Fig 1.
SORN regimes and neuronal avalanches.
(A) Fraction of active connections in the SORN, starting from a random connected graph with 0.1 active connections. It exhibits three self-organization phases: decay, growth, and stable. (B) Activity threshold θ for a typical snapshot of SORN activity a(t) (150 time steps). Avalanche duration is indicated in blue and avalanche size in shaded red. The neuronal avalanches were measured only during the stable phase.
Fig 2.
Power-law distributed neuronal avalanches in the SORN’s stable phase.
(A), (B) Normalized distributions of duration T and size S of neuronal avalanches, respectively, for NE = 200. The raw data points of 50 independent SORN simulations are shown in gray. The power-law fit is shown in blue/red and the power-law with exponential cut-off fit is shown in black for comparison. (C) Avalanches’ average size 〈S〉(T) as a function of duration, for simulated data (gray) and theoretical prediction (red). The dashed black line shows a power-law with exponent γ = 1.3, approximately fitting the raw data from SORN simulations. (D), (E) Scaling of avalanches’ distributions for networks of different sizes. Dashed lines show the exponents α and τ calculated from pure power-laws for NE = 200 (shown in the top row). (F) Power-law range for networks of different sizes, obtained by estimating the cut-off point. All distributions show combined data of 50 independent simulations.
Fig 3.
Robustness to choice of activity threshold.
(A) Activity distribution function for a SORN with NE = 200. The shaded area shows the approximate region where the power-laws hold. The activity peak, as expected due to the target firing rate, is 10% of the number of excitatory neurons. (B) Avalanche size distribution for different activity thresholds θ set as activity percentiles. Although showing different exponents, the power-laws hold for different thresholds (as seen, for example, for θ set at the 5th or 10th percentiles of the activity distribution). Curves show combined data from 50 simulations.
Fig 4.
(A), (B) Distribution of avalanche durations and sizes, respectively, for NE = 200 units, comparing typical SORNs (black), randomly initialized SORNs without plasticity action (red) and SORNs with all five plasticity mechanisms frozen at the stable phase (cyan). (C), (D) Distribution of avalanche durations and sizes, respectively, for the same network size, comparing SORNs with frozen IP (red) and frozen STDP, iSTDP, SN and SP (cyan) at the stable phase. Curves are combined data from 50 independent simulations, and shaded regions show the effects of variations in the activity threshold (θ between the 5th and 25th percentiles of the activity distribution).
Fig 5.
Noise level influences the SORN dynamical regime.
Left, top row: avalanches’ size (A) and activity (B) distributions for SORN with different Gaussian noise levels: low (σ2 = 0.005), intermediate (σ2 = 0.05) and high (σ2 = 5). Very weak or strong noise levels break down the power-laws, suggesting a different non-critical regime. Left, bottom row: Avalanches’ size (C) and activity (D) distributions for the random spike noise source (see text), showing a similar effect. Gray dashed lines are binomial distributions (n = NE = 200, p = μIP = 0.1), the theoretical prediction for independent neurons, and shaded areas show the effects of variations in the activity threshold (θ between the 5th and 25th percentiles of the activity distribution). All curves show combined data of 50 independent simulations. (E), (F), (G) Typical raster plots of excitatory unit activity at low, intermediate and high Gaussian noise levels, respectively, for NE = 200.
Fig 6.
SORN readaptation under external input.
(A), (B) Duration and size distributions, respectively, after external input onset: transient readaptation period (red) and remaining 2 × 106 time steps (cyan). Before input and Readaptation curves show combined data from 50 independent simulations. Input onset curves show data from 250 input onset trials, and shaded regions show the effects of variations in the activity threshold (θ between the 5th and 25th percentiles of the activity distribution).
Fig 7.
(A) SORN performance for the Counting Task for sequences of different sizes, with (blue) and without (red) membrane noise. Original SORN refers to the model without iSTDP, SP and membrane noise, as introduced in [32](B), (C) Duration and size distributions, respectively, during the Counting Task for different input sequence sizes n (in the presence of membrane noise). (D) SORN performance for the Random Sequence Task for sequences of different sizes. (E), (F) Duration and size distributions, respectively, during the Random Sequence Task for different input sequence lengths L. Curves show the average of 50 independent simulations and error bars show the 5%–95% percentile interval.