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Neural network function, density or geometry? | | Anca Radulescu
; | | Date: |
18 Apr 2013 | | Abstract: | We consider an oriented network in which two subgraphs (modules X and Y),
with a given intra-modular edge density, are inter-connected by a fixed number
of edges, in both directions. We study the adjacency spectrum of this network,
focusing in particular on two aspects: the changes in the spectrum in response
to varying the intra and inter-modular edge density, and the effects on the
spectrum of perturbing the edge configuration, while keeping the densities
fixed.
Since the general case is quite complex analytically, we adopted a
combination of analytical approaches to particular cases, and numerical
simulations for more results. After investigating the behavior of the mean and
standard deviation of the eigenvalues, we conjectured the robustness of the
adjacency spectrum to variations in edge geometry, when operating under a fixed
density profile. We remark that, while this robustness increases with the size
N of the network, it emerges at small sizes, and should not be thought of as a
property that holds only in the large N limit. We argue that this may be
helpful when studying applications on small networks of nodes.
We interpret our results in the context of existing literature, which has
been placing increasing attention to random graph models, with edges connecting
two given nodes with certain probabilities. We discuss whether properties such
as Wigner’s semicircle law, or effects of community structure, still hold in
our context.
Finally, we suggest possible applications of the model to understanding
synaptic restructuring during learning algorithms, and to classifying emotional
responses based on the geometry of the emotion-regulatory neural circuit. In
this light, we argue that future directions should be directed towards relating
hardwiring to the temporal behavior of the network as a dynamical system . | | Source: | arXiv, 1304.5232 | | Services: | Forum | Review | PDF | Favorites | |
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