Online normalizer calculation for softmax

Abstract

The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reduction in memory accesses should improve Softmax performance on actual hardware. The benchmarks confirm this hypothesis: Softmax accelerates by up to 1.3x and Softmax+TopK combined and fused by up to 5x.

1) Added link to the benchmark code, 2) Benchmarked Safe Softmax + Top-K fused and attributed part of 5x explicitly to fusion in sections 5.2 and 6, 3) Stylistic changes, 4) Minor clarifications