Homeostatic processes stabilize hebbian learning in the visual cortex

R. ROSSI-POOL, G. MATO

San Diego

Conferencia; 40th Meeting Society for Neuroscience; 2010

Society for Neuroscience

We study how homeostatic processes interact with hebbian learning in the intracortical connections of a model of hypercolumn of the visual cortex. Correlation based hebbian plasticity by itself leads to a connectivity pattern that is either very weakly modulated or unstable. In the first case the model of hypercolumn does not display contrast invariance while in the second the neuronal activity is unbounded. Moreover, in this case the spatial invariance of the connectivity pattern is lost show that a homeostatic plasticity rule combined with a background of non-plastic uniform inhibition succeeded in bringing the matrix into a stable operating regime, where the connectivity matrix still shows translational symmetry. The presence of homeostatic plasticity stabilizes the effect ofhebbian plasticity. The system can reach non-trivial solutions, where the recurrent intracortical connections are strongly modulated. The modulation is strong enough to generate contrast invariance. The homeostasis is implemented by global rescaling of the presynaptic connections. We studied the system analytically after reducing the evolution of the connections to a three-dimensional dynamical system in terms of the first two Fourier components of the connectivity matrix and the average value of the homeostasis parameter. We have determined the conditions for the existence of a stable fixed point of the dynamical system that lies in a region where the model displays contrast invariance. This behavior is remarkably robust. The fixed points do not depend on the time constants of the model, although time constants can affect their stability. Stability is typically lost via a Hopf bifurcation. In contrast, the fixed points depend strongly on the target value of the homeostatic process and the modulation of the external stimuli.The dynamics has a fast relaxation controlled by the hebbian plasticity and a slower phase controlled by the homeostasis. The net asymptotic interaction between orientation columns displays "Mexican hat" shape. These results w ere verified using numerical simulations of a firing-rate based model. In the simulations the connectivity matrix is described by an arbitrary number of Fourier components. We show that a suitable final state can be reached even if the initial conditions are random or weakly modulated. The methods described in this work can also be applied to other models of the primary visual cortex.