Continuous Attractors with Morphed/Correlated Maps

Continuous attractor networks are used to model the storage and representation of analog quantities, such as position of a visual stimulus. The storage of multiple continuous attractors in the same network has previously been studied in the context of self-position coding. Several uncorrelated maps of environments are stored in the synaptic connections, and a position in a given environment is represented by a localized pattern of neural activity in the corresponding map, driven by a spatially tuned input. Here we analyze networks storing a pair of correlated maps, or a morph sequence between two uncorrelated maps. We find a novel state in which the network activity is simultaneously localized in both maps. In this state, a fixed cue presented to the network does not determine uniquely the location of the bump, i.e. the response is unreliable, with neurons not always responding when their preferred input is present. When the tuned input varies smoothly in time, the neuronal responses become reliable and selective for the environment: the subset of neurons responsive to a moving input in one map changes almost completely in the other map. This form of remapping is a non-trivial transformation between the tuned input to the network and the resulting tuning curves of the neurons. The new state of the network could be related to the formation of direction selectivity in one-dimensional environments and hippocampal remapping. The applicability of the model is not confined to self-position representations; we show an instance of the network solving a simple delayed discrimination task.Author Summary: How is your position in an environment represented in the brain, and how does the representation distinguish between multiple environments? One of the proposed answers relies on continuous attractor neural networks. Consider the web page of your campus map as a network of pixels. Every pixel is a neuron, and nearby pixels excite each other, while distant pairs are inhibited. As a result of their interactions, a bunch of close-by pixels will light up, indicating your current position as suggested by your web-cam (the sensory input). When you travel to another campus, the common assumption holds that pixels are completely scrambled and the excitatory/inhibitory pattern of connections is summed to the existing one. Now these connections and the sensory input will activate the pixels corresponding to your location in the new campus. The active pixels will look like noise in the old map. But what if the campuses are similar, i.e. the pixels are not completely scrambled? We show that the network has a novel way of distinguishing between the environments, by lighting up distinct subsets of pixels for each campus. This emergent selectivity for the environment could be a mechanism underlying hippocampal remapping and directional selectivity of place cells in 1D environments.