On learning and energy-entropy dependence in recurrent and nonrecurrent signed networks
- 93 Downloads
Learning of patterns by neural networks obeying general rules of sensory transduction and of converting membrane potentials to spiking frequencies is considered. Any finite number of cellsA can sample a pattern playing on any finite number of cells ∇ without causing irrevocable sampling bias ifA = ℬ orA ∩ ℬ =. Total energy transfer from inputs ofA to outputs of ℬ depends on the entropy of the input distribution. Pattern completion on recall trials can occur without destroying perfect memory even ifA = ℬ by choosing the signal thresholds sufficiently large. The mathematical results are global limit and oscillation theorems for a class of nonlinear functional-differential systems.
Key wordslearning stimulus sampling nonlinear difference-differential equations global limits and oscillations flows on signed networks functional-differential systems energy-entropy dependence pattern completion recurrent and nonrecurrent anatomy sensory transduction rules ratio limit theorems
Unable to display preview. Download preview PDF.
- 1.S. Grossberg, “Some networks that can learn, remember, and reproduce any number of complicated space-time patterns (I),”J. Math. Mechanics (July 1969).Google Scholar
- 2.S. Grossberg, “Some networks that can learn, remember, and reproduce any number of complicated space-time patterns (II),”SIAM J. Applied Math., submitted for publication.Google Scholar
- 3.S. Grossberg, “How do overlapping nonrecurrent synaptic fields learn without mutual interference?” (in preparation).Google Scholar
- 4.R. B. Livingston, “Brain mechanisms in conditioning and learning,” in:Neurosciences Research Symposium Summaries, F. O. Schmittet al., eds. (MIT Press, Cambridge, Massachusetts, 1967), Vol. 2.Google Scholar
- 5.S. Grossberg, “On neural pattern discrimination,”J, Theoret. Biol., submitted for publication.Google Scholar
- 6.S. Grossberg, “On learning, information, lateral inhibition, and transmitters,”Math. Biosci. 4:255–310 (1969).Google Scholar
- 7.S. Grossberg, “A prediction theory for some nonlinear functional-differential equations (II),”J. Math. Anal. Appl. 22:490–522 (1968).Google Scholar
- 8.P. Hartman,Ordinary Differential Equations (John Wiley and Sons, New York, 1964).Google Scholar
- 9.S. Grossberg, “A prediction theory for some nonlinear functional-differential equations (I),”J. Math. Anal. Appl. 21:643–694 (1968).Google Scholar
- 10.S. Grossberg, “Some nonlinear networks capable of learning a spatial pattern of arbitrary complexity,”Proc. Natl. Acad. Sci. (U.S.) 59:368–372 (1968).Google Scholar
© Plenum Publishing Corporation 1969