Related papers: Initial conditions in the neural field model
A general dynamical process model of psychiatric disorders is proposed that specifies the basic cognitive processes involved in the transition from beliefs about self, others and world that are normal and adaptive, to beliefs that are…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
We provide a brief review of the common assumptions about biological learning with findings from experimental neuroscience and contrast them with the efficiency of gradient-based learning in recurrent neural networks. The key issues…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
We extend the theory of neural fields which has been developed in a deterministic framework by considering the influence spatio-temporal noise. The outstanding problem that we here address is the development of a theory that gives rigorous…
A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
We present a new paradigm in the study of brain mental dynamics on the basis of the stable transient activity neural networks observed in experiments. This new approach is in contrast to traditional system analysis usually adopted in…
Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection…
Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…
Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally. Moreover, selecting a suitable model complexity requires a…
This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models…
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
We estimate the initial conditions of a multivariable dynamical system from a scalar signal, using a modified Newton-Raphson method incorporating the time evolution. We can estimate initial conditions of periodic and chaotic systems and the…