This paper proposes a set of methods that enables low precision posit ™ arithmetic to be successfully used for the training of generative adversarial networks (GANs) with minimal quality loss. We show that ultra low precision posits, as small as 6 bits, can achieve high quality output for the generation phase after training. We also evaluate floating-point (float) formats and compare them to 8-bit posits in the context of GAN training. Our scaling and adaptive calibration techniques are capable of producing superior training quality for 8-bit posits that surpasses 8-bit floats and matches the results of 16-bit floats. Hardware simulation results indicate that our methods have higher energy efficiency compared to both 16- and 8-bit float training systems.

This article presents GRAM (GPU-based Runtime Adaption for Mixed-precision) a framework for the effective use of mixed precision arithmetic for CUDA programs. Our method provides a fine-grain tradeoff between output error and performance. It can create many variants that satisfy different accuracy requirements by assigning different groups of threads to different precision levels adaptively at runtime . To widen the range of applications that can benefit from its approximation, GRAM comes with an optional half-precision approximate math library. Using GRAM, we can trade off precision for any performance improvement of up to 540%, depending on the application and accuracy requirement.

Approximate computing, a technique that forgoes quantifiable output accuracy in favor of performance gains, is useful for improving the energy efficiency of error-resilient software, especially in the embedded setting. The identification of program components that can tolerate error plays a crucial role in balancing the energy vs. accuracy trade off in approximate computing. Manual analysis for approximability is not scalable and therefore automated tools which employ static or dynamic analysis have been proposed. However, static techniques are often coarse in their approximations while dynamic efforts incur high overhead. In this work we present ApproxSymate, a framework for automatically identifying program approximations using symbolic execution. ApproxSymate first statically computes symbolic error expressions for program components and then uses a dynamic sensitivity analysis to compute their approximability. A unique feature of this tool is that it explores the previously not considered dimension of program path for approximation which enables safer transformations. Our evaluation shows that ApproxSymate averages about 96% accuracy in identifying the same approximations found in manually annotated benchmarks, outperforming existing automated techniques.

Strassen's recursive algorithm for matrix-matrix multiplication has seen slow adoption in practical applications despite being asymptotically faster than the traditional algorithm. A primary cause for this is the comparatively weaker numerical stability of its results. Techniques that aim to improve the errors of Strassen stand the risk of losing any potential performance gain. Moreover, current methods of evaluating such techniques for safety are overly pessimistic or error prone and generally do not allow for quick and accurate comparisons. In this paper we present an efficient technique to obtain rigorous error bounds for floating point computations based on an implementation of unum arithmetic. Using it, we evaluate three techniques - exact dot product, fused multiply-add, and matrix quadrant rotation - that can potentially improve the numerical stability of Strassen's algorithm for practical use. We also propose a novel error-based heuristic rotation scheme for matrix quadrant rotation. Finally we apply techniques that improve numerical safety with low overhead to a LINPACK linear solver to demonstrate the usefulness of the Strassen algorithm in practice.

False sharing is a major class of performance bugs in parallel applications. Detecting false sharing is difficult as it does not change the program semantics. We introduce an efficient and effective approach for detecting false sharing based on machine learning.