Universal approximation theorem: Difference between revisions

Revision as of 20:33, 23 October 2011

Revision as of 20:37, 23 November 2011

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Let φ(·) be a nonconstant, bounded, and [[monotonic function|monotonically]]-increasing [[continuous function|continuous]] function. Let ''I''_''m'' denote the ''m''-dimensional unit hypercube [0,1]^''m''. The space of continuous functions on ''I''_''m''₀ is denoted by ''C''(''I''_''m''). Then, given any function ''f'' ∈ ''C''(''I''_''m'') and є &gt; 0, there exist an integer ''N'' and sets of real constants ''α''_''i'', ''b''_''i'' ∈ '''R''', ''w''_''i'' ∈ '''R'''^''m'', where ''i'' = 1, ..., ''N'' such that we may define:

: <math>