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Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs.…

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…

Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…

The staleness problem is a well-known problem when working with dynamic data, due to the absence of events for a long time. Since the memory of the node is updated only when the node is involved in an event, its memory becomes stale.…

Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly…

Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Probabilistic models and stochastic neural networks can explicitly handle…

Recurrent neural networks (RNNs) trained on compositional tasks can exhibit functional modularity, in which neurons can be clustered by activity similarity and participation in shared computational subtasks. Unlike brains, these RNNs do not…

The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…

Recently, many works have demonstrated that Symmetric Non-negative Matrix Factorization~(SymNMF) enjoys a great superiority for various clustering tasks. Although the state-of-the-art algorithms for SymNMF perform well on synthetic data,…

We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…

Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in…

We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that…

In this paper, we discuss the embedding problem for centrosymmetric matrices, which are higher order generalizations of the matrices occurring in Strand Symmetric Models. These models capture the substitution symmetries arising from the…

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons…

The biological neural network is a vast and diverse structure with high neural heterogeneity. Conventional Artificial Neural Networks (ANNs) primarily focus on modifying the weights of connections through training while modeling neurons as…

Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from…

Spike sorting refers to the problem of assigning action potentials observed in extra-cellular recordings of neural activity to the neuron(s) from which they originate. We cast this problem as one of learning a convolutional dictionary from…

Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…

Memory information in the brain is commonly believed to be stored in the synapse. However, a recent groundbreaking electrophysiology research has raised the possibility that memory information may actually be stored inside the neuron…