Fig. 1: A topographic recurrent network model encodes spatiotemporal information of video frames via internal wave activity.

a Schematic of the complex-valued neural network (cv-NN) model. Nodes (circles) are arranged on a two-dimensional grid and are recurrently connected (blue) locally in space like the cortical sheet. A natural image input projects locally into the network via feedforward connections (red), mimicking retinotopy. b Example dynamic of the network model. Due to the spatially local projection of the input image, an imprint of the image is visible in the grid of network activity. Due to the local recurrent connectivity, intrinsic wave activity is generated alongside the input projection. c Top row: In a sequence of six frames, exactly one of the first five contains a point stimulus, and the other frames do not. These frames are sequentially input to the network. Second row: When the cv-NN has no recurrence, the stimulus projection remains stationary. Third row: With recurrence, from the time of stimulus, cv-NN activity contains a projection of the stimulus and a wave radiating outward. Fourth row: Activity in a randomly connected recurrent neural network (RNN) following stimulus onset has a spatially disorganized structure, reflecting its lack of topography and distance-dependent time delays. Right: A linear classifier that received the final network state in the no-recurrence case could not predict the time or location beyond chance-level accuracy (5% overall), and in the random-RNN case, could predict the time but not the location beyond chance (25% overall). In contrast, using the classifier with the sixth with-recurrence network state allowed 100% accuracy since the feedforward projection of the point stimulus triggered a radiating wave that encoded the time and location of the stimulus in the subsequent network states. N = 100 trials for each group. Mean ± standard deviation of 5.09 ± 0.94, 100 ± 0, and 24.42 ± 4.13, respectively. Source data are provided as a Source Data file.