Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. These nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher-order input correlations. The particular input correlation decomposed and the form of the decomposition depend on the location of nonlinearities in the plasticity rule.

Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. These nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher- order input correlations. The particular input correlation decomposed and the form of the decomposition depend on the location of nonlinearities in the plasticity rule.

Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized, nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. We show that these nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher-order input correlations. The particular input correlation decomposed, and the form of the decomposition, depend on the location of nonlinearities in the plasticity rule. For simple, biologically motivated parameters, the neuron learns tensor eigenvectors of higher-order input correlations. We prove that each tensor eigenvector is an attractor and determine their basins of attraction. We calculate the volume of those basins, showing that the dominant eigenvector has the largest basin of attraction. We then study arbitrary learning rules, and find that any learning rule that admits a finite Taylor expansion into the neural input and output also has stable equilibria at tensor eigenvectors of its higher-order input correlations. Nonlinearities in synaptic plasticity thus allow a neuron to encode higher-order input correlations in a simple fashion.

We present a method to distinguish direct connections between two neurons fromcommon input originating from other, unmeasured neurons. The distinction is computed from the spike times of the two neurons in response to a white noise stimulus. Although the method is based on a highly idealized linear-nonlinear approximation of neural response, we demonstrate via simulation that the approach can work with a more realistic, integrate-and-fireneuron model. We propose that the approach exemplified by this analysis may yield viable tools for reconstructing stimulus-driven neural networks from data gathered in neurophysiology experiments.

We present a method to distinguish direct connections between two neurons from common input originating from other, unmeasured neurons. The distinction is computed from the spike times of the two neurons in response to a white noise stimulus. Although the method is based on a highly idealized linear-nonlinear approximation of neural response, we demonstrate via simulation that the approach can work with a more realistic, integrate-and-fire neuron model. We propose that the approach exemplified by this analysis may yield viable tools for reconstructing stimulus-driven neural networks from data gathered in neurophysiology experiments.

We present a method to distinguish direct connections between two neurons from common input originating from other, unmeasured neurons. The distinction is computed from the spike times of the two neurons in response to a white noise stimulus. Although the method is based on a highly idealized linear-nonlinear approximation of neural response, we demonstrate via simulation that the approach can work with a more realistic, integrate-and-fire neuron model. We propose that the approach exemplified by this analysis may yield viable tools for reconstructing stimulus-driven neural networks from data gathered in neurophysiology experiments.

Hebbian learning rules are generally formulated as static rules.

Hebbian learning rules are generally formulated as static rules.