# High-Accuracy Low-Precision Training

## TL;DR

This paper introduces HALP, a low-precision stochastic gradient descent method that maintains convergence rates comparable to full-precision algorithms by using variance reduction and bit centering, enabling faster and more efficient training.

## Contribution

The paper presents HALP, a novel low-precision training algorithm that achieves full-precision convergence rates using variance reduction and bit centering techniques.

## Key findings

- HALP can run up to 4x faster than full-precision SVRG on CPU.
- HALP matches the convergence trajectory of full-precision algorithms.
- HALP outperforms plain low-precision SGD on deep learning tasks.

## Abstract

Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the number of bits of precision is lowered, quantization noise is added to the model, which limits statistical accuracy. To address this issue, we describe a simple low-precision stochastic gradient descent variant called HALP. HALP converges at the same theoretical rate as full-precision algorithms despite the noise introduced by using low precision throughout execution. The key idea is to use SVRG to reduce gradient variance, and to combine this with a novel technique called bit centering to reduce quantization error. We show that on the CPU, HALP can run up to $4 \times$ faster than full-precision SVRG and can match its convergence trajectory. We implemented HALP in TensorQuant, and show that it exceeds the validation performance of plain low-precision SGD on two deep learning tasks.