Redundant representations in macaque retinal populations are consistent with efficient coding

E Doi, J L Gauthier, G D Field, J Shlens, A Sher, M Greschner, T Machado, K Mathieson, D Gunning, A M Litke, L Paninski, E J Chichilnisky and E P Simoncelli

Published in Computational and Systems Neuroscience (CoSyNe), (II-71), Feb 2011.

This paper has been superseded by:
Efficient coding of spatial information in the primate retina
E Doi, J Gauthier, G Field, J Shlens, A Sher, M Greschner, T Machado, L Jepson, K Mathieson, D Gunning, A Litke, L Paninski, EJ Chichilnisky and E P Simoncelli.
J. Neuroscience , vol.32(46), pp. 16256--16264, Nov 2012.

Early investigations of efficient coding with the linear-Gaussian model showed striking similarities to experimental data (Atick & Redlich, 1990; van Hateren, 1992). However, direct comparison with the retinal ganglion cell (RGC) receptive fields has been hampered by three limitations: (a) RGC receptive fields under photopic conditions should be written in terms of weights on the cone photoreceptors, and these data were obtained only recently (Field et al, 2010); (b) RGCs are inhomogeneous, both within and between cell types (e.g., Gauthier et al, 2009), as are their cone inputs, and the input-to-output cell ratio is not 1:1. Most theoretical studies assumed homogeneity and a 1:1 cell ratio for analytical tractability (although see Li & Atick (1994), Campa et al (1995), Doi & Lewicki (2007)); (c) Efficient coding depends on neural resource constraints, and including a cost for synaptic weights significantly alters the solution (Doi et al, 2010a). Together, these advances enable us to conduct a direct comparison, and here we present four results: (1) Retinal receptive fields transmit 74-82% of the information in natural images, relative to the optimal linear-Gaussian solution. By comparison, a weight matrix that produces the same average output power, and has the same average squared weights, but is otherwise random (Wrnd) achieves only 35-38%; (2) Optimal weights mimic retinal weights in generating highly redundant representations of natural images; (3) The optimal weights are non-unique, but the inner-product of projective fields (ipPF) is uniquely constrained (Doi et al, 2010b), and the optimal ipPF provides a good match to the data; (4) Although the optimal weights are non-unique, a solution that achieves the optimum and best fits the data can be found (Doi et al, 2010b). The error of this solution is 36.1%, significantly smaller than the best-fit error for Wrnd: 89.5B13.2%.
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