Related papers: Modeling bias in decision-making attractor network…

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…

Perceptual decision making is the subject of many experimental and theoretical studies. Whereas most modeling analysis are based on statistical processes of accumulation of evidence, less attention is being devoted to the modeling with…

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…

Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…

Navigation is crucial for animal behavior and is assumed to require an internal representation of the external environment, termed a cognitive map. The precise form of this representation is often considered to be a metric representation of…

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…

Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…

A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints,…

We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…

Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…

Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically…

In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well…

The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…

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…

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…

Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design…

We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case…

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…

We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…