In　order　to　scale　the　computational　ability　of　a　single　multi-value　multi-threshold　neuron,　this　paper　introduces　two　geometrical　concepts:　correlation　and　generalized　spectrum.　By　using　the　correlation,　we　give　the　upper　bound　of　the　number　of　different　output　functions　for　a　group　of　fixed　input　functions.　By　using　the　generalized　spectrum,　we　give　the　lower　bound　of　the　number　of　input　functions　in　order　to　realize　arbitrary　output　functions.　This　lower　bound　is　also　the　lower　bound　of　the　complexity　of　a　three　layer　feedforward　neural　network　with　one　hidden　layer　to　realize　arbitrary　multi-valued　functions.