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. 2020 Sep 3:14:79.
doi: 10.3389/fncom.2020.00079. eCollection 2020.

Excitation-Inhibition Balanced Neural Networks for Fast Signal Detection

Gengshuo Tian  1 , Shangyang Li  1   2 , Tiejun Huang  1 , Si Wu  1   2
Affiliations

Excitation-Inhibition Balanced Neural Networks for Fast Signal Detection

Gengshuo Tian et al. Front Comput Neurosci. .

Abstract

Excitation-inhibition (E-I) balanced neural networks are a classic model for modeling neural activities and functions in the cortex. The present study investigates the potential application of E-I balanced neural networks for fast signal detection in brain-inspired computation. We first theoretically analyze the response property of an E-I balanced network, and find that the asynchronous firing state of the network generates an optimal noise structure enabling the network to track input changes rapidly. We then extend the homogeneous connectivity of an E-I balanced neural network to include local neuronal connections, so that the network can still achieve fast response and meanwhile maintain spatial information in the face of spatially heterogeneous signal. Finally, we carry out simulations to demonstrate that our model works well.

Keywords: E-I balanced network; Fokker-Planck equation; asynchronous state; fast tracking; optimal noise structure.

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Figures

Figure 1
Figure 1
An illustration of the mechanism of fast response for a neural population. (A) The integration and firing process of a neuron receiving a noiseless input. The integration time is constrained by the membrane time constant. (B) A distribution of membrane potentials across a neural population enables it to respond to input changes rapidly. Red dots represent neurons whose potentials are close to the firing threshold, which are the first ones to respond to input changes.
Figure 2
Figure 2
Simulation results of an uncoupled neural population. (A) The membrane potential distribution of a neural population receiving independent white noise-corrupted signals with a constant VMR of 1. The red curve is the theoretical prediction given by Equation (18), and the blue histogram is the actual simulation result. (B) The tracking performance of a neural population depends on the input noise structure. The blue curve is the theoretical prediction of steady-state firing rate given by Equation (19). The red curve is the network performance when the VMR is constant (β = 1), which tracks the input change almost instantaneously. The green curve is the network performance when the noise variance, rather than the VMR, is constant (σ ≡ 1), where a significant delay is present. Other parameters are: N = 2, 500, τ = 1, θ = 1, and μ changing from 1 to 5 at time t = 5.
Figure 3
Figure 3
Simulation results of a homogeneous E-I balanced network tracking a time-varying input. The network receives a sinusoidal input centered at μF = 0.1 with an amplitude of 0.05. σaF2/μF=0.1 remains constant. The blue curve is the theoretic prediction given by Equation (7). The red curve is the instantaneous average firing rate of excitatory neurons. The parameters are: N=1×104,qI=0.2,pab=0.25,θ=15,τE=15,τI=10,τE,s=6,τI,s=5,fE=3,fI=2,jEE=0.25,jEI=-1,jIE=0.4,jII=-1.
Figure 4
Figure 4
Schematic of the network structure in the context of processing Spike Camera data.
Figure 5
Figure 5
Performance of the network with local connections in response to time-varying stimuli. (A) Network response to the sudden appearance of an object. The Spike Camera layer receives a disc-shaped visual input centered at (0.25, 0.5) with a radius of 0.05, whose magnitude changes abruptly from 1.5 to 15 at t = 75. A background noise is added. The blue curve is the firing rate of the area corresponding to the visual input in the Spike Camera layer. The red curve is the rate of the excitatory neurons at the same area in the balanced network layer, which is normalized for better comparison with the blue curve. (B) Same as panel (A), except that the input amplitude follows the sinusoidal function μ(t) = A(sin(B*2πt/T)) + C, A = 30, B = 3/2, C = 30. (C,D) The stimulus is an object moving across the visual field in constant velocity. The object has the same shape as panels (A,B), with a magnitude of 10. Panels (C,D) show the tracking of the x and y coordinates, respectively. The blue curve is the object location decoded from the activity of the Spike Camera layer, and the red curve is that of the balanced network layer. (E,F) Same as panels (C,D), except that the stimulus moves counterclockwise on a circle in constant speed. The network parameters are θ = 15, τF = 1, τE = 15, τI = 10, τF,s = τE,s = 5, τI,s = 2.5, pEF = 0.05, pIF = 0.025, pEE = 0.02, pEI = 0.08, pIE = 0.06, pII = 0.08, AF = 0.05, AE = 0.02, AI = 0.02, jEF = 140, jIF = 93.3, jEE = 80, jEI = −320, jIE = 40, jII = −320.
Figure 6
Figure 6
Quantifying the network's performance with temporal and spatial phase lag. To examine the effect of the synaptic time constant on tracking performance, we define τb,s = kτb, s0, b = F, E, I, where τb, s0 is the set of parameters used in Figure 5. (A) Temporal phase lag in the second task (Figure 5B) with different signal periods. (B) Spatial phase lag in the fourth task (Figures 5E,F) with different circular motion periods. Ten trials for each data point. Error bars show standard deviations.
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