How disorder impacts information content in continuous attractor networks*

Attractor networks are a theme with long tradition to model information storage in the brain. Continuous attractor neural networks (CANN), in particular, have been employed to describe the storage of information about space and orientation. However, it stays controversial how useful this paradigm really is to explain actual processes, for example, in mammals, the representation of space in grid and place cells in the entorhinal cortex and the hippocampus, respectively.

 A common criticism is that the disorder present in the connections might deteriorate the system's capability to reliably preserve the information of a certain pattern.

In order to investigate if this criticism is valid, a measure is needed to objectively quantify the information content of a given neural network. Using the replica-trick, we compute the Fisher information for a network receiving space-dependent input whose connections are composed of a distance-dependent and a disordered component. We observe that the decay of the Fisher information is slow for not too large disorder strength, indicating that CANNs have a regime in which information is preserved despite the detrimental influence of disorder. In this regime, a considerable part of this information can be extracted by a linear readout.