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Recent experimental studies indicate that synaptic changes induced by neuronal activity are discrete jumps between a small number of stable states. Learning in systems with discrete synapses is known to be a computationally hard problem.…
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in $\mathbb{R}^d$. Combinatorial objects known…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale's law. The combinatorial code of a Dale network is characterized in terms of two conditions: (i) a condition on the…
Neural networks with synaptic weights constructed according to the weighted Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of noise(finite temperature), when the number of stored patterns is finite and in the…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first,…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
Understanding brain function, constructing computational models and engineering neural prosthetics require assessing two problems, namely encoding and decoding, but their relation remains controversial. For decades, the encoding problem has…
Despite intensive research, the mechanisms underlying how neurons encode external inputs remain poorly understood. Recent work has focused on the response of a single neuron to a weak, subthreshold periodic signal. By simulating the…
The neural coding is yet to be discovered. The neuronal operational modes that arise with fixed inputs but with varying degrees of stimulation help to elucidate their coding properties. In neurons receiving {\it in vivo} stimulation, we…
A good understanding of how neurons use electrical pulses (i.e, spikes) to encode the signal information remains elusive. Analyzing spike sequences generated by individual neurons and by two coupled neurons (using the stochastic…
Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
Neuromorphic computing has recently gained momentum with the emergence of various neuromorphic processors. As the field advances, there is an increasing focus on developing training methods that can effectively leverage the unique…
Neural codes serve as a language for neurons in the brain. Convex codes, which arise from the pattern of intersections of convex sets in Euclidean space, are of particular relevance to neuroscience. Not every code is convex, however, and…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of…
A fundamental aspect of limitations in learning any computation in neural architectures is characterizing their optimal capacities. An important, widely-used neural architecture is known as autoencoders where the network reconstructs the…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
How does the brain encode spatial structure? One way is through hippocampal neurons called place cells, which become associated to convex regions of space known as their receptive fields: each place cell fires at a high rate precisely when…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer…
Recently, brain-inspired spiking neural networks (SNNs) have demonstrated promising capabilities in solving pattern recognition tasks. However, these SNNs are grounded on homogeneous neurons that utilize a uniform neural coding for…