4,625 research outputs found
Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere
Among the various architectures of Recurrent Neural Networks, Echo State
Networks (ESNs) emerged due to their simplified and inexpensive training
procedure. These networks are known to be sensitive to the setting of
hyper-parameters, which critically affect their behaviour. Results show that
their performance is usually maximized in a narrow region of hyper-parameter
space called edge of chaos. Finding such a region requires searching in
hyper-parameter space in a sensible way: hyper-parameter configurations
marginally outside such a region might yield networks exhibiting fully
developed chaos, hence producing unreliable computations. The performance gain
due to optimizing hyper-parameters can be studied by considering the
memory--nonlinearity trade-off, i.e., the fact that increasing the nonlinear
behavior of the network degrades its ability to remember past inputs, and
vice-versa. In this paper, we propose a model of ESNs that eliminates critical
dependence on hyper-parameters, resulting in networks that provably cannot
enter a chaotic regime and, at the same time, denotes nonlinear behaviour in
phase space characterised by a large memory of past inputs, comparable to the
one of linear networks. Our contribution is supported by experiments
corroborating our theoretical findings, showing that the proposed model
displays dynamics that are rich-enough to approximate many common nonlinear
systems used for benchmarking
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
Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes
We present a novel approach to efficiently compute tight non-convex
enclosures of the image through neural networks with ReLU, sigmoid, or
hyperbolic tangent activation functions. In particular, we abstract the
input-output relation of each neuron by a polynomial approximation, which is
evaluated in a set-based manner using polynomial zonotopes. While our approach
can also can be beneficial for open-loop neural network verification, our main
application is reachability analysis of neural network controlled systems,
where polynomial zonotopes are able to capture the non-convexity caused by the
neural network as well as the system dynamics. This results in a superior
performance compared to other methods, as we demonstrate on various benchmarks
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