employs linear projections to the input matrix or signal data during the top-level GEMM and CONV blocking and reordering. The GEMM and CONV kernel processing then uses the projected inputs and the results are accumulated to form the final outputs. Throughput and energy scaling takes place by decreasing the number of projections computed by each kernel, which in turn produces approximate results, i.e. lowers the precision of the performed computation. Existing realizations of error-tolerant multimedia applications can opt to utilize a small number of the input projections (typically just one) in order to save energy and processing cycles, while all error-intolerant systems can compute all input projections and obtain full-precision outputs. Results derived from a voltage-and frequency-scaled ARM Cortex A15 processor running face recognition demonstrate that the proposed approach allows for 5-fold to 10-fold increase of processing throughput and more than 80% decrease of energy consumption against optimized GEMM and CONV kernels without any impact in the expected recognition and matching precision.

Security in Approximate Computing and Approximate Computing for Security: Challenges and Opportunities

“…• Software Approximation: Power consumption is reduced using simplified functions or data in programs. For example, loop perforation [14], precision scaling [15], [16], [17], using program versions of different accuracy [18], and data sampling [19], • Approximate Architectures: Approximate errors can be detected or optimized in approximate accelerators [20] or programmable processors [21]. Other techniques include memory access skipping [22], lossy compression [23], [24], and unreliable emerging technologies [25].…”

“…Therefore, nondeterministic approximate designs have limited reproducibility. The examples of deterministic approximate computing techniques in the above mentioned publications are [14], [16], [18], [15], [17], [19], [23], [24], [29], [30], [32], [33], [34], [35], [36], [34], [35], [36]. The non-deterministic approximate computing techniques of the above mentioned research include [20], [21], [25], [26], [27], [28], [40], [41].…”

Edge-Supported Approximate Analysis for Long Running Computations

“…Precision Scaling: Anam et al [1] explore the tradeoff in precision for energy and throughput in a generic matrix multiplication and one dimensional convolution. Yeh et al [13] apply dynamic precision tuning in floating point computation.…”