Efficient coding predicts synaptic conductance

Retinothalamic and thalamocortical synapses are efficient in the sense that each synapse conveys as many bits per Joule as possible, but efficiency falls rapidly if synaptic conductance deviates from its natural value Harris et al. (2015, 2019). However, the manner in which efficiency falls with conductance remains unexplained. Recently, Malkin et al. (2026) showed that synaptic noise is minimised given the available energy, consistent with a minimal energy boundary. Here, this boundary is expressed in terms of Shannon's information theory Shannon and Weaver (1949), which yields a model that predicts the efficiency values observed in Harris et al. (2015) across a 120-fold change in synaptic conductance ( $R^2=0.769$ , $p<0.001$ ). This model also predicts that, for a synapse at its natural conductance, each pre-synaptic spike provides an average of 3.58 bits to its post-synaptic neuron, which is consistent with physiological values. Crucially, given the biophysical constraints that, a) synaptic efficiency is maximised at the natural conductance, and, b) synaptic noise variance is minimised in accordance with the minimal energy boundary, the proposed model contains no free parameters, so it is predictive rather than descriptive. The results presented here are consistent with the general principle that CNS neurons maximise information efficiency (bits per Joule), rather than information rate (bits per second).