Probabilistic synapses

Learning, especially rapid learning, is critical for survival. However, learning is hard: a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of probability distributions over weights - not just point estimates - is the optimal strategy. Here we hypothesize that synapses take that optimal strategy: they do not store just the mean weight; they also store their degree of uncertainty - in essence, they put error bars on the weights. They then use that uncertainty to adjust their learning rates, with higher uncertainty resulting in higher learning rates. We also make a second, independent, hypothesis: synapses communicate their uncertainty by linking it to variability, with more uncertainty leading to more variability. More concretely, the value of a synaptic weight at a given time is a sample from its probability distribution. These two hypotheses cast synaptic plasticity as a problem of Bayesian inference, and thus provide a normative view of learning. They are consistent with known learning rules, offer an explanation for the large variability in the size of post-synaptic potentials, and make several falsifiable experimental predictions.