Energy Efficient Plasticity in Probabilistic Synapses

: Expression Mechanisms and Bayesian Principles

Abstract

Reliable communication between neurons requires precise synaptic transmission, however neural circuits face a tradeoff between reliable transmission and energy costs. Increasing the probability of successful transmission requires energy-intensive calcium flux and vesicle turnover. Thus, synapses must balance reliability against energy conservation---a balance that critically influences synaptic plasticity and performance.

We investigated this tradeoff by characterising the energy driven mechanisms that enhance synaptic reliability, formalising reliability costs in the form of an energy-precision power-law. We then embedded this cost model into the objective of artificial neural networks (ANNs) with trainable stochastic synapses, and simulated learning on image classification tasks. In these networks, higher synaptic precision improved performance but incurred greater energy penalty. The tradeoff was optimised by inhomogeneous patterns of synaptic noise, where reliability was scaled by testable measures of synapse importance---input rate and learning rate. Such reliability scalings have been observed in biology and are consistent with the Bayesian synapse hypothesis; where synapse noise carries maximal statistical efficiency---any less and the synapse becomes biased; from this perspective synapse noise is a feature, not a bug. Formal analysis of the performance-reliability tradeoff provided an elegant link between any power-law reliability cost and negative Gaussian entropy---an essential term in the evidence-lower-bound (ELBO)---optimised in variational inference to approximate Bayesian inference.

We also identified that quantal state expressed through variables: \(n\) (vesicle number), \(p\) (release probability), and \(q\) (quantal size) is uniquely determined by synaptic energy budgets. When the budget is set to its minimal bound, the resulting quantal state attains empirical measurements of synapse variance. Curiously the energy model that best predicted the data naturally recovers a power-law between the minimal energy budget and maximal synaptic precision. This monotone relationship implies that synapses lie on the minimal noise-energy frontier; and that plasticity selects the exact expression mechanisms needed to achieve this. Further, the connection between the ELBO and the naturally re-occuring energy-precision power-law implies that Bayesian patterns of synapse noise are an emergent property of maximally efficient synaptic expression.

We further show that plasticity is associated with increased energy budgets and that these budget updates directly increment synapse reliability, suggesting that learning events dynamically adjust energy budgets to enhance reliability. The Bayesian reading is that learning events provide evidence, decrease statistical uncertainty, and inform judicious energy investment. Together, this work unifies energy efficiency and Bayesian inference as two-sides of the same coin; whether one side carries more value depends on whether the currency of the true reliability cost is physical or statistical.

Date of Award	30 Sept 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Conor Houghton (Supervisor) & Laurence Aitchison (Supervisor)