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We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (\pfcn), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating…
Recently deep neural networks have received considerable attention due to their ability to extract and represent high-level abstractions in data sets. Deep neural networks such as fully-connected and convolutional neural networks have shown…
Spiking Neural Networks (SNNs) that operate in an event-driven manner and employ binary spike representation have recently emerged as promising candidates for energy-efficient computing. However, a cost bottleneck arises in obtaining…
The "fire together, wire together" Hebbian model is a central principle for learning in neuroscience, but surprisingly, it has found limited applicability in modern machine learning. In this paper, we take a first step towards bridging this…
A goal of low-level neural processes is to build an efficient code extracting the relevant information from the sensory input. It is believed that this is implemented in cortical areas by elementary inferential computations dynamically…
Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…
Spiking neural networks (SNNs) have manifested remarkable advantages in power consumption and event-driven property during the inference process. To take full advantage of low power consumption and improve the efficiency of these models…
Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network…
This study explores how the selection of neuron models and learning rules impacts the classification performance of Spiking Neural Networks (SNNs), with a focus on applications in bio-signal processing. We compare biologically inspired…
Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent developments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of…
Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are…
Spiking Neural Networks (SNNs), inspired by the brain, are characterized by minimal power consumption and swift inference capabilities on neuromorphic hardware, and have been widely applied to various visual perception tasks. Current…
Modern Hopfield networks have enjoyed recent interest due to their connection to attention in transformers. Our paper provides a unified framework for sparse Hopfield networks by establishing a link with Fenchel-Young losses. The result is…
Training a deep neural network requires a large amount of single-task data and involves a long time-consuming optimization phase. This is not scalable to complex, realistic environments with new unexpected changes. Humans can perform fast…
The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear)…
A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural…
Nonlinear interactions in the dendritic tree play a key role in neural computation. Nevertheless, modeling frameworks aimed at the construction of large-scale, functional spiking neural networks, such as the Neural Engineering Framework,…
Federated Learning (FL) has attracted much interest due to the significant advantages it brings to training deep neural network (DNN) models. However, since communications and computation resources are limited, training DNN models in FL…