Quantization based on the binary codes is gaining attention because each quantized bit can be directly utilized for computations without dequantization using look-up tables. Previous attempts, however, only allow for integer numbers of quantization bits, which ends up restricting the search space for compression ratio and accuracy. In this paper, we propose an encryption algorithm/architecture to compress quantized weights so as to achieve fractional numbers of bits per weight.Decryption during inference is implemented by digital XOR-gate networks added into the neural network model while XOR gates are described by utilizing tanh(x) for backward propagation to enable gradient calculations. We perform experiments using MNIST, CIFAR-10, and ImageNet to show that inserting XOR gates learns quantization/encrypted bit decisions through training and obtains high accuracy even for fractional sub 1-bit weights. As a result, our proposed method yields smaller size and higher model accuracy compared to binary neural networks.
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well. Quantization is an efficient method to address such concerns by compressing DNNs such that computations can be simplified while required storage footprint is significantly reduced. Unfortunately, commercial CPUs and GPUs do not fully support quantization because only fixed data transfers (such as 32 bits) are allowed. As a result, even if weights are quantized into a few bits, CPUs and GPUs cannot access multiple quantized weights without memory bandwidth waste. Success of quantization in practice, hence, relies on an efficient computation engine design, especially for matrix multiplication that is a basic computation engine in most DNNs. In this paper, we propose a novel matrix multiplication method, called BiQGEMM, dedicated to quantized DNNs. BiQGEMM can access multiple quantized weights simultaneously in one instruction. In addition, BiQGEMM pre-computes intermediate results that are highly redundant when quantization leads to limited available computation space. Since pre-computed values are stored in lookup tables and reused, BiQGEMM achieves lower amount of overall computations. Our extensive experimental results show that BiQGEMM presents higher performance than conventional schemes when DNNs are quantized.
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy because decomposed layers hinder training convergence. In this paper, we propose a new training technique that finds a flat minimum in the view of low-rank approximation without a decomposed structure during training. By preserving the original model structure, 2-dimensional low-rank approximation demanding lowering (such as im2col) is available in our proposed scheme. We show that CNN models can be compressed by low-rank approximation with much higher compression ratio than conventional training methods while maintaining or even enhancing model accuracy. We also discuss various 2-dimensional low-rank approximation techniques for CNNs.
Model compression techniques, such as pruning and quantization, are becoming increasingly important to reduce the memory footprints and the amount of computations. Despite model size reduction, achieving performance enhancement on devices is, however, still challenging mainly due to the irregular representations of sparse matrix formats. This paper proposes a new representation to encode the weights of Sparse Quantized Neural Networks, specifically reduced by find-grained and unstructured pruning method. The representation is encoded in a structured regular format, which can be efficiently decoded through XOR gates during inference in a parallel manner. We demonstrate various deep learning models that can be compressed and represented by our proposed format with fixed and high compression ratio. For example, for fully-connected layers of AlexNet on ImageNet dataset, we can represent the sparse weights by only 0.09 bits/weight for 1-bit quantization and 91\% pruning rate with a fixed decoding rate and full memory bandwidth usage.
Pruning is an efficient model compression technique to remove redundancy in the connectivity of deep neural networks (DNNs). Computations using sparse matrices obtained by pruning parameters, however, exhibit vastly different parallelism depending on the index representation scheme. As a result, fine-grained pruning has not gained much attention due to its irregular index form leading to large memory footprint and low parallelism for convolutions and matrix multiplications. In this paper, we propose a new network pruning technique that generates a low-rank binary index matrix to compress index data while decompressing index data is performed by simple binary matrix multiplication. This proposed compression method finds a particular fine-grained pruning mask that can be decomposed into two binary matrices. We also propose a tile-based factorization technique that not only lowers memory requirements but also enhances compression ratio. Various DNN models can be pruned with much fewer indexes compared to previous sparse matrix formats while maintaining the same pruning rate.
Model compression has been introduced to reduce the required hardware resources while maintaining the model accuracy. Lots of techniques for model compression, such as pruning, quantization, and low-rank approximation, have been suggested along with different inference implementation characteristics. Adopting model compression is, however, still challenging because the design complexity of model compression is rapidly increasing due to additional hyper-parameters and computation overhead in order to achieve a high compression ratio. In this paper, we propose a simple and efficient model compression framework called DeepTwist which distorts weights in an occasional manner without modifying the underlying training algorithms. The ideas of designing weight distortion functions are intuitive and straightforward given formats of compressed weights. We show that our proposed framework improves compression rate significantly for pruning, quantization, and low-rank approximation techniques while the efforts of additional retraining and/or hyper-parameter search are highly reduced. Regularization effects of DeepTwist are also reported.
Model compression has gained a lot of attention due to its ability to reduce hardware resource requirements significantly while maintaining accuracy of DNNs. Model compression is especially useful for memory-intensive recurrent neural networks because smaller memory footprint is crucial not only for reducing storage requirement but also for fast inference operations. Quantization is known to be an effective model compression method and researchers are interested in minimizing the number of bits to represent parameters. In this work, we introduce an iterative technique to apply quantization, presenting high compression ratio without any modifications to the training algorithm. In the proposed technique, weight quantization is followed by retraining the model with full precision weights. We show that iterative retraining generates new sets of weights which can be quantized with decreasing quantization loss at each iteration. We also show that quantization is efficiently able to leverage pruning, another effective model compression method. Implementation issues on combining the two methods are also addressed. Our experimental results demonstrate that an LSTM model using 1-bit quantized weights is sufficient for PTB dataset without any accuracy degradation while previous methods demand at least 2-4 bits for quantized weights.