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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 (L2/3 pyramidal cells), which was enabled by automated analysis of serial section electron microscopy images with improved handling of image defects. We used the map to identify constraints on the learning algorithms employed by the cortex. Previous cortical studies modeled a continuum of synapse sizes (Arellano et al., 2007) by a log-normal distribution (Loewenstein, Kuras and Rumpel, 2011; de Vivo et al., 2017; Santuy et al., 2018). 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 (Sorra and Harris, 1993; Koester and Johnston, 2005; Bartol et al., 2015; Kasthuri et al., 2015; Dvorkin and Ziv, 2016; Bloss et al., 2018; Motta et al., 2019). 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. We discuss the implications for the stability-plasticity dilemma.

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