Related papers: Thermodynamic limit in learning period three

Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…

Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g. state of neurons) and slow-changing trainable variables (e.g. weights and biases). We show that the…

We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have two positive Lyapunov exponents in numerical experiments. In order to possess this…

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed…

This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter…

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these…

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…

Associative networks theory is increasingly providing tools to interpret update rules of artificial neural networks. At the same time, deriving neural learning rules from a solid theory remains a fundamental challenge. We make some steps in…

Through periodic Training we can gradually buildup a reproducible responses in a disordered system where plasticity dominates over elasticity as is known in classical amorphous materials and soft matter 1, 6. Here we show that a similar…

The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

The training algorithms for AI systems all introduce far-from-equilibrium dynamical processes, and understanding the irreversibility of these algorithms is a fundamental step towards understanding the learning dynamics of modern AI systems.…

We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…

The retrieval abilities of spatially uniform attractor networks can be measured by the average overlap between patterns and neural states. We found that metric networks, with local connections, however, can carry information structured in…

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…

How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…

We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…