Neural modeling fields: Difference between revisions

Revision as of 16:42, 3 October 2008

Revision as of 16:45, 3 October 2008

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Dynamic logic maximizes similarity L, associates bottom-up signals X with top-down signals M, and finds values of parameters S_m, without combinatorial complexity, as follows.

First, assign any values to unknown parameters, {'''S'''_m}. Then, compute association variables f(m|n),

:<big>f(m|n) = r(m) l('''X'''(n)|m) / &sum;_m'=1..M r(m') l('''X'''(n)|m').</big>

Equation for f(m|n) looks like the Bayes formula for a posteriori probabilities; if l(n|m) in the result of learning become conditional likelihoods, f(m|n) become Bayesian probabilities for signal n originating from object m. The dynamic logic of the Modeling Fields (MF) is defined as follows

:<big>df(m|n)/dt = f(m|n) &sum;_m'=1..M {[&delta;_mm' - f(m'|n)] • [&part;ln l(n|m')/&part;'''M'''_m'] &part;'''M'''_m'/&part;'''S'''_m' dSd'''S'''_m'/dt,</big>

:<big>dSmd'''S'''_m/dt = &sum;_n=1..N f(m|n)[&part;ln l(n|m)/&part;'''M'''_m]&part;'''M'''_m/&part;'''S'''_m,</big>