Title: MixQuant: A Quantization Bit-width Search that Can Optimize the Performance of your Quantization Method. Abstract: Quantization is a technique for creating efficient Deep Neural Networks (DNNs), which involves performing computations and storing tensors at lower bit-widths than f32 floating point precision. Quantization reduces model size and inference latency, and therefore allows for DNNs to be deployed on platforms with constrained computational resources and real-time systems. However, quantization can lead to numerical instability caused by roundoff error which leads to inaccurate computations and therefore, a decrease in quantized model accuracy. In this paper we focus on simulated quantized inference, where the quantized model parameters are stored in low-precision, but the mathematical operations on them (e.g. matrix multiplications and additions) are performed with floating point arithmetic. This means that the DNN parameters are first quantized from f32 to, for example, int4, and then dequantized back to f32 to perform computations. We show that the roundtrip process of quantizing and dequantizing the model parameters leads to roundoff error, which may lead to numerical instability. Similarly to prior works, which have shown that both biases and activations are more sensitive to quantization and are best kept in full precision or quantized with higher bit-widths, we show that some weights are more sensitive than others which should be reflected on their quantization bit-width. To that end we propose MixQuant, a search algorithm that finds the optimal custom quantization bit-width for each layer weight based on roundoff error and can be combined with any quantization method as a form of pre-processing optimization. We show that combining MixQuant with BRECQ, a state-of-the-art quantization method, yields better quantized model accuracy than BRECQ alone. Additionally, we combine MixQuant with vanilla asymmetric quantization to show that MixQuant has the potential to optimize the performance of any quantization technique.