1-Bit FQT: Pushing the Limit of Fully Quantized Training to 1-bit

ICLR 2025 Conference Submission13456 Authors

Keywords: efficient machine learning, quantization methods, efficient training algorithms, fully quantized training

Abstract: Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Average 1-bit Quantization (AQ) strategy. The strategy leverages the heterogeneity of gradients to mitigate gradient variance by pruning less informative gradients and enhancing the numerical precision of remaining gradients. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6\%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13× compared to full precision training.

Primary Area: infrastructure, software libraries, hardware, systems, etc.

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Submission Number: 13456