Related papers: Deep Learning of Chaos Classification

The dynamics of recurrent neural networks (RNNs), and particularly their response to inputs, play a critical role in information processing. In many applications of RNNs, only a specific subset of the neurons generally receive inputs.…

In this paper, we present MLEANN (Meta-Learning Evolutionary Artificial Neural Network), an automatic computational framework for the adaptive optimization of artificial neural networks wherein the neural network architecture, activation…

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…

Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…

Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use…

We develop a deep learning algorithm for constructing globally accurate approximations to functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize key…

Classification of long sequential data is an important Machine Learning task and appears in many application scenarios. Recurrent Neural Networks, Transformers, and Convolutional Neural Networks are three major techniques for learning from…

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…

Recurrent neural networks (RNNs) are non-linear dynamic systems. Previous work believes that RNN may suffer from the phenomenon of chaos, where the system is sensitive to initial states and unpredictable in the long run. In this paper,…

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase…

Deep learning harnesses massive parallel floating-point processing to train and evaluate large neural networks. Trends indicate that deeper and larger neural networks with an increasing number of parameters achieve higher accuracy than…

Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

Deep neural networks have recently achieved state of the art performance thanks to new training algorithms for rapid parameter estimation and new regularization methods to reduce overfitting. However, in practice the network architecture…

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…