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Learning from experience depends at least in part on changes in neuronal connections. We present the largest map of connectivity to date between cortical neurons of a defined type (layer 2/3 [L2/3] pyramidal cells in mouse primary visual cortex), which was enabled by automated analysis of serial section electron microscopy images with improved handling of image defects (250 × 140 × 90 μm3 volume). We used the map to identify constraints on the learning algorithms employed by the cortex. Previous cortical studies modeled a continuum of synapse sizes by a log-normal distribution. A continuum is consistent with most neural network models of learning, in which synaptic strength is a continuously graded analog variable. Here, we show that synapse size, when restricted to synapses between L2/3 pyramidal cells, is well modeled by the sum of a binary variable and an analog variable drawn from a log-normal distribution. Two synapses sharing the same presynaptic and postsynaptic cells are known to be correlated in size. We show that the binary variables of the two synapses are highly correlated, while the analog variables are not. Binary variation could be the outcome of a Hebbian or other synaptic plasticity rule depending on activity signals that are relatively uniform across neuronal arbors, while analog variation may be dominated by other influences such as spontaneous dynamical fluctuations. We discuss the implications for the longstanding hypothesis that activity-dependent plasticity switches synapses between bistable states.

Inhibitory neurons in mammalian cortex exhibit diverse physiological, morphological, molecular, and connectivity signatures. While considerable work has measured the average connectivity of several interneuron classes, there remains a fundamental lack of understanding of the connectivity distribution of distinct inhibitory cell types with synaptic resolution, how it relates to properties of target cells, and how it affects function. Here, we used large-scale electron microscopy and functional imaging to address these questions for chandelier cells in layer 2/3 of the mouse visual cortex. With dense reconstructions from electron microscopy, we mapped the complete chandelier input onto 153 pyramidal neurons. We found that synapse number is highly variable across the population and is correlated with several structural features of the target neuron. This variability in the number of axo-axonic ChC synapses is higher than the variability seen in perisomatic inhibition. Biophysical simulations show that the observed pattern of axo-axonic inhibition is particularly effective in controlling excitatory output when excitation and inhibition are co-active. Finally, we measured chandelier cell activity in awake animals using a cell-type-specific calcium imaging approach and saw highly correlated activity across chandelier cells. In the same experiments, in vivo chandelier population activity correlated with pupil dilation, a proxy for arousal. Together, these results suggest that chandelier cells provide a circuit-wide signal whose strength is adjusted relative to the properties of target neurons.