相关论文: Stability and Geometry of Attractors in Neural Cel…

A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…

A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled…

Neural Cellular Automata (NCA) models have shown remarkable capacity for pattern formation and complex global behaviors stemming from local coordination. However, in the original implementation of NCA, cells are incapable of adjusting their…

In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…

Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…

We present and study a probabilistic neural automaton in which the fraction of simultaneously-updated neurons is a parameter, rho (0, 1) . For small rho, there is relaxation towards one of the attractors and a great sensibility to external…

Neural Cellular Automata (NCA) is a class of Cellular Automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this paper, we focus on NCA models used for texture synthesis, where…

Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…

Continuous attractor neural networks generate a set of smoothly connected attractor states. In memory systems of the brain, these attractor states may represent continuous pieces of information such as spatial locations and head directions…

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…

Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron…

Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their…

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic…

Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase.…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise…

Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…