Figure 1. Associative memory storage in a recurrent network of inhibitory and excitatory neurons in the presence of errors and noise. A, Error propagation through the network. Inhibitory neurons (red circles) and excitatory neurons (blue triangles) form an all-to-all potentially (structurally) connected network. Red and blue arrows represent actual (functional) connections. Spiking errors (errors contained in
), synaptic noise (
), and intrinsic noise (
) accompany signal transmission (orange lightning signs). Errors in the neurons’ outputs at a given time step become spiking errors in the next time step. B, Fluctuations in PSPs for two associations with target neuron outputs 0 (left) and 1 (right). Large black dots denote PSPs in the absence of errors and noise. Small dots represent PSPs on different trials in the presence of errors and noise. Orange areas to the left of the PSP probability densities (solid lines) represent the probabilities of erroneous spikes (left) and spike failures (right). C, The probability of successful learning by a neuron is a sharply decreasing function of memory load m/N. Solid curves represent the probabilities of successful learning obtained with nonlinear optimization (see Materials and Methods) for neurons receiving N = 200, 400, and 800 homogeneous inputs. The numerical values of βlearn and rin = rout ≡ rlearn are provided in the figure. The values of all other parameters of the model were adapted from Chapeton et al. (2015). At 0.5 success probability, the neuron is said to be loaded to capacity, α. The dashed black line represents the theoretical (critical) capacity, αc, obtained with the replica method in the N → ∞ limit. D, αc as a function of βlearn for different input noise strengths (colored lines). In the case of rin = 0, solution of Equation 1 (blue line) coincides with the solution of the traditional model (Zhang et al., 2019b), which uses a generic robustness parameter (black dots). E, Map of αc for a neuron receiving homogeneous input as a function of rin and rout. F, Same as a function of βlearn and rin = rout ≡ rlearn. The maps in E, F were obtained with the replica method (see Materials and Methods), and the green asterisks correspond to the values of parameters used in C. Dashed isocontours are drawn as a guide to the eye.