Sparse Deep Predictive Coding captures contour integration capabilities of the early visual system

Abstract

Both neurophysiological and psychophysical experiments have pointed out the crucial role of recurrent and feedback connections to process context-dependent information in the early visual cortex. While numerous models have accounted for feedback effects at either neural or representational level, none of them were able to bind those two levels of analysis. Is it possible to describe feedback effects at both levels using the same model? We answer this question by combining Predictive Coding (PC) and Sparse Coding (SC) into a hierarchical and convolutional framework. In this Sparse Deep Predictive Coding (SDPC) model, the SC component models the internal recurrent processing within each layer, and the PC component describes the interactions between layers using feedforward and feedback connections. Here, we train a 2-layered SDPC on two different databases of images, and we interpret it as a model of the early visual system (V1~&~V2). We first demonstrate that once the training has converged, SDPC exhibits oriented and localized receptive fields in V1 and more complex features in V2. Second, we analyze the effects of feedback on the neural organization beyond the classical receptive field of V1 neurons using interaction maps. These maps are similar to association fields and reflect the Gestalt principle of good continuation. We demonstrate that feedback signals reorganize interaction maps and modulate neural activity to promote contour integration. Third, we demonstrate at the representational level that the SDPC feedback connections are able to overcome noise in input images. Therefore, the SDPC captures the association field principle at the neural level which results in better disambiguation of blurred images at the representational level.

Publication
PLoS Computational Biology

Fig 1. Architecture of a 2-layered SDPC model.
Fig 1. Architecture of a 2-layered SDPC model.
One often compares biological vision to a camera-like system where an image would be processed according to a sequence of successive transformations. In particular, this “feedforward” view is prevalent in models of visual processing such as deep learning. However, neuroscientists have long stressed that more complex information flow is necessary to reach natural vision efficiency. In particular, recurrent and feedback connections in the visual cortex allow to integrate contextual information in our representation of visual stimuli. These modulations have been observed both at the low-level of neural activity and at the higher level of perception.
Fig 2. Results of training SDPC on the natural images (left column) and on the face database (right column) with a feedback strength kFB = 1.
Fig 2. Results of training SDPC on the natural images (left column) and on the face database (right column) with a feedback strength kFB = 1.
Fig 14. Illustration of the hierarchical generative model learned by the SDPC model on the face database.
Fig 14. Illustration of the hierarchical generative model learned by the SDPC model on the face database.
In this study, we present an architecture that describes biological vision at both levels of analysis. It suggests that the brain uses feedforward and feedback connections to compare the sensory stimulus with its own internal representation. In contrast to classical deep learning approaches, we show that our model learns interpretable features.
Fig 5. Example of a 9 × 9 interaction map of a V1 area centered on neurons strongly responding to a central preferred orientation of 30°.
Fig 5. Example of a 9 × 9 interaction map of a V1 area centered on neurons strongly responding to a central preferred orientation of 30°.
Fig 7. Example of a 9 × 9 interaction map of a V1 area centered on neurons strongly responding to a central preferred orientation of 45°, and colored with the relative response w.r.t. no feedback.
Fig 7. Example of a 9 × 9 interaction map of a V1 area centered on neurons strongly responding to a central preferred orientation of 45°, and colored with the relative response w.r.t. no feedback.
Moreover, we demonstrate that feedback signals modulate neural activity to promote good continuity of contours. Finally, the same model can disambiguate images corrupted by noise. To the best of our knowledge, this is the first time that the same model describes the effect of recurrent and feedback modulations at both neural and representational levels.
Fig 10. Effect of the feedback strength on noisy images from natural images database.
Fig 10. Effect of the feedback strength on noisy images from natural images database.

Victor Boutin
Victor Boutin
Phd in Computational Neuroscience

During my PhD, I focused on predictive coding in bio-inspired neural networks.

Angelo Franciosini
Angelo Franciosini
Phd candidate in Computational Neuroscience

During my PhD, I am focusing on predictive coding in a bio-inspired neural network.

Laurent U Perrinet
Laurent U Perrinet
Researcher in Computational Neuroscience

My research interests include Machine Learning and computational neuroscience applied to Vision.

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