Embedded computer vision applications for robotics, security cameras, and mobile phone apps require the usage of mobile neural network architectures like MobileNet-v2 or MNAS-Net in order to reduce RAM consumption and accelerate processing. An additional option for further resource consumption reduction is 8-bit neural network quantization. Unfortunately, the known methods for neural network quantization lead to significant accuracy reduction (more than 1.2%) for mobile architectures and require long training with quantization procedure. To overcome this limitation, we propose a method that allows to quantize mobile neural network without significant accuracy loss. Our approach is based on trainable quantization thresholds for each neural network filter, that allows to accelerate training with quantization procedure upÂ to 10 times in comparison with the standard techniques. Using the proposed technique, we quantize the modern mobile architectures of neural networks with the accuracy loss not exceeding 0.1%. Ready-for-use models and code are available at: https://github.com/agoncharenko1992/FAT-fast-adjustable-threshold.