Fig. 7: Integral feedback allows diverse Hebbian-capable systems to achieve contrastive learning.
From: Temporal Contrastive Learning through implicit non-equilibrium memory
A Synaptic current sij in synapse ij impacts a variable uij(t) which is under integral feedback control. That is, the deviation of uij(t) from a setpoint u0 is integrated over time and fed back to uij, causing uij(t) to return to u0 after transient perturbations due changes in sij(t). We can achieve contrastive learning by updating synaptic weights wij using uij(t), as opposed to Hebbian learning by updating wij based on sij(t). B Mechanical or vascular networks can undergo Hebbian learning if flow or strain produce molecular species (blue hexagon uij) that drive downstream processes that modify radii or stiffnesses of network edges. But if those blue molecules are negatively autoregulated (through the green species as shown), these networks can achieve contrastive learning. C Molecular interaction networks can undergo Hebbian learning if the concentrations of dimers sij, formed through mass-action kinetics, drives expression of linker molecules lij (here, purple-green rectangles) that mediate binding interactions between monomers i, j. But if transcriptionally active dimers uij additionally stimulate regulatory molecules (black circle) which inhibit uij, then levels of linker molecules lij will provide interactions learned through contrastive rules. D Stresses in networks of viscoelastic mechanical elements (dashpots connected in series to springs) reflect the time-derivatives of strains due to relaxation in dashpots. These stresses can be used to generate contrastive updates of spring stiffnesses. E Nanofluidic memristor networks can undergo Hebbian updates by changing memristor conductance in response to current flow. However, if capacitors are added as shown, voltage changes sij across a memristor results in a transient current uij; conductance changes due to these currents uij result in contrastive learning.
