Title: An Inter-Layer Weight Prediction and Quantization for Deep Neural Networks based on Smoothly Varying Weight Hypothesis. Abstract: Due to a resource-constrained environment, network compression has become an important part of deep neural networks research. In this paper, we propose a new compression method, Inter-Layer Weight Prediction (ILWP) and quantization method which quantize the predicted residuals between the weights in all convolution layers based on an inter-frame prediction method in conventional video coding schemes. Furthermore, we found a phenomenon Smoothly Varying Weight Hypothesis (SVWH) which is that the weights in adjacent convolution layers share strong similarity in shapes and values, i.e., the weights tend to vary smoothly along with the layers. Based on SVWH, we propose a second ILWP and quantization method which quantize the predicted residuals between the weights in adjacent convolution layers. Since the predicted weight residuals tend to follow Laplace distributions with very low variance, the weight quantization can more effectively be applied, thus producing more zero weights and enhancing the weight compression ratio. In addition, we propose a new inter-layer loss for eliminating non-texture bits, which enabled us to more effectively store only texture bits. That is, the proposed loss regularizes the weights such that the collocated weights between the adjacent two layers have the same values. Finally, we propose an ILWP with an inter-layer loss and quantization method. Our comprehensive experiments show that the proposed method achieves a much higher weight compression rate at the same accuracy level compared with the previous quantization-based compression methods in deep neural networks.