Related papers: Evaluating generation of chaotic time series by co…

The emergence of deep learning led to the broad usage of neural networks in the time series domain for various applications, including finance and medicine. While powerful, these models are prone to adversarial attacks: a benign targeted…

Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For…

Generative Adversarial Networks have become a core technique in Machine Learning to generate unknown distributions from data samples. They have been used in a wide range of context without paying much attention to the possible theoretical…

The Generative Adversarial Network (GAN) has achieved great success in generating realistic (real-valued) synthetic data. However, convergence issues and difficulties dealing with discrete data hinder the applicability of GAN to text. We…

Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…

The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonlinearity in the…

Developments in deep generative models have allowed for tractable learning of high-dimensional data distributions. While the employed learning procedures typically assume that training data is drawn i.i.d. from the distribution of interest,…

In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…

Real-world data can be multimodal distributed, e.g., data describing the opinion divergence in a community, the interspike interval distribution of neurons, and the oscillators natural frequencies. Generating multimodal distributed…

Generative Adversarial Networks have recently shown promise for video generation, building off of the success of image generation while also addressing a new challenge: time. Although time was analyzed in some early work, the literature has…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

Time series anomaly detection plays a critical role in automated monitoring systems. Most previous deep learning efforts related to time series anomaly detection were based on recurrent neural networks (RNN). In this paper, we propose a…

Generative Adversarial Networks (GANs) have shown remarkable results in modeling complex distributions, but their evaluation remains an unsettled issue. Evaluations are essential for: (i) relative assessment of different models and (ii)…

Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce…

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…

Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…

This study shows that a mixture of RNN experts model can acquire the ability to generate sequences combining multiple primitive patterns by means of self-organizing chaos. By training of the model, each expert learns a primitive sequence…

Neural networks are vulnerable to adversarially-constructed perturbations of their inputs. Most research so far has considered perturbations of a fixed magnitude under some $l_p$ norm. Although studying these attacks is valuable, there has…

Traditional algorithms to optimize artificial neural networks when confronted with a supervised learning task are usually exploitation-type relaxational dynamics such as gradient descent (GD). Here, we explore the dynamics of the neural…