The Gradient Clusteron: A model neuron that learns via dendritic nonlinearities, structural plasticity, and gradient descent

Synaptic clustering on neuronal dendrites has been hypothesized to play an important role in implementing pattern recognition. Neighboring synapses on a dendritic branch can interact in a synergistic, cooperative manner via the nonlinear voltage-dependence of NMDA receptors. Inspired by the NMDA receptor, the single-branch clusteron learning algorithm (Mel 1991) takes advantage of location-dependent multiplicative nonlinearities to solve classification tasks by randomly shuffling the locations of “under-performing” synapses on a model dendrite during learning (“structural plasticity”), eventually resulting in synapses with correlated activity being placed next to each other on the dendrite. We propose an alternative model, the gradient clusteron, or G-clusteron, which uses an analytically-derived gradient descent rule where synapses are “attracted to” or “repelled from” each other in an input- and location- dependent manner. We demonstrate the classification ability of this algorithm by testing it on the MNIST handwritten digit dataset and show that, when using a softmax activation function, the accuracy of the G-clusteron on the All-vs-All MNIST task (∼85%) approaches that of logistic regression (∼93%). In addition to the location update rule, we also derive a learning rule for the synaptic weights of the G-clusteron (“functional plasticity”) and show that a G-clusteron that utilizes the weight update rule can achieve ∼89% accuracy on the MNIST task. We also show that a G-clusteron with both the weight and location update rules can learn to solve the XOR problem from arbitrary initial conditions.