Preprint on possible neural architectures underlying information- geometric measures

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Dear colleagues,

Our preprint,

'Investigation of Possible Neural Architectures Underlying
Information-Geometric Measures', M. Tatsuno and M. Okada, to appear in
Neural Computation

is now available for download at,

http://www.mns.brain.riken.go.jp/~okada/Tatsuno_Okada.pdf

The preliminary results of this study have been reported in the following
articles.

'Possible neural mechanisms underlying information-geometric measure
parameters', M. Tatsuno and M. Okada, Society for Neuroscience Abstracts,
28, 675.15, 2002.

'How does the information-geometric measure depend on underlying neural
mechanisms?', M. Tatsuno and M. Okada, Neurocomputing, Vol. 52 - 54, pp. 649
- 654, 2003.

Best regards,

Masami TATSUNO
ARL Division of Neural Systems, Memory and Aging
Life Sciences North Building, Room 384
The University of Arizona
Tucson, AZ 85724, USA

----- Abstract -----
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 both on the
intrinsic connections and on 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, and a possible criterion for
choosing an appropriate orthogonal coordinate is also discussed. This
paper 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.

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