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.
HadamRNN: Binary and Sparse Ternary Orthogonal RNNs
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Institut de Recherche Technologique Saint Exupéry（圣埃克苏佩里技术研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
In the past years, Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous model size and massive computation cost have become the main obstacle for deployment of such powerful algorithm in the low power and resource-limited mobile systems. As the countermeasure to this problem, deep neural networks with ternarized weights (i.e. -1, 0, +1) have been widely explored to greatly reduce the model size and computational cost, with limited accuracy degradation. In this work, we propose a novel ternarized neural network training m…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guarantees with high probability; however, sparse ternary {0, -1, +1} projections are more suitable for hardware implementation. In this paper, we present a deep learning approach to obtain very sparse ternary projections for compressed sensing. Our deep learning architecture jointly …
We demonstrate that 1x1-convolutions in 1D time-channel separable convolutions may be replaced by constant, sparse random ternary matrices with weights in $\{-1,0,+1\}$. Such layers do not perform any multiplications and do not require training. Moreover, the matrices may be generated on the chip during computation and therefore do not require any memory access. With the same parameter budget, we can afford deeper and more expressive models, improving the Pareto frontiers of existing models on several tasks. For command recognition on Google Speech Commands v1, we improve the state-of-the-art …
Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or binary codes, which has been widely applied in classification. Usually, the quantization will seriously degrade the accuracy of classification due to high quantization errors. Interestingly, however, we observe that the quantization could provide comparable and often superior accuracy, as the data to be quantized are sparse features generated with common fi…
Deep neural networks are widely used in machine learning applications. However, the deployment of large neural networks models can be difficult to deploy on mobile devices with limited power budgets. To solve this problem, we propose Trained Ternary Quantization (TTQ), a method that can reduce the precision of weights in neural networks to ternary values. This method has very little accuracy degradation and can even improve the accuracy of some models (32, 44, 56-layer ResNet) on CIFAR-10 and AlexNet on ImageNet. And our AlexNet model is trained from scratch, which means it's as easy as to tra…
State University of New York at Binghamton（宾汉姆顿纽约州立大学）
Deep neural networks (DNNs) have been widely and successfully applied to various applications, but they require large amounts of memory and computational power. This severely restricts their deployment on resource-limited devices. To address this issue, many efforts have been made on training low-bit weight DNNs. In this paper, we focus on training ternary weight \{-1, 0, +1\} networks which can avoid multiplications and dramatically reduce the memory and computation requirements. A ternary weight network can be considered as a sparser version of the binary weight counterpart by replacing some…
The computation and storage requirements for Deep Neural Networks (DNNs) are usually high. This issue limits their deployability on ubiquitous computing devices such as smart phones, wearables and autonomous drones. In this paper, we propose ternary neural networks (TNNs) in order to make deep learning more resource-efficient. We train these TNNs using a teacher-student approach based on a novel, layer-wise greedy methodology. Thanks to our two-stage training procedure, the teacher network is still able to use state-of-the-art methods such as dropout and batch normalization to increase accurac…
Tsinghua University（清华大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
There is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discrete. The second one is how to remove the full-precision hidden weights in the training phase to break the bottlenecks of memory/computation consumption. To address the first issue, we present a multi-step neuronal activation discretization method and a derivative approximation tech…
Deep learning is formulated as a discrete-time optimal control problem. This allows one to characterize necessary conditions for optimality and develop training algorithms that do not rely on gradients with respect to the trainable parameters. In particular, we introduce the discrete-time method of successive approximations (MSA), which is based on the Pontryagin's maximum principle, for training neural networks. A rigorous error estimate for the discrete MSA is obtained, which sheds light on its dynamics and the means to stabilize the algorithm. The developed methods are applied to train, in …
The ability to obtain accurate food security metrics in developing areas where relevant data can be sparse is critically important for policy makers tasked with implementing food aid programs. As a result, a great deal of work has been dedicated to predicting important food security metrics such as annual crop yields using a variety of methods including simulation, remote sensing, weather models, and human expert input. As a complement to existing techniques in crop yield prediction, this work develops neural network models for predicting the sentiment of Twitter feeds from farming communities…
