Augmenting Recurrent Neural Networks Resilience by Dropout

This brief discusses the simple idea that dropout regularization can be used to efficiently induce resiliency to missing inputs at prediction time in a generic neural network. We show how the approach can be effective on tasks where imputation strategies often fail, namely, involving recurrent neural networks and scenarios where whole sequences of input observations are missing. The experimental analysis provides an assessment of the accuracy-resiliency tradeoff in multiple recurrent models, including reservoir computing methods, and comprising real-world ambient intelligence and biomedical time series.

Sensitivity analysis of multilayer perceptron to input and weight perturbations

An important issue in the design and implementation of a neural network is the sensitivity of its output to input and weight perturbations. In this paper, we discuss the sensitivity of the most popular and general feedforward neural networks--multilayer perceptron (MLP). The sensitivity is defined as the mathematical expectation of the output errors of the MLP due to input and weight perturbations with respect to all input and weight values in a given continuous interval. The sensitivity for a single neuron is discussed first and an analytical expression that is a function of the absolute values of input and weight perturbations is approximately derived. Then an algorithm is given to compute the sensitivity for the entire MLP. As intuitively expected, the sensitivity increases with input and weight perturbations, but the increase has an upper bound that is determined by the structural configuration of the MLP, namely the number of neurons per layer and the number of layers. There exists an optimal value for the number of neurons in a layer, which yields the highest sensitivity value. The effect caused by the number of layers is quite unexpected. The sensitivity of a neural network may decrease at first and then almost keeps constant while the number increases.

Computation of madalines' sensitivity to input and weight perturbations

The sensitivity of a neural network's output to its input and weight perturbations is an important measure for evaluating the network's performance. In this letter, we propose an approach to quantify the sensitivity of Madalines. The sensitivity is defined as the probability of output deviation due to input and weight perturbations with respect to overall input patterns. Based on the structural characteristics of Madalines, a bottom-up strategy is followed, along which the sensitivity of single neurons, that is, Adalines, is considered first and then the sensitivity of the entire Madaline network. By means of probability theory, an analytical formula is derived for the calculation of Adalines' sensitivity, and an algorithm is designed for the computation of Madalines' sensitivity. Computer simulations are run to verify the effectiveness of the formula and algorithm. The simulation results are in good agreement with the theoretical results.

A quantified sensitivity measure for multilayer perceptron to input perturbation

The sensitivity of a neural network's output to its input perturbation is an important issue with both theoretical and practical values. In this article, we propose an approach to quantify the sensitivity of the most popular and general feedforward network: multilayer perceptron (MLP). The sensitivity measure is defined as the mathematical expectation of output deviation due to expected input deviation with respect to overall input patterns in a continuous interval. Based on the structural characteristics of the MLP, a bottom-up approach is adopted. A single neuron is considered first, and algorithms with approximately derived analytical expressions that are functions of expected input deviation are given for the computation of its sensitivity. Then another algorithm is given to compute the sensitivity of the entire MLP network. Computer simulations are used to verify the derived theoretical formulas. The agreement between theoretical and experimental results is quite good. The sensitivity measure can be used to evaluate the MLP's performance.

A Low-Sensitivity Recurrent Neural Network

The problem of high sensitivity in modeling is well known. Small perturbations in the model parameters may result in large, undesired changes in the model behavior. A number of authors have considered the issue of sensitivity in feedforward neural networks from a probabilistic perspective. Less attention has been given to such issues in recurrent neural networks. In this article, we present a new recurrent neural network architecture, that is capable of significantly improved parameter sensitivity properties compared to existing recurrent neural networks. The new recurrent neural network generalizes previous architectures by employing alternative discrete-time operators in place of the shift operator normally used. An analysis of the model demonstrates the existence of parameter sensitivity in recurrent neural networks and supports the proposed architecture. The new architecture performs significantly better than previous recurrent neural networks, as shown by a series of simple numerical experiments.