The bulletin of mathematical biophysics

, Volume 24, Issue 3, pp 335–343 | Cite as

A canonical form for neural nets without circles

  • Jacob Towber


By “neural net” will be meant “neural net without circles.” Every neural net effects a transformation from inputs (i.e., firing patterns of the input neurons) to outputs (firing patterns of the output neurons). Two neural nets will be calledequivalent if they effect the same transformation from inputs to outputs.

A canonical form is found for neural nets with respect to equivalence; i.e., a class of neural nets is defined, no two of which are equivalent, and which contains a neural net equivalent to any given neural net.


Canonical Form Biophysics Volume Output Neuron Firing Pattern Preceding Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Kleene, S. 1956. “Representation of Events in Nerve Nets,” inAutomata Studies, Annals of Mathematical Studies, #34. (Edited by C. E. Shannon and J. McCarthy.) Princeton: Princeton University Press.Google Scholar
  2. Landahl, H. D., and R. Runge. 1946. “Outline of a Matrix Calculus for Neural Nets”.Bull. Math. Biophysics,8, 75–81.CrossRefGoogle Scholar

Copyright information

© University of Chicago 1962

Authors and Affiliations

  • Jacob Towber
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicagoUSA

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