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Investigation of Possible Neural Architectures Underlying Information-Geometric Measures

masami{at}email.arizona.edu, ARL Division of Neural Systems, Memory and Aging, The University of Arizona, Tucson, AZ 85724-5115, U.S.A., and Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Saitama, 351-0198, Japan

Masato Okada

okada{at}brain.riken.go.jp, Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Saitama, 351-0198, Japan, and Intelligent Cooperation and Control, PRESTO, JST, c/o RIKEN BSI, Saitama 351-0198, Japan

A novel analytical method based on information geometry was recently proposed, and this method may provide useful insights into the statistical interactions within neural groups. The link between information-geometric measures and the structure of neural interactions has not yet been elucidated, however, because of the ill-posed nature of the problem. Here, possible neural architectures underlying information-geometric measures are investigated using an isolated pair and an isolated triplet of model neurons. By assuming the existence of equilibrium states, we derive analytically the relationship between the information-geometric parameters and these simple neural architectures. For symmetric networks, the first- and second-order information-geometric parameters represent, respectively, the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log-linear model and the number of neurons in the network are the same. For asymmetric networks, however, these parameters are dependent on both the intrinsic connections and the external inputs to each neuron. In addition, we derive the relation between the information-geometric parameter corresponding to the two-neuron interaction and a conventional cross-correlation measure. We also show that the information-geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log-linear model. This finding suggests a need to examine the information-geometric method carefully. A possible criterion for choosing an appropriate orthogonal coordinate is also discussed. This article points out the importance of a model-based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis.