Input-dominated Hebbian learning enables image-computable E-I networks

Recurrent network models of excitatory (E) and inhibitory (I) neurons with supralinear activation functions have successfully explained several cortical computations, including response normalization and surround suppression. Unlike more abstract approaches, such networks allow direct comparisons with experimentally measured neural activities and synaptic strengths. However, the scope of these networks remained limited as their connectivity needed to be designed by hand or fitted by complex machine learning algorithms to yield stable activity and computations. Here we present a method to efficiently construct stable recurrent E-I networks with connectivity that reflect the statistical regularities of high-dimensional natural images using a diverse set of feedforward receptive fields. We build on recent work that demonstrated the emergence of functional E-I networks via online Hebbian learning from an input population with homogeneous tuning curves, and employ a simple covariance plasticity rule at all recurrent synapses without constraints on input tuning. When the network's activity is dominated by feedforward inputs, we can solve for the steady-state weight matrix analytically. This allows us to construct stable networks with recurrent weights adapted to complex input statistics without hand-tuning or numerical optimization. We demonstrate our approach by constructing two fully connected networks of 6,500 neurons and >40 million synapses each, encoding natural image datasets resembling the upper and lower visual field of mice, respectively. We found that correlations between cross-oriented receptive fields in the upper visual field were weaker than those in the lower visual field, while iso-oriented receptive fields were more strongly correlated in the upper visual field. These statistics became reflected in the networks' synaptic connectivity and predicted weaker cross-orientation, but stronger iso-orientation surround suppression in the lower compared to the upper visual field. In summary, our method enables image-computable models of stable, supralinear E-I networks that allow for detailed comparison with heterogeneous cortical circuits.