Design Space Exploration of Neural Network Activation Function Circuits

The widespread application of artificial neural networks has prompted researchers to experiment with FPGA and customized ASIC designs to speed up their computation. These implementation efforts have generally focused on weight multiplication and signal summation operations, and less on activation functions used in these applications. Yet, efficient hardware implementations of nonlinear activation functions like Exponential Linear Units (ELU), Scaled Exponential Linear Units (SELU), and Hyperbolic Tangent (tanh), are central to designing effective neural network accelerators, since these functions require lots of resources. In this paper, we explore efficient hardware implementations of activation functions using purely combinational circuits, with a focus on two widely used nonlinear activation functions, i.e., SELU and tanh. Our experiments demonstrate that neural networks are generally insensitive to the precision of the activation function. The results also prove that the proposed combinational circuit-based approach is very efficient in terms of speed and area, with negligible accuracy loss on the MNIST, CIFAR-10 and IMAGENET benchmarks. Synopsys Design Compiler synthesis results show that circuit designs for tanh and SELU can save between 3.13-7.69 and 4.45-8:45 area compared to the LUT/memory-based implementations, and can operate at 5.14GHz and 4.52GHz using the 28nm SVT library, respectively. The implementation is available at: https://github.com/ThomasMrY/ActivationFunctionDemo.Comment: 5 pages, 5 figures, 16 conferenc

Artificial Neural Network in Cosmic Landscape

In this paper we propose that artificial neural network, the basis of machine learning, is useful to generate the inflationary landscape from a cosmological point of view. Traditional numerical simulations of a global cosmic landscape typically need an exponential complexity when the number of fields is large. However, a basic application of artificial neural network could solve the problem based on the universal approximation theorem of the multilayer perceptron. A toy model in inflation with multiple light fields is investigated numerically as an example of such an application.Comment: v2, add some new content

Mean Field Methods for a Special Class of Belief Networks

The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive

Preserving Differential Privacy in Convolutional Deep Belief Networks

The remarkable development of deep learning in medicine and healthcare domain presents obvious privacy issues, when deep neural networks are built on users' personal and highly sensitive data, e.g., clinical records, user profiles, biomedical images, etc. However, only a few scientific studies on preserving privacy in deep learning have been conducted. In this paper, we focus on developing a private convolutional deep belief network (pCDBN), which essentially is a convolutional deep belief network (CDBN) under differential privacy. Our main idea of enforcing epsilon-differential privacy is to leverage the functional mechanism to perturb the energy-based objective functions of traditional CDBNs, rather than their results. One key contribution of this work is that we propose the use of Chebyshev expansion to derive the approximate polynomial representation of objective functions. Our theoretical analysis shows that we can further derive the sensitivity and error bounds of the approximate polynomial representation. As a result, preserving differential privacy in CDBNs is feasible. We applied our model in a health social network, i.e., YesiWell data, and in a handwriting digit dataset, i.e., MNIST data, for human behavior prediction, human behavior classification, and handwriting digit recognition tasks. Theoretical analysis and rigorous experimental evaluations show that the pCDBN is highly effective. It significantly outperforms existing solutions