One of the most striking aspects of early visual processing in the retina is the immediate parcellation of visual information into multiple parallel pathways, formed by different retinal ganglion cell types each tiling the entire visual field. Existing theories of efficient coding have been unable to account for the functional advantages of such cell-type diversity in encoding natural scenes. Here we go beyond previous theories to analyze how a simple linear retinal encoding model with different convolutional cell types efficiently encodes naturalistic spatiotemporal movies given a fixed firing rate budget. We find that optimizing the receptive fields and cell densities of two cell types makes them match the properties of the two main cell types in the primate retina, midget and parasol cells, in terms of spatial and temporal sensitivity, cell spacing, and their relative ratio. Moreover, our theory gives a precise account of how the ratio of midget to parasol cells decreases with retinal eccentricity. Also, we train a nonlinear encoding model with a rectifying nonlinearity to efficiently encode naturalistic movies, and again find emergent receptive fields resembling those of midget and parasol cells that are now further subdivided into ON and OFF types. Thus our work provides a theoretical justification, based on the efficient coding of natural movies, for the existence of the four most dominant cell types in the primate retina that together comprise 70% of all ganglion cells.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

There are currently two seemingly unrelated frameworks for understanding these patterns. Mechanistic models account for hexagonal firing fields as the result of pattern-forming dynamics in a recurrent neural network with hand-tuned centersurround connectivity. Normative models specify a neural architecture, a learning rule, and a navigational task, and observe that grid-like firing fields emerge due to the constraints of solving this task. Here we provide an analytic theory that unifies the two perspectives by casting the learning dynamics of neural networks trained on navigational tasks as a pattern forming dynamical system. This theory provides insight into the optimal solutions of diverse formulations of the normative task, and shows that symmetries in the representation of space correctly predict the structure of learned firing fields in trained neural networks. Further, our theory proves that a nonnegativity constraint on firing rates induces a symmetry-breaking mechanism which favors hexagonal firing fields. We extend this theory to the case of learning multiple grid maps and demonstrate that optimal solutions consist of a hierarchy of maps with increasing length scales. These results unify previous accounts of grid cell firing and provide a novel framework for predicting the learned representations of recurrent neural networks.