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Integrating Temporal Information to Spatial Information in a Neural Circuit

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 Added by Mien Brabeeba Wang
 Publication date 2019
and research's language is English




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In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times; such spiking neural networks are inspired by networks of neurons and synapses that occur in brains. 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 (FCSC) and Total Spikes Counting (TSC), which model spike and rate coding aspects of translating temporal information into spatial information respectively. Assuming an upper bound of $T$ on the length of the temporal input signal, we design two networks that solve these two problems, each using $O(log T)$ neurons and terminating in time $1$. We also prove that there is no network with less than $T$ neurons that solves either question in time $0$.



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Feed-forward neural networks consist of a sequence of layers, in which each layer performs some processing on the information from the previous layer. A downside to this approach is that each layer (or module, as multiple modules can operate in parallel) is tasked with processing the entire hidden state, rather than a particular part of the state which is most relevant for that module. Methods which only operate on a small number of input variables are an essential part of most programming languages, and they allow for improved modularity and code re-usability. Our proposed method, Neural Function Modules (NFM), aims to introduce the same structural capability into deep learning. Most of the work in the context of feed-forward networks combining top-down and bottom-up feedback is limited to classification problems. The key contribution of our work is to combine attention, sparsity, top-down and bottom-up feedback, in a flexible algorithm which, as we show, improves the results in standard classification, out-of-domain generalization, generative modeling, and learning representations in the context of reinforcement learning.
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