Revision as of 14:22, 10 June 2010 edit Albertzeyer (talk \| contribs) 243 edits cleanup ← Previous edit		Revision as of 14:25, 10 June 2010 edit undo Albertzeyer (talk \| contribs) 243 edits →Formal statement: ehm, i guess that was a typo? doesnt make sense otherwise Next edit →
Line 13: <blockquote> Let φ(·) be a nonconstant, bounded, and [[monotonic function\|monotonically]]-increasing [[continuous function\|continuous]] function. Let ''I''<sub>''m''<sub>0</sub></sub> denote the ''m''<sub>0</sub>-dimensional unit hypercube [0,1]<sup>''m''<sub>0</sub></sup>. The space of continuous functions on ''I''<sub>''m''<sub>0</sub></sub> is denoted by ''C''(''I''<sub>''m''<sub>0</sub></sub>). Then, given any function ''f'' Э ∈ ''C''(''I''<sub>''m''<sub>0</sub></sub>) and є > 0, there exist an integer ''m''<sub>1</sub> and sets of real constants ''α''<sub>''i''</sub>, ''b''<sub>''i''</sub> and ''w''<sub>''ij''</sub>, where ''i'' = 1, ..., ''m''<sub>1</sub> and ''j'' = 1, ..., ''m''<sub>0</sub> such that we may define: : <math> Line 28: for all ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''m''<sub>0</sub></sub> that lie in the input space. </blockquote> ==References==

Universal approximation theorem: Difference between revisions