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Synaptic plasticity as Bayesian inference


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 is the optimal strategy. Here we hypothesize that synapses take that strategy; in essence, when they estimate weights, they include error bars. They then use that uncertainty to adjust their learning rates, with more uncertain weights having higher learning rates. We also make a second, independent, hypothesis: synapses communicate their uncertainty by linking it to variability in postsynaptic potential size, with more uncertainty leading to more variability. These two hypotheses cast synaptic plasticity as a problem of Bayesian inference, and thus provide a normative view of learning. They generalize known learning rules, offer an explanation for the large variability in the size of postsynaptic potentials and make falsifiable experimental predictions.

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Fig. 1: The delta rule is suboptimal.
Fig. 2: Bayesian learning rules track the target weight and estimate uncertainty.
Fig. 3: Bayesian learning rules exhibit lower error than classical ones.
Fig. 4: Recurrent neural network.
Fig. 5: Normalized variability versus presynaptic firing rate as a diagnostic of our theory.

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L.A. and P.E.L. were supported by the Gatsby Charitable Foundation. P.E.L. was also supported by the Wellcome Trust (110114/Z/15/Z). J.J. and J.-P.P. were supported by the Swiss National Science Foundation (PP00P3 150637 and 31003A 175644). J.A.M. was supported by University College London (UCL) Graduate Research and UCL Overseas Research Scholarships. A.P. was supported by a grant from the Simons Collaboration for the Global Brain and the Swiss National Foundation (31003A 165831).

Author information




A.P. and P.E.L. were involved in the initial formulation of the problem. L.A. and P.E.L. conducted the theoretical development. L.A., J.J. and J.A.M. performed the simulations and data analysis. P.E.L., J.-P.P. and A.P. wrote the manuscript.

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Correspondence to Laurence Aitchison.

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Supplementary Notes 1–6, Supplementary Figs. 1–7 and Supplementary Tables 1 and 2.

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Aitchison, L., Jegminat, J., Menendez, J.A. et al. Synaptic plasticity as Bayesian inference. Nat Neurosci 24, 565–571 (2021).

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