Related papers: Building a Chaotic Proved Neural Network

Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of…

Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…

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…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…

The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state…

Convolutional and recurrent neural networks have been widely employed to achieve state-of-the-art performance on classification tasks. However, it has also been noted that these networks can be manipulated adversarially with relative ease,…

A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.

A popular theory of perceptual processing holds that the brain learns both a generative model of the world and a paired recognition model using variational Bayesian inference. Most hypotheses of how the brain might learn these models assume…

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…

Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…

We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic…

Meta-learning usually refers to a learning algorithm that learns from other learning algorithms. The problem of uncertainty in the predictions of neural networks shows that the world is only partially predictable and a learned neural…

Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems…

We studied neural automata -or neurobiologically inspired cellular automata- which exhibits chaotic itinerancy among the different stored patterns or memories. This is a consequence of activity-dependent synaptic fluctuations, which…

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…

In contrast to biological neural circuits, conventional artificial neural networks are commonly organized as strictly hierarchical architectures that exclude direct connections among neurons within the same layer. Consequently, information…

Adversarial examples have raised several open questions, such as why they can deceive classifiers and transfer between different models. A prevailing hypothesis to explain these phenomena suggests that adversarial perturbations appear as…

In theory, a neural network can be trained to act as an artificial specification for a program by showing it samples of the programs executions. In practice, the training turns out to be very hard. Programs often operate on discrete domains…

The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems perform…