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Well characterized sequences of dynamical states play an important role for motor control and associative neural computation in the brain. Autonomous dynamics involving sequences of transiently stable states have been termed associative…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…

Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic…

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…

Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…

In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…

Propagation of oscillatory signals through the cortex and coherence is shaped by the connectivity structure of neuronal circuits. This study systematically investigates the network and stimulus properties that shape network responses. The…

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…

Neuroscientific evidence shows that for most brain networks all pathways between cortical regions either pass through the thalamus or a transthalamic parallel route exists for any direct corticocortical connection. This paper seeks to…

Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train. Recent works have shed light on such phenomena analyzing when…

Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…

Over the past two decades, an increasing array of control-theoretic methods have been used to study the brain as a complex dynamical system and better understand its structure-function relationship. This article provides an overview on one…

Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters…

Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural…

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between…

Understanding how learning algorithms shape the computational strategies that emerge in neural networks remains a fundamental challenge in machine intelligence. While network architectures receive extensive attention, the role of the…

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…

Cerebellar-like networks, in which input activity patterns are separated by projection to a much higher-dimensional space before classification, are a recurring neurobiological motif, present in the cerebellum, dentate gyrus, insect…