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Register a new userNoise Optimization for Artificial Neural Networks
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Added by
Li Xiao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Adding noises to artificial neural network(ANN) has been shown to be able to improve robustness in previous work. In this work, we propose a new technique to compute the pathwise stochastic gradient estimate with respect to the standard deviation of the Gaussian noise added to each neuron of the ANN. By our proposed technique, the gradient estimate with respect to noise levels is a byproduct of the backpropagation algorithm for estimating gradient with respect to synaptic weights in ANN. Thus, the noise level for each neuron can be optimized simultaneously in the processing of training the synaptic weights at nearly no extra computational cost. In numerical experiments, our proposed method can achieve significant performance improvement on robustness of several popular ANN structures under both black box and white box attacks tested in various computer vision datasets.
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Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is known as a successful regularizer, but it is still not clear enough why such training techniques work well in practice and how we can maximize their benefit in the presence of two conflicting objectives---optimizing to true data distribution and preventing overfitting by regularization. This paper addresses the above issues by 1) interpreting that the conventional training methods with regularization by noise injection optimize the lower bound of the true objective and 2) proposing a technique to achieve a tighter lower bound using multiple noise samples per training example in a stochastic gradient descent iteration. We demonstrate the effectiveness of our idea in several computer vision applications.
As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is its reservoir --- a directed and weighted network of neurons that projects the input time series into a high dimensional space where linear regression or classification can be applied. Despite extensive studies, the impact of the reservoir network on the ESN performance remains unclear. Combining tools from physics, dynamical systems and network science, we attempt to open the black box of ESN and offer insights to understand the behavior of general artificial neural networks. Through spectral analysis of the reservoir network we reveal a key factor that largely determines the ESN memory capacity and hence affects its performance. Moreover, we find that adding short loops to the reservoir network can tailor ESN for specific tasks and optimize learning. We validate our findings by applying ESN to forecast both synthetic and real benchmark time series. Our results provide a new way to design task-specific ESN. More importantly, it demonstrates the power of combining tools from physics, dynamical systems and network science to offer new insights in understanding the mechanisms of general artificial neural networks.
What makes an artificial neural network easier to train and more likely to produce desirable solutions than other comparable networks? In this paper, we provide a new angle to study such issues under the setting of a fixed number of model parameters which in general is the most dominant cost factor. We introduce a notion of variability and show that it correlates positively to the activation ratio and negatively to a phenomenon called {Collapse to Constants} (or C2C), which is closely related but not identical to the phenomenon commonly known as vanishing gradient. Experiments on a styled model problem empirically verify that variability is indeed a key performance indicator for fully connected neural networks. The insights gained from this variability study will help the design of new and effective neural network architectures.
Machine Learning (ML) can help solve combinatorial optimization (CO) problems better. A popular approach is to use a neural net to compute on the parameters of a given CO problem and extract useful information that guides the search for good solutions. Many CO problems of practical importance can be specified in a matrix form of parameters quantifying the relationship between two groups of items. There is currently no neural net model, however, that takes in such matrix-style relationship data as an input. Consequently, these types of CO problems have been out of reach for ML engineers. In this paper, we introduce Matrix Encoding Network (MatNet) and show how conveniently it takes in and processes parameters of such complex CO problems. Using an end-to-end model based on MatNet, we solve asymmetric traveling salesman (ATSP) and flexible flow shop (FFSP) problems as the earliest neural approach. In particular, for a class of FFSP we have tested MatNet on, we demonstrate a far superior empirical performance to any methods (neural or not) known to date.
A major challenge in both neuroscience and machine learning is the development of useful tools for understanding complex information processing systems. One such tool is probes, i.e., supervised models that relate features of interest to activation patterns arising in biological or artificial neural networks. Neuroscience has paved the way in using such models through numerous studies conducted in recent decades. In this work, we draw insights from neuroscience to help guide probing research in machine learning. We highlight two important design choices for probes $-$ direction and expressivity $-$ and relate these choices to research goals. We argue that specific research goals play a paramount role when designing a probe and encourage future probing studies to be explicit in stating these goals.
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