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Synaptic balancing: A biologically plausible local learning rule that provably increases neural network noise robustness without sacrificing task performance

Fig 5

Dynamics of synaptic balancing in a 12-neuron ring network with single perturbed synapse.

(a). Left: A ring network is at an initial equilibrium C*ⁱ with all synaptic costs equal to 1. Nodes indicate neurons; arrows indicate directed synapses. Center: Synapse A, from neuron j to i, is instantaneously potentiated to a synaptic cost of . Right: Synaptic balancing relaxes to a new equilibrium C*^f. Synapse colors and thickness indicate synaptic cost. Neuron colors indicate value of h*^f according to color scheme of panel (c). (b) Time course of synaptic balancing following perturbation. Incoming synapses to neuron i (A and D) are weakened and outgoing synapses from neuron i (B and C) are strengthened. Incoming synapses to neuron j (B and E) are strengthened and outgoing synapses from neuron j (A and F) are weakened. Synapses (H and G) that are distant from the site of perturbation respond more slowly than proximate synapses though they reach the same equilibrium values. (c) Three eigenmodes v₃, v₅, v₇, with eigenvalues λ₃, λ₅, λ₇, of the Laplacian matrix L⁰ corresponding to the conductance matrix at the moment of perturbation. Color indicates mode value at each neuron. (d) Dynamics of h approximately decompose into the basis of Laplacian eigenmodes. The scalar projection of h onto each mode v is shown along with the quadratic approximation (39), using L⁰ as Laplacian. Line color matches eigenvalue color in panel (c).

doi: https://doi.org/10.1371/journal.pcbi.1010418.g005