Quasi-Chaotic Oscillators Based on Modular Quantum Circuits

Digital circuits based on residue number systems have been considered to produce a pseudo-random behavior. The present work is an initial step towards the complete implementation of those systems for similar applications using quantum technology. We propose the implementation of a quasi-chaotic oscillator based on quantum modular addition and multiplication and we prove that quantum computing allows the parallel processing of data, paving the way for a fast and robust multi-channel encryption/decryption scheme. The resulting structure is assessed by several experiments in order to ascertain the desired noise-like behavior.

On Effects of Compression with Hyperdimensional Computing in Distributed Randomized Neural Networks

A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized algorithms can be framed in this prospect steering. We recently proposed a model for distributed classification based on randomized neural networks and hyperdimensional computing, which takes into account cost of information exchange between agents using compression. The use of compression is important as it addresses the issues related to the communication bottleneck, however, the original approach is rigid in the way the compression is used. Therefore, in this work, we propose a more flexible approach to compression and compare it to conventional compression algorithms, dimensionality reduction, and quantization techniques.

Hyperdimensional Computing for Efficient Distributed Classification with Randomized Neural Networks

In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In particular, randomized algorithms are currently having a resurgence, given their generalized elementary approach. By using randomized neural networks, we study distributed classification, which can be employed in situations were data cannot be stored at a central location nor shared. We propose a more efficient solution for distributed classification by making use of a lossy compression approach applied when sharing the local classifiers with other agents. This approach originates from the framework of hyperdimensional computing, and is adapted herein. The results of experiments on a collection of datasets demonstrate that the proposed approach has usually higher accuracy than local classifiers and getting close to the benchmark - the centralized classifier. This work can be considered as the first step towards analyzing the variegated horizon of distributed randomized neural networks.

Perceptron Theory for Predicting the Accuracy of Neural Networks

Many neural network models have been successful at classification problems, but their operation is still treated as a black box. Here, we developed a theory for one-layer perceptrons that can predict performance on classification tasks. This theory is a generalization of an existing theory for predicting the performance of Echo State Networks and connectionist models for symbolic reasoning known as Vector Symbolic Architectures. In this paper, we first show that the proposed perceptron theory can predict the performance of Echo State Networks, which could not be described by the previous theory. Second, we apply our perceptron theory to the last layers of shallow randomly connected and deep multi-layer networks. The full theory is based on Gaussian statistics, but it is analytically intractable. We explore numerical methods to predict network performance for problems with a small number of classes. For problems with a large number of classes, we investigate stochastic sampling methods and a tractable approximation to the full theory. The quality of predictions is assessed in three experimental settings, using reservoir computing networks on a memorization task, shallow randomly connected networks on a collection of classification datasets, and deep convolutional networks with the ImageNet dataset. This study offers a simple, bipartite approach to understand deep neural networks: the input is encoded by the last-but-one layers into a high-dimensional representation. This representation is mapped through the weights of the last layer into the postsynaptic sums of the output neurons. Specifically, the proposed perceptron theory uses the mean vector and covariance matrix of the postsynaptic sums to compute classification accuracies for the different classes. The first two moments of the distribution of the postsynaptic sums can predict the overall network performance quite accurately.