A065246 Formal neural networks with n components.

1, 4, 196, 1124864, 12545225621776, 7565068551396549351877632, 11519413104737198429297238164593057431690816, 3940200619639447921227904010014361380507973927046544666794829340424572177149721061141426654884915640806627990306816

Offset: 0

Author

Labos Elemer, Oct 26 2001

Keywords

• nonn

Comments

Number of {0,1}^n to {0,1}^n vector-vector maps of which all components are formal neurons (=threshold gates).

Examples

			For n=2 the 14 threshold gates determine 14*14=196 neural nets each built purely from threshold gates. For n=3, 104=A000609(3) formal neurons gives 104^3=a(3) networks, all component functions of which are linearly separable {0,1}^3 -> {0,1} vector-scalar functions.
		

References

• Labos E. (1996): Long Cycles and Special Categories of Formal Neuronal Networks. Acta Biologica Hungarica, 47: 261-272.
• Labos E. and Sette M. (1995): Long Cycle Generation by McCulloch-Pitts Networks(MCP-Nets) with Dense and Sparse Weight Matrices. Proc. of BPTM, McCulloch Memorial Conference [eds:Moreno-Diaz R. and Mira-Mira J., pp. 350-359.], MIT Press, Cambridge,MA,USA.
• McCulloch, W. S. and Pitts W. (1943): A Logical Calculus Immanent in Nervous Activity. Bull. Math. Biophys. 5:115-133.

Crossrefs

Cf. A000609, A065247, A065248, A064436.

Formula

a(n)=A000609(n)^n; for n>1 a(n) < A057156(n).