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Manifold transform by recurrent cortical circuit enhances robust encoding of familiar stimuli
Fig 3
Manifold transformation in the familiarity association experiment.
(A) Conceptual illustration of a visual feature manifold. Consider a smooth surface of local visual features on which a sparse coding dictionary provides discrete samples (
) [13]. Nuisance transformations of a visual stimulus, such as noise or changing viewpoints, correspond to flows along this manifold (blue dotted lines). The circles and triangles represent distinct sets of activated dictionary elements for two perceptually similar stimuli generated by the nuisance transformation (xi and x(n(i))), with arrows indicating response amplitudes. Because the dictionary is unordered, a smooth manifold flow can result in dissimilar sparse code activations (top). (B) Schematic of the manifold transform performed by the learned circuit. The model considers two types of relationships: a ’concept manifold’ (blue curve) representing the neural codes of distinct stimuli such as a target image xi (black dot) and a dissimilar stimulus xj (blue dot); and a ’variants manifold’ (red curve) representing the neural codes of variations of the same concept, such as xi and a related similar stimulus xn(i) (red dot). The learned circuit encoder, 
, maps the sparse codes to a new representation, r. This transformation compresses the variants manifold, reducing the distance between xi and xn(i) to better reflect their geometric relationship. For visual simplicity, the concept manifold is depicted as unchanged by the encoder. (C) Example images from the stimulus set (CIFAR100, publicly available here, also see [21]), corrupted with 10%, 30%, and 50% salt-and-pepper occlusion noise. (D) Schematic of the neural manifold geometry in the familiarity association experiment. The orange rings represent the signal variance for stimuli at different noise levels, forming a “signal cone.” Each target image and its corrupted samples would form an opposite “noise cone”. The blue rings represent the noise variances inside the noise cone at varying noise levels. From a specific noise sample (the red dot), the level distance is marked by the light blue arrow, the residual distance is marked by the deep blue arrow, and the signal distance is marked by the orange arrow. (E) Across noise levels, 
and 
over the first 200 epochs show a two-phase trajectory: a minimum at epoch 30 (dashed line), and an overall decrease. This indicates a compression of the neural manifold in both level and residual directions. Ribbons represent the standard deviation across different target images. (F) 
, 
and 
over first 200 epoch at all noise levels. The net decrease in both relative distances is primarily due to the larger increase in 
. (G, H) The relative distances exhibit a reverse correlation with neuronal tuning selectivity and the magnitude of SI. The darkness of the scatter indicates the number of epochs, with deeper colors corresponding to earlier epochs. The solid lines represent the fitted regression lines, with the corresponding Pearson correlation coefficient noted aside.
doi: https://doi.org/10.1371/journal.pcbi.1013587.g003