Preprint on possible neural architectures underlying information-geometric measures

[Masami TATSUNO]

Dear Connectionists,

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.