Related papers: Initial conditions in the neural field model
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
Neural activity fluctuates over a wide range of timescales within and across brain areas. Experimental observations suggest that diverse neural timescales reflect information in dynamic environments. However, how timescales are defined and…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…
This article summarizes principles and ideas from the emerging area of applying \textit{conditional computation} methods to the design of neural networks. In particular, we focus on neural networks that can dynamically activate or…
Flexible modulation of temporal dynamics in neural sequences underlies many cognitive processes. For instance, we can adaptively change the speed of motor sequences and speech. While such flexibility is influenced by various factors such as…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
By dynamic planning, we refer to the ability of the human brain to infer and impose motor trajectories related to cognitive decisions. A recent paradigm, active inference, brings fundamental insights into the adaptation of biological…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
A coupled map is suggested to investigate various spatial or temporal designs in biology: Several cells (or tissues) in an organ are considered as connected to each other in terms of some molecular diffusions or electrical potential…
Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…
The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high…
Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
How the very first nervous systems evolved remains a fundamental open question. Molecular and genomic techniques have revolutionized our knowledge of the molecular ingredients behind this transition but not yet provided a clear picture of…