Information in a recurrent Retina-V1 network with realistic noise, feedback and nonlinearities

Abstract

Quantitative estimation of information flow in early vision with psychophysically realistic networks is still an open issue. This is because, up to date, the necessary elements (general and plausible network, accurate noise, and reliable information measures) have not been put together. As a result, previous works made different approximations that limit the generality of their results. This work combines the following elements for the first time: (1) General and plausible recurrent net: a cascade of linear+nonlinear psychophysically tuned layers [IEEE TIP.06, J.Neurophysiol.19, J.Math.Neurosci.20, Neurocomp.24], augmented to consider top-down feedback following [Nat.Neurosci.21,Neurips.22]. (2) Accurate noise in every layer, which is tuned to reproduce psychometric functions both in contrast detection and discrimination following [J.Vision 25]. (3) Reliable information measures that have been checked with analytical results, both in general [IEEE PAMI 24], and in similar visual neuroscience contexts [Neurocomp.24], and hence can be applied in this (more general) case where analytical results are difficult to obtain. The joint use of these elements allows a reliable study of information flow depending on different connectivity schemes (different nonlinearities and interactions), different noise sources, and different stimuli. Results show the benefits of feedback in two ways: (1) the information loss in the data processing inequality along the pathway is reduced by the V1 -- > LGN recurrence for values of feedback that give stable steady state solutions, and (2) the stability of the net is assessed though standard Poincaré analysis and we find an optimal value for the feedback in terms of the accuracy of the reconstructed signal from the cortical representation.

Figures (5)

• Figure 1: The feedback learned in SommerNIPS22 can be seen as an inverse transform. (a) Illustrative set of V1-like connectivity weights in $LGN \rightarrow V1$: a local-frequency transform. In this illustration, an orthonormal set of Haar functions compatible with the model used in SommerNIPS22. (b) Result of SommerNIPS22: learned weights in the $V1 \rightarrow LGN$: the influence of the response of a V1 neuron in LGN strongly resembles the receptive field of the V1 neuron. (c) One dimensional example of the Haar transform showing that such feedback weights are actually implementing an inverse transform.
• Figure 2: Estimation of early and late noise in our models. Left panel highlights in green the point indicating the optimal amplitudes of the early and late noise sources (vertical and horizontal axis respectively) which are compatible with the psychophysical behavior (lower error is better). Right panel shows the corresponding fit (black curves) of the experimental psychometric functions of Wichmann02 (blue circles) as prescribed in Malo25.
• Figure 3: Stability and reconstruction error depending on feedback. Left Poincaré Stability Diagram for different feedback strengths ($c_i^{1/2}$ values in blue). Right Error if we reconstruct the signal from the noisy V1 linear layer for different feedback strengths including the no-feedback $c_1 = 0$ scenario. Quality of the reconstructions has an optimum for $c_1>0$, which differs from the no-feedback, $c_1 = 0$, scenario.
• Figure 4: Illustrative reconstructed images assuming different feedback strengths. Quality of the reconstructions has an optimum for $c_1>0$, which differs from the no-feedback, $c_1 = 0$, scenario.
• Figure 5: Illustrative reconstructed images assuming different feedback strengths. Quality of the reconstructions has an optimum for $c_1>0$, which differs from the no-feedback, $c_1 = 0$, scenario.