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Title: An Inter-Layer Weight Prediction and Quantization for Deep Neural Networks based on Smoothly Varying Weight Hypothesis

Paper content:
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.
Deep neural networks have demonstrated great performance for various tasks in many fields, such as image classification (LeCun et al. 1990a; Krizhevsky et al. 2012; He et al. 2016) , object detection (Ren et al. 2015; He et al. 2017; Redmon & Farhadi 2018) , image captioning (Jia et al., 2015) , and speech recognition Xiong et al. 2018) .
Wide and deep neural networks achieved great accuracy with the aid of the enormous number of weight parameters and high computational cost (Simonyan & Zisserman 2014; He et al. 2016; ).
However, as demands toward constructing the neural networks in the resource-constrained environments have been increasing, making the resource-efficient neural network while maintaining its accuracy becomes an important research area of deep neural networks.
Several studies have aimed to solve this problem.
In LeCun et al. (1990b) , Hassibi & Stork (1993) , Han et al. (2015b) and Li et al. (2016) , network pruning methods were proposed for memory-efficient architecture, where unimportant weights were forced to have zero values in terms of accuracy.
In Fiesler et al. (1990) , Gong et al. (2014) and Han et al. (2015a) , weights were quantized and stored in memory, enabling less memory usage of deep neural networks.
On the other hand, some literature decomposed convolution operations into sub operations (e.g., depth-wise separable convolution) requiring less computation costs at similar accuracy levels (Howard et al. 2017; Sandler et al. 2018; Ma et al. 2018) .
In this paper, we show that the weights between the adjacent two convolution layers tend to share high similarity in shapes and values.
We call this phenomenon Smoothly Varying Weight Hypothesis (SVWH).
This paper explores an efficient neural network method that fully takes the advantage of SVWH.
Specifically, inspired by the prediction techniques widely used in video compression field (Wiegand et al. 2003; Sullivan et al. 2012 ), we propose a new weight compression scheme based on an inter-layer weight prediction technique, which can be successfully incorporated into the depth-wise separable convolutional blocks (Howard et al. 2017; Sandler et al. 2018; Ma et al. 2018) .
Contributions: Main contributions of this paper are listed below:
• From comprehensive experiments, we find out that the weights between the adjacent layers tend to share strong similarities, which lead us to establishing SVWH.
• Based on SVWH, we propose a simple and effective Inter-Layer Weight Prediction (ILWP) and quantization framework enabling a more compressed neural networks than only applying quantization on the weights of the neural networks.
• To further enhance the effectiveness of the proposed ILWP, we devise a new regularization function, denoted as inter-layer loss, that aims to minimize the difference between collocated weight values in the adjacent layers, resulting in significant bit saving for non-texture bits (i.e., bits for indices of prediction).
• Our comprehensive experiments demonstrate that, the proposed scheme achieves about 53% compression ratio on average in 8-bit quantization at the same accuracy level compared to the traditional quantization method (without prediction) in both MobileNetV1 (Howard et al., 2017) and MobileNetV2 (Sandler et al., 2018) .
We propose a new inter-layer weight prediction with inter-layer loss for efficient deep neural networks.
Motivated by our observation that the weights in the adjacent layers tend to vary smoothly, we successfully build a new weight compression framework combining the inter-layer weight prediction scheme, the inter-layer loss, quantization and Huffman coding under SVWH condition.
Intuitively, our prediction scheme significantly decreases the entropy of the weights by making them much narrower Laplace distributions, thus leading remarkable compression ratio of the weight parameters in neural networks.
Also, the proposed inter-layer loss effectively eliminates the nontexture bits for the best predictions.
To the best of our knowledge, this work is the first to report the phenomenon of the weight similarities between the neighbor layers and to build a prediction-based weight compression scheme in modern deep neural network architectures.

assistant: text: We propose a new compression method, Inter-Layer Weight Prediction (ILWP) and quantization method which quantize the predicted residuals between the weights in convolution layers.