FP8 training has emerged as a promising method for improving training efficiency. Existing frameworks accelerate training by applying FP8 computation to linear layers while leaving optimizer states and activations in higher precision, which fails to fully optimize memory usage. This paper introduces COAT (Compressing Optimizer States and Activations for FP8 Training), a novel FP8 training framework designed to significantly reduce memory footprint when training large models. COAT addresses current limitations through two key innovations: (1) Dynamic Range Expansion, which aligns optimizer state distributions more closely with the FP8 representation range, thereby reducing quantization error, and (2) Mixed-Granularity Activation Quantization, which optimizes activation memory using a combination of per-tensor and per-group quantization strategies. Experiments demonstrate that COAT effectively reduces end-to-end training memory footprint by 1.54 compared to BF16 while achieving nearly lossless performance across various tasks, such as Large Language Model pretraining and fine-tuning and Vision Language Model training. COAT also achieves a 1.43 end-to-end training speedup compared to BF16, performing on par with or surpassing TransformerEngine's speedup. COAT enables efficient full-parameter training of large models on fewer GPUs, and facilitates doubling the batch size in distributed training settings, providing a practical solution for scaling large-scale model training. The code is available at https://github.com/NVlabs/COAT. Both the optimizer states and activations are quantized to FP8 in COAT. Part of the work done during an internship at NVIDIA. However, the training of such models, which often comprise billions of parameters, demands substantial computational resources and memory. This presents substantial challenges, making the training of these foundation models very challenging (Smith et al., 2022; Hoffmann et al., 2022). Low-precision training has emerged as a promising approach to make FMs training more efficient (Micikevicius et al., 2017; Wang et al., 2018; Zhu et al., 2020; Xi et al., 2023; Wortsman et al., 2023; Xi et al., 2024).

Deep learning has grown rapidly thanks to its state-of-the-art performance across a wide range of real-world applications. While neural networks have been trained using IEEE-754 binary32 arithmetic, the rapid growth of computational demands in deep learning has boosted interest in faster, low precision training. Mixed-precision training that combines IEEE-754 binary16 with IEEE-754 binary32 has been tried, and other $16$-bit formats, for example Google's bfloat16, have become popular. In floating-point arithmetic there is a tradeoff between precision and representation range as the number of exponent bits changes; denormal numbers extend the representation range. This raises questions of how much exponent range is needed, of whether there is a format between binary16 (5 exponent bits) and bfloat16 (8 exponent bits) that works better than either of them, and whether or not denormals are necessary. In the current paper we study the need for denormal numbers for mixed-precision training, and we propose a 1/6/9 format, i.e., 6-bit exponent and 9-bit explicit mantissa, that offers a better range-precision tradeoff. We show that 1/6/9 mixed-precision training is able to speed up training on hardware that incurs a performance slowdown on denormal operations or eliminates the need for denormal numbers altogether. And, for a number of fully connected and convolutional neural networks in computer vision and natural language processing, 1/6/9 achieves numerical parity to standard mixed-precision.