Approximating Arbitrary Functions With Sigmoids

Number of neurons to combine:

Expresión 8: "n" equals 10

200

Approximation:

Expresión 10: "f" left parenthesis, 0 , right parenthesis plus Start sum from "i" equals 1 to "n" , end sum, left parenthesis, "f" left parenthesis, StartFraction, "i" Over "n" , EndFraction , right parenthesis minus "f" left parenthesis, StartFraction, "i" minus 1 Over "n" , EndFraction , right parenthesis , right parenthesis "s" left parenthesis, "w" times left parenthesis, "x" minus StartFraction, "i" minus 1 half Over "n" , EndFraction , right parenthesis , right parenthesis Tiene una gráfica. Para hacer seguimiento de audio, presione ALT+T.

The functions added together (along with f(0)) to make the approximation:

Expresión 12: "i" Subscript, "a" "l" "l" , Baseline equals left bracket, 1 , ... , "n" , right bracket equals una lista de números. 10 items

equals

Expresión 13: left parenthesis, "f" left parenthesis, StartFraction, "i" Subscript, "a" "l" "l" , Baseline Over "n" , EndFraction , right parenthesis minus "f" left parenthesis, StartFraction, "i" Subscript, "a" "l" "l" , Baseline minus 1 Over "n" , EndFraction , right parenthesis , right parenthesis "s" left parenthesis, "w" times left parenthesis, "x" minus StartFraction, "i" Subscript, "a" "l" "l" , Baseline Over "n" , EndFraction , right parenthesis , right parenthesis Tiene una gráfica. Para hacer seguimiento de audio, presione ALT+T.

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