Hebbian Learning: A Kernel-Based Perspective

Poster Session F - Tuesday, April 16, 2024, 8:00 – 10:00 am EDT, Sheraton Hall ABC

Yunqi Huang¹ (yunqi.huang@mail.utoronto.ca), Milad Lankarany², Gabriele D’Eleuterio¹; ¹University of Toronto, ²Krembil Research Institute

Hebb’s rule, governing adjustments in synaptic strength and firing thresholds, can be described in terms of the covariance of presynaptic and postsynaptic rates. The Hebbian process is moreover believed to minimize the risks associated with future outcomes. We take a new perspective here in which Hebbian learning is viewed through a reproducing-kernel-Hilbert-space framework. Based on conditional mean embedding, we show theoretically that the collective change in synaptic conductances during learning can be expressed in terms of a conditional expectation, modulated by a covariance operator, on the feature space of past stimuli given present stimuli. To test our hypothesis, we simulate a network of 500 neurons using a Hodgkin-Huxley model and inputs from actual biological data. The change in conductances calculated in the simulation support our theoretical findings. This conditional expectation establishes a crucial link between past and present stimuli, suggesting a memory-recollection mechanism during the learning process. In essence, learning involves direct inference of past stimuli based on present stimuli.

Topic Area: OTHER