 Award ID(s):
 1934568
 NSFPAR ID:
 10282348
 Date Published:
 Journal Name:
 Proceedings of the National Academy of Sciences
 Volume:
 117
 Issue:
 41
 ISSN:
 00278424
 Page Range / eLocation ID:
 25505 to 25516
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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WinnerTakeAll (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 spikebased WTA network to the inherent randomness of the input spike trains. In this work, we consider a spikebased k–WTA model where in 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 1ms, and model then 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 informationtheoretic lower bound on the decision time. We show that to guarantee a (minimax) decision error≤δ(whereδ∈(0,1)), the waiting time of any WTA circuit is at least((1−δ) log(k(n−k) + 1)−1)TR,whereR ⊆(0,1) is a finite set of rates, and TR is a difficulty parameter of a WTA task with respect to setRfor independent input spike trains.Additionally,TR is independent ofδ,n, andk. We then design a simple WTA circuit whose waiting time isO((log(1δ)+ logk(n−k))TR), provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is orderoptimal (i.e., it 2 matches the above lower bound up to a multiplicative constant factor) in terms of its scaling inn,k, and TR.more » « less

Winnertakeall (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 spikebased WTA network to the inherent randomness of the input spike trains.In this work, we consider a spikebased 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 then 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 informationtheoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error≤δ(whereδ∈(0,1)), the waiting time of any WTA circuit is at least ((1−δ)log(k(n−k)+1)−1)TR,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 2524L. Su, C.J. Chang, and N. Lynch O((log(1δ)+logk(n−k))TR),provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is orderoptimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling inn,k, and TR.more » « less

The notion that a neuron transmits the same set of neurotransmitters at all of its postsynaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decisionmaking tasks, and it plays a key role in the current understanding of the structurefunction relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this singlepopulation network model in the context of two competing pools of neurons to demonstrate that effective decisionmaking dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical twopopulation balanced neuronal network, we argue that the onepopulation network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the twopopulation network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.more » « less

Blohm, Gunnar (Ed.)
Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population of
N weaklycoupled neurons to achieve errors that scale as . But more interestingly, recent work has introduced networks of leaky integrateandfire (LIF) neurons that achieve coding errors that scale$1/\sqrt{N}$
superclassically as 1/N by combining the principles of predictive coding and fast and tight inhibitoryexcitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actuallyimprove coding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by derivinganalytical expressions for coding error as a function of spike propagation delay and noise levels in predictive coding tightbalance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as powerlaws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits. 
Robots are active agents that operate in dynamic scenarios with noisy sensors. Predictions based on these noisy sensor measurements often lead to errors and can be unreliable. To this end, roboticists have used fusion methods using multiple observations. Lately, neural networks have dominated the accuracy charts for perceptiondriven predictions for robotic decisionmaking and often lack uncertainty metrics associated with the predictions. Here, we present a mathematical formulation to obtain the heteroscedastic aleatoric uncertainty of any arbitrary distribution without prior knowledge about the data. The approach has no prior assumptions about the prediction labels and is agnostic to network architecture. Furthermore, our class of networks, Ajna, adds minimal computation and requires only a small change to the loss function while training neural networks to obtain uncertainty of predictions, enabling realtime operation even on resourceconstrained robots. In addition, we study the informational cues present in the uncertainties of predicted values and their utility in the unification of common robotics problems. In particular, we present an approach to dodge dynamic obstacles, navigate through a cluttered scene, fly through unknown gaps, and segment an object pile, without computing depth but rather using the uncertainties of optical flow obtained from a monocular camera with onboard sensing and computation. We successfully evaluate and demonstrate the proposed Ajna network on four aforementioned common robotics and computer vision tasks and show comparable results to methods directly using depth. Our work demonstrates a generalized deep uncertainty method and demonstrates its utilization in robotics applications.