Fig 1.
(A) Schematic figure of the model. (B) Spike-time dependent synaptic weight change in log- spike-timing-dependent plasticity (STDP). (C) Normalized temporal cross-correlogram of input neurons receiving common sources (gray line), and kernel functions of plasticity propagated by feedforward correlation (blue line) and feedback correlation (green line).
Table 1.
Definition of variables.
Table 2.
Parameter settings.
Fig 2.
Lateral inhibition enables minor source detection by spike-timing-dependent plasticity (STDP) through membrane hyperpolarization.
(A) Schematic figure of the simplified model. SA and SB (on the left side) are the sources that project to subsets of input neurons (colored triangles). Gray triangles are background neurons, black triangles (on the right) are output neurons, and red circles are inhibitory neurons. (B) Development of synaptic weights. Thick lines are mean synaptic weights from A-neurons (blue), B-neurons (red), and Background-neurons (orange) to each output neuron. Thin lines are traces of individual synaptic weights. Gray bar shows the timing at which figure C is calculated. (C) Peristimulus time histograms (PSTHs) of membrane potentials averaged within output neuron groups. T = 0 indicates the timing of events at external layers. The three figures are calculated from the data at t = 0–1 min, 7–8 min, and 29–30 min. (D) Development of mean cross-correlation and mutual information between external sources and population activity of output neurons for the simulation depicted in panels B and C. (E) Delay dependence of mean cross-correlation and mutual information. Both values were calculated from five simulations. (F) Cross-correlation between the output group that detected the minor source and the minor source activity for various response probabilities qB with a fixed qA (= 0.6). When none of output groups detected the minor source, the larger value calculated for the two output groups was used. Throughout the study, error bars represent standard deviation calculated from five simulations, unless otherwise indicated.
Fig 3.
Lateral inhibition is strong, fast, and sharp.
(A) Nullclines of the average synaptic weight changes at different inhibitory amplitudes wZ = 0.1, 0.215, 0.4. The inset in the middle graph is a magnified view of boxed area. (B) Specialization indices wSI for various inhibitory weights. Positive wSI indicates the winner-share-all state, whereas negative wSI indicates the winner-take-all state. Blue lines are analytical estimations and cyan squares are the results of simulations. Vertical lines correspond to the values at which the nullclines in Figure A are calculated. (C) The same graphs for various synaptic delays. The average synaptic delay of both lateral excitatory (dYmin+dYmax)/2 and inhibitory (dZmin+dZmax)/2 connections was changed, while the variability was kept at dYmax—dYmin = dZmax—dZmin = 1.0 ms. (D) IPSP rise time dependence. The inset shows IPSP curves at {τZA, τZB} = {0.5, 2.5} (gray line), {1.5, 7.5} (dark gray line), and {2.5, 12.5} (black line).
Fig 4.
Optimal correlation timescale changes depending on noise characteristics.
(A) Response kernels of input neurons to external events (left) and cross-correlation among input neurons responding to the same source calculated from simulated data (right) for three different correlation timescale parameters θt. (B) Raster plots of input neurons for various θt. Only 100 correlated neurons are plotted although there are 400 input neurons in total. (C) Analytically calculated correlation kernels g1X, g2X (left), and their ratio g1X/g2X. (D) Specialization index wSI for various response probabilities qB while fixing qA = 0.6. Lines represent wR at analytically estimated stable points, and dotted squares represent simulation results. (E) Raster plots of two types of noise. The upper panel shows random noise, whereas the lower panel depicts crosstalk noise. In both panels, the first 100 neurons respond primarily to the cyan source, and the next 100 neurons respond to the purple source. For random noise, the noise (black dots) is independent from the signals, whereas the crosstalk noise (purple dots in the lower half, cyan dots in the upper half) is correlated with the signal for the other population. (F, G) The effects of random noise (F) and crosstalk noise (G) at various correlation timescales.
Fig 5.
Lateral connection structuring by excitatory and inhibitory spike-timing-dependent plasticity (STDP).
(A) Schematic figures of connections between the output layer and the lateral layer. In the simulation, each layer consists of 20 neurons. (B) The effect of crosstalk noise on different lateral structures. Analytical results are shown as bold lines, and the results from simulations are shown as dotted lines. (C) Minor source detection with different lateral structures. Because the specialization index is not well defined for a network with random lateral connections, the average synaptic weights from source A to those output neurons that prefer source A were measured instead. (D) Synaptic weight development at three connections. In the left and right columns, panels show synaptic weights of excitatory/inhibitory synapses projected to the neuron group 1 (top) and group 2 (bottom). In the middle graph, panels correspond to excitatory synapses projected from the neuron group 1 (top) and group 2 (bottom). In all panels, thin lines indicate the development of individual synapses, thick lines represent average weights onto output neurons, and colors indicate A-neurons (blue), B-neurons (red), and Background-neurons (orange). (E, F) Performance of the network with different lateral structures in noisy signal detection (E) and minor signal detection (F). Here (and only here), a pre-learned network is used to investigate responses for various inputs.
Fig 6.
Correlation propagation shapes lateral connection structure.
(A) Comparison between feature selectivity ϕY (blue dots) calculated from simulation results and analytically calculated correlation kernel function g1Y (green line) for lateral excitatory connections. Thin green horizontal line represents g1Y = 0. (B) Comparison between the degree of mutual inhibition ϕY (blue dots) calculated from the simulation and analytically calculated correlation kernel g1Z (green line) for lateral inhibitory connections. Negative g1Z is correlated with a high degree of mutual inhibition, as expected (see Methods). (C) Ratio of output neurons tuned for the minor source in a minor source detection task under Hebbian and anti-Hebbian inhibitory spike-timing-dependent plasticity.
Fig 7.
With lateral inhibition, spike-timing-dependent plasticity (STDP) mimics Bayesian independent component analysis (ICA).
(A) Schematic figure of the model with four sources. (B) Synaptic weight development in input neuron space. Arrows qA to qD are response probability vectors of the four sources, and PC1 to PC4 are normalized principal components of the correlation matrix C. Lines represent traces of average synaptic weight from each input group to the output groups that learned corresponding sources during the learning process. (C) Comparison of performance among the ideal observer, Bayesian ICA learning, and STDP learning. (D) LTP/LTD time window of Bayesian ICA learning. (E) Behaviors of log-membrane potential (color lines) in the STDP model, and estimated log-posterior (black lines) in the Bayesian ICA algorithm for the same stimuli. Vertical lines represent timings of external events. Log-membrane potentials are normalized to align the mean and the variance to the corresponding log-posteriors.
Fig 8.
Blind source separation by spike-timing-dependent plasticity (STDP).
(A) Four original auditory signals (from the top to the fourth set of signals) and one mixed signal (bottom). (B) Amplitudes of original signals (black lines) and those estimated from output firing rates (colored lines). (C) Spectra of auditory sources aqh(f) (left). Raster plots of input neuron activity. Colors were probabilistically assigned based on expected sources. All figures were calculated from the 30’00”–30’10” portion of the auditory signals and simulation.