Can the Brain Use Waves to Solve Planning Problems?

Abstract

A variety of behaviors like spatial navigation or bodily motion can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state.

Does the Brain Infer Invariance Transformations from Graph Symmetries?

“…Its symmetries represent the invariances of the environmental stimuli that have shaped the network during the training process. It can now serve as a substrate on which different neural algorithms can be implemented, like object classification, mental imagery tasks, or the planning of bodily motions [7]. In particular, when a new object is perceived for the first time, it is decomposed into the same set of features that form the graph's nodes, and its symmetries can directly be applied to the new object.…”

“…Wave-like propagation of cortical activity has been observed in many experiments. In a different article [7] we proposed that such waves are used to solve planning problems and gave an overview of empirical support for this idea. It is appealing to speculate that both perception and planning problems which are subject to (invariance) transformations could be supported by essentially the same mechanism.…”

“…Indeed there is evidence that somatosensory cortex follows the theme of connectivity described above with tactile stimuli detectors having receptive fields similar to those in V1 and recurrent connections depending on their likelihood of simultaneous stimulation -cf. [7] and references therein. Yet characterizing the relevant invariances explicitly is harder than in vision or audio due to the interplay between sensory perception and bodily posture.…”