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Learning Sparse & Ternary Neural Networks with Entropy-Constrained Trained Ternarization (EC2T)

arXiv.org Machine Learning

Deep neural networks (DNN) have shown remarkable success in a variety of machine learning applications. The capacity of these models (i.e., number of parameters), endows them with expressive power and allows them to reach the desired performance. In recent years, there is an increasing interest in deploying DNNs to resource-constrained devices (i.e., mobile devices) with limited energy, memory, and computational budget. To address this problem, we propose Entropy-Constrained Trained Ternarization (EC2T), a general framework to create sparse and ternary neural networks which are efficient in terms of storage (e.g., at most two binary-masks and two full-precision values are required to save a weight matrix) and computation (e.g., MAC operations are reduced to a few accumulations plus two multiplications). This approach consists of two steps. First, a super-network is created by scaling the dimensions of a pre-trained model (i.e., its width and depth). Subsequently, this super-network is simultaneously pruned (using an entropy constraint) and quantized (that is, ternary values are assigned layer-wise) in a training process, resulting in a sparse and ternary network representation. We validate the proposed approach in CIFAR-10, CIFAR-100, and ImageNet datasets, showing its effectiveness in image classification tasks.


Post-training deep neural network pruning via layer-wise calibration

arXiv.org Artificial Intelligence

We present a post-training weight pruning method for deep neural networks that achieves accuracy levels tolerable for the production setting and that is sufficiently fast to be run on commodity hardware such as desktop CPUs or edge devices. We propose a data-free extension of the approach for computer vision models based on automatically-generated synthetic fractal images. We obtain state-of-the-art results for data-free neural network pruning, with ~1.5% top@1 accuracy drop for a ResNet50 on ImageNet at 50% sparsity rate. When using real data, we are able to get a ResNet50 model on ImageNet with 65% sparsity rate in 8-bit precision in a post-training setting with a ~1% top@1 accuracy drop. We release the code as a part of the OpenVINO(TM) Post-Training Optimization tool.


Deep Neural Network Compression with Single and Multiple Level Quantization

arXiv.org Machine Learning

Network quantization is an effective solution to compress deep neural networks for practical usage. Existing network quantization methods cannot sufficiently exploit the depth information to generate low-bit compressed network. In this paper, we propose two novel network quantization approaches, single-level network quantization (SLQ) for high-bit quantization and multi-level network quantization (MLQ) for extremely low-bit quantization (ternary).We are the first to consider the network quantization from both width and depth level. In the width level, parameters are divided into two parts: one for quantization and the other for re-training to eliminate the quantization loss. SLQ leverages the distribution of the parameters to improve the width level. In the depth level, we introduce incremental layer compensation to quantize layers iteratively which decreases the quantization loss in each iteration. The proposed approaches are validated with extensive experiments based on the state-of-the-art neural networks including AlexNet, VGG-16, GoogleNet and ResNet-18. Both SLQ and MLQ achieve impressive results.


Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights

arXiv.org Artificial Intelligence

This paper presents incremental network quantization (INQ), a novel method, targeting to efficiently convert any pre-trained full-precision convolutional neural network (CNN) model into a low-precision version whose weights are constrained to be either powers of two or zero. Unlike existing methods which are struggled in noticeable accuracy loss, our INQ has the potential to resolve this issue, as benefiting from two innovations. On one hand, we introduce three interdependent operations, namely weight partition, group-wise quantization and re-training. A well-proven measure is employed to divide the weights in each layer of a pre-trained CNN model into two disjoint groups. The weights in the first group are responsible to form a low-precision base, thus they are quantized by a variable-length encoding method. The weights in the other group are responsible to compensate for the accuracy loss from the quantization, thus they are the ones to be re-trained. On the other hand, these three operations are repeated on the latest re-trained group in an iterative manner until all the weights are converted into low-precision ones, acting as an incremental network quantization and accuracy enhancement procedure. Extensive experiments on the ImageNet classification task using almost all known deep CNN architectures including AlexNet, VGG-16, GoogleNet and ResNets well testify the efficacy of the proposed method. Specifically, at 5-bit quantization, our models have improved accuracy than the 32-bit floating-point references. Taking ResNet-18 as an example, we further show that our quantized models with 4-bit, 3-bit and 2-bit ternary weights have improved or very similar accuracy against its 32-bit floating-point baseline. Besides, impressive results with the combination of network pruning and INQ are also reported. The code is available at https://github.com/Zhouaojun/Incremental-Network-Quantization.


Instant Quantization of Neural Networks using Monte Carlo Methods

arXiv.org Machine Learning

Low bit-width integer weights and activations are very important for efficient inference, especially with respect to lower power consumption. We propose Monte Carlo methods to quantize the weights and activations of pre-trained neural networks without any re-training. By performing importance sampling we obtain quantized low bit-width integer values from full-precision weights and activations. The precision, sparsity, and complexity are easily configurable by the amount of sampling performed. Our approach, called Monte Carlo Quantization (MCQ), is linear in both time and space, with the resulting quantized, sparse networks showing minimal accuracy loss when compared to the original full-precision networks. Our method either outperforms or achieves competitive results on multiple benchmarks compared to previous quantization methods that do require additional training.