Counting solutions from finite samplings

Details Counting solutions from finite samplings Counting solutions from finite samplings

2011-11-18

arxiv.org/abs/1111.4278v3

Phys. Rev. E 85, 026118 (2012)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 figures and 1 table, further discussions added

Scientific paper

10.1103/PhysRevE.85.026118

We formulate the solution counting problem within the framework of inverse Ising problem and use fast belief propagation equations to estimate the entropy whose value provides an estimate on the true one. We test this idea on both diluted models (random 2-SAT and 3-SAT problems) and fully-connected model (binary perceptron), and show that when the constraint density is small, this estimate can be very close to the true value. The information stored by the salamander retina under the natural movie stimuli can also be estimated and our result is consistent with that obtained by Monte Carlo method. Of particular significance is sizes of other metastable states for this real neuronal network are predicted.

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