The basic idea behind mixed precision training is simple: halve the precision ( fp32 → fp16), halve the training time. PyTorch, which is much more memory-sensitive, uses fp32 as its default dtype instead.
fp16, aka half-precision or "half", max rounding error of ~2^-10.fp32, aka single-precision or "single", max rounding error of ~2^-23.fp64, aka double-precision or "double", max rounding error of ~2^-52.The technical standard for floating point numbers, IEEE 754 (for a deep dive I recommend the P圜on 2019 talk " Floats are Friends: making the most of IEEE754.00000000000000002"), sets the following standards: Since we can have infinitely precise numbers (think π), but limited space in which to store them, we have to make a compromise between precision (the number of decimals we can include in a number before we have to start rounding it) and size (how many bits we use to store the number). In computer engineering, decimal numbers like 1.0151 or 566132.8 are traditionally represented as floating point numbers. Discuss which network archetypes will benefit the most from amp.īefore we can understand how mixed precision training works, we first need to review a little bit about floating point numbers.Benchmark three different networks trained using amp.Introduce tensor cores: what they are and how they work.Take a deep dive into mixed-precision training as a technique.This post is a developer-friendly introduction to mixed precision training. The soon-to-be-released API will allow you to implement mixed precision training into your training scripts in just five lines of code! This is where the automatic in automatic mixed-precision training comes in. However, up until now these tensor cores have remained difficult to use, as it has required writing reduced precision operations into your model by hand. Recent generations of NVIDIA GPUs come loaded with special-purpose tensor cores specially designed for fast fp16 matrix operations. Mixed-precision training is a technique for substantially reducing neural net training time by performing as many operations as possible in half-precision floating point, fp16, instead of the (PyTorch default) single-precision floating point, fp32. One of the most exciting additions expected to land in PyTorch 1.6, coming soon, is support for automatic mixed-precision training. Finally, we provide a detailed performance analysis of all precision levels on a large number of hardware microarchitectures and show that significant speedup is achieved with mixed FP32/16-bit.TLDR: the mixed-precision training module forthcoming in PyTorch 1.6 delivers on its promise, delivering speed-ups of 50-60% in large model training jobs with just a handful of new lines of code. We find that the difference in accuracy between FP64 and FP32 is negligible in almost all cases, and that for a large number of cases even 16-bit is sufficient. We then carry out an in-depth characterization of LBM accuracy for six different test systems with increasing complexity: Poiseuille flow, Taylor-Green vortices, Karman vortex streets, lid-driven cavity, a microcapsule in shear flow (utilizing the immersed-boundary method), and, finally, the impact of a raindrop (based on a volume-of-fluid approach). Based on this observation, we develop customized 16-bit formats-based on a modified IEEE-754 and on a modified posit standard-that are specifically tailored to the needs of the LBM. For this, we first show that the commonly occurring number range in the LBM is a lot smaller than the FP16 number range. Here we evaluate the possibility to use even FP16 and posit16 (half) precision for storing fluid populations, while still carrying arithmetic operations in FP32. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64 (double) precision, especially on GPUs. Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory intensive.
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