Title: Integrating Temporal Information to Spatial Information in a Neural Circuit
In this paper, we consider a network of spiking neurons with a deterministic synchronous firing rule at discrete time. We propose three problems – “first consecutive spikes counting”,“total spikes counting” and “k-spikes temporal to spatial encoding” – to model how brains extract temporal information into spatial information from different neural codings. For a max input length T, we design three networks that solve these three problems with matching lower bounds in bothtime O(T) and number of neurons O(logT) in all three questions. more »« less
Wang, Brabeeba; Lynch, Nancy(
, 33rd International Symposium on Distributed Computing (DISC))
null
(Ed.)
In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems: "First Consecutive Spikes Counting" and "Total Spikes Counting", which model temporal-coding and rate-coding aspects of temporal-to-spatial translation respectively. Assuming an upper bound of T on the length of the temporal input signal, we design two networks that solve two problems, each using O(log T) neurons and terminating in time T+1. We also prove that these bounds are tight.
Wang, Brabeeba; Lynch, Nancy(
, 33rd International Symposium on Distributed Computing (DISC))
In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems:“First Consecutive Spikes Counting” and “Total Spikes Counting”, which model temporal-coding and rate-coding aspects of temporal-to-spatial translation respectively. Assuming an upper bound of T on the length of the temporal input signal, we design two networks that solve two problems, each using O(logT) neurons and terminating in time T+ 1. We also prove that these bounds are tight.
Hitron, Yael; Parter, Merav(
, European Symposium on Algorithms (ESA))
We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired 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 leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron y is required to fire for t consecutive rounds with probability at least 1−δ, and should stop firing after at most 2t rounds with probability 1−δ for some input parameter δ∈(0,1). Our key result is a construction of a neural timer with O(loglog1/δ) spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of Ω(min{loglog1/δ,logt}) neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks. Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks.
Understanding the neural code has been one of the central aims of neuroscience research for decades. Spikes are commonly referred to as the units of information transfer, but multi-unit activity (MUA) recordings are routinely analyzed in aggregate forms such as binned spike counts, peri-stimulus time histograms, firing rates, or population codes. Various forms of averaging also occur in the brain, from the spatial averaging of spikes within dendritic trees to their temporal averaging through synaptic dynamics. However, how these forms of averaging are related to each other or to the spatial and temporal units of information representation within the neural code has remained poorly understood.
Materials and methods
In this work we developed NeuroPixelHD, a symbolic hyperdimensional model of MUA, and used it to decode the spatial location and identity of static images shown ton= 9 mice in the Allen Institute Visual Coding—NeuroPixels dataset from large-scale MUA recordings. We parametrically varied the spatial and temporal resolutions of the MUA data provided to the model, and compared its resulting decoding accuracy.
Results
For almost all subjects, we found 125ms temporal resolution to maximize decoding accuracy for both the spatial location of Gabor patches (81 classes for patches presented over a 9×9 grid) as well as the identity of natural images (118 classes corresponding to 118 images) across the whole brain. This optimal temporal resolution nevertheless varied greatly between different regions, followed a sensory-associate hierarchy, and was significantly modulated by the central frequency of theta-band oscillations across different regions. Spatially, the optimal resolution was at either of two mesoscale levels for almost all mice: the area level, where the spiking activity of all neurons within each brain area are combined, and the population level, where neuronal spikes within each area are combined across fast spiking (putatively inhibitory) and regular spiking (putatively excitatory) neurons, respectively. We also observed an expected interplay between optimal spatial and temporal resolutions, whereby increasing the amount of averaging across one dimension (space or time) decreases the amount of averaging that is optimal across the other dimension, and vice versa.
Discussion
Our findings corroborate existing empirical practices of spatiotemporal binning and averaging in MUA data analysis, and provide a rigorous computational framework for optimizing the level of such aggregations. Our findings can also synthesize these empirical practices with existing knowledge of the various sources of biological averaging in the brain into a new theory of neural information processing in which theunit of informationvaries dynamically based on neuronal signal and noise correlations across space and time.
We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired 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, we introduce the neural timer problem. In this problem, one is given a time parameter t, an input neuron x, and an output neuron y. It is then required to design a minimum sized neural network (measured by the number of auxiliary neurons) in which every spike from x in a given round i, makes the output y fire for the subsequent t consecutive rounds.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 leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron y is required to fire for t consecutive rounds with probability at least 1−δ, and should stop firing after at most 2 t rounds with probability 1−δ for some input parameter δ∈(0,1). Our key result is a construction of a neural timer with O(log log 1/δ) spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of Ω(min{log log 1/δ,logt}) neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks.Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks. In the spirit of distributed synchronizers [Awerbuch-Peleg, FOCS’90], we provide a general transformation (or simulation) that can take any synchronized network solution and simulate it in an asynchronous setting (where edges have arbitrary response latencies) while incurring a small overhead w.r.t the number of neurons and computation time.
Wang, Mien Brabeea, and Lynch, Nancy. Integrating Temporal Information to Spatial Information in a Neural Circuit. Retrieved from https://par.nsf.gov/biblio/10161875. 7th Workshop on Biological Distributed Algorithms (BDA) .
Wang, Mien Brabeea, & Lynch, Nancy. Integrating Temporal Information to Spatial Information in a Neural Circuit. 7th Workshop on Biological Distributed Algorithms (BDA), (). Retrieved from https://par.nsf.gov/biblio/10161875.
Wang, Mien Brabeea, and Lynch, Nancy.
"Integrating Temporal Information to Spatial Information in a Neural Circuit". 7th Workshop on Biological Distributed Algorithms (BDA) (). Country unknown/Code not available. https://par.nsf.gov/biblio/10161875.
@article{osti_10161875,
place = {Country unknown/Code not available},
title = {Integrating Temporal Information to Spatial Information in a Neural Circuit},
url = {https://par.nsf.gov/biblio/10161875},
abstractNote = {In this paper, we consider a network of spiking neurons with a deterministic synchronous firing rule at discrete time. We propose three problems – “first consecutive spikes counting”,“total spikes counting” and “k-spikes temporal to spatial encoding” – to model how brains extract temporal information into spatial information from different neural codings. For a max input length T, we design three networks that solve these three problems with matching lower bounds in bothtime O(T) and number of neurons O(logT) in all three questions.},
journal = {7th Workshop on Biological Distributed Algorithms (BDA)},
author = {Wang, Mien Brabeea and Lynch, Nancy},
}
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