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Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. Sofar, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural Networks 97] to the asynchronous setting by taking into account edge and node delays.  Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays)more »

We study input compression in a biologically inspired model of neural computation. We demonstrate that a network consisting of a random projection step (implemented via random synaptic connectivity) followed by a sparsification step (implemented via winnertakeall competition) can reduce wellseparated highdimensional input vectors to wellseparated lowdimensional vectors. By augmenting our network with a third module, we can efficiently map each input (along with any small perturbations of the input) to a unique representative neuron, solving a neural clustering problem. Both the size of our network and its processing time, i.e., the time it takes the network to compute the compressedmore »

We consider the task of measuring time with probabilistic threshold gates implemented by bioinspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect. We first consider a deterministic implementation of a neural timer and show that Θ(logt) (deterministic) threshold gates are both sufficient and necessary. This raised the question of whether randomness can be leveragedmore »

We consider the task of measuring time with probabilistic threshold gates implemented by bioinspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect. Discovering the underlying mechanisms by which the brain perceives the duration of time is one of the largest open enigma in computational neuroscience. To gain a better algorithmic understanding onto these processes,more »

A graph spanner is a fundamental graph structure that faithfully preserves the pairwise distances in the input graph up to a small multiplicative stretch. The common objective in the computation of spanners is to achieve the bestknown existential sizestretch tradeoff efficiently. Classical models and algorithmic analysis of graph spanners essentially assume that the algorithm can read the input graph, construct the desired spanner, and write the answer to the output tape. However, when considering massive graphs containing millions or even billions of nodes not only the input graph, but also the output spanner might be too large for a singlemore »