Spike-Based Winner-Take-All Computation : Fundamental Limits and Order-Optimal Circuits
Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based k-WTA model wherein n randomly generated input spike trains compete with each other based on their underlying firing rates and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the n input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error ≤δ (where δ∈(0,1)), the waiting time of any WTA circuit is at least [Formula: see text]where R⊆(0,1) is a finite set of rates and TR is a difficulty parameter of a WTA task with respect to set R for independent input spike trains. Additionally, TR is independent of δ, n, and k. We then design a simple WTA circuit whose waiting time is [Formula: see text]provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in n, k, and TR.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2019 |
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| Erschienen: |
2019 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:31 |
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| Enthalten in: |
Neural computation - 31(2019), 12 vom: 12. Dez., Seite 2523-2561 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Su, Lili [VerfasserIn] |
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| Anmerkungen: |
Date Completed 16.03.2020 Date Revised 16.03.2020 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1162/neco_a_01242 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM302206132 |
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| 520 | |a Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based k-WTA model wherein n randomly generated input spike trains compete with each other based on their underlying firing rates and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the n input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error ≤δ (where δ∈(0,1)), the waiting time of any WTA circuit is at least [Formula: see text]where R⊆(0,1) is a finite set of rates and TR is a difficulty parameter of a WTA task with respect to set R for independent input spike trains. Additionally, TR is independent of δ, n, and k. We then design a simple WTA circuit whose waiting time is [Formula: see text]provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in n, k, and TR | ||
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| 700 | 1 | |a Lynch, Nancy |e verfasserin |4 aut | |
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