Softmax Bias Correction for Quantized Generative Models

Abstract: Post-training quantization (PTQ) is the go-to compression technique for large generative models, such as stable diffusion or LLMs. PTQ methods commonly keep the softmax activation in higher precision as it has been shown to be very sensitive to quantization noise. However, this can lead to a significant runtime and power overhead during inference on resource-constraint edge devices. In this work, we investigate the source of the softmax sensitivity to quantization and show that the quantization operation leads to a large bias in the softmax output, causing accuracy degradation. To overcome this issue, we propose an offline bias correction technique that improves the quantizability of softmax without additional compute during deployment, as it can be readily absorbed into the quantization parameters. We demonstrate the effectiveness of our method on stable diffusion v1.5 and 125M-size OPT LLM, achieving significant accuracy improvement for 8-bit quantized softmax.