{"entities":{"Q156":{"pageid":201,"ns":120,"title":"Item:Q156","lastrevid":370,"modified":"2026-08-17T19:10:25Z","type":"item","id":"Q156","labels":{"en":{"language":"en","value":"Formula: Artificial Neuron"}},"descriptions":{},"aliases":{},"claims":{"P1":[{"mainsnak":{"snaktype":"value","property":"P1","hash":"6056844c4a6d3699fbafab69805eed5ca36eab0e","datavalue":{"value":{"entity-type":"item","numeric-id":4,"id":"Q4"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q156$4CF3E851-DBE8-438D-A912-F04218D201FA","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"39fbc2622eaf66d4c62076bb46d7edd7bd883161","datavalue":{"value":"$\\begin{aligned}\\text{Let } \\mathbf{x} = (x_1,\\dots,x_n)^\\top \\in \\mathbb{R}^n \\text{ be the input vector} \\\\\\text{Let } \\mathbf{w} = (w_1,\\dots,w_n)^\\top \\in \\mathbb{R}^n \\text{ be the weight vector} \\\\\\text{Let } b \\in \\mathbb{R} \\text{ be the scalar bias} \\\\\\text{The affine pre\u2011activation is } z = \\mathbf{w}^\\top \\mathbf{x} + b = \\sum_{i=1}^n w_i x_i + b \\\\\\text{Choose a non\u2011linear activation } \\sigma: \\mathbb{R} \\to \\mathbb{R} \\\\\\text{The artificial neuron output is } y = \\sigma(z) \\in \\mathbb{R} \\\\\\text{Typical activations: } \\sigma(z) = \\mathbf{1}_{z \\ge 0} \\text{ (step)}, \\quad \\sigma(z) = (1+e^{-z})^{-1} \\text{ (sigmoid)}, \\quad \\sigma(z) = \\max(0,z) \\text{ (ReLU)}\\end{aligned}$","type":"string"},"datatype":"string"},"type":"statement","id":"Q156$0DD3824B-085B-4FEC-B4BC-7BEE3CCFBC4A","rank":"normal"}],"P28":[{"mainsnak":{"snaktype":"value","property":"P28","hash":"9ddb23030eec75ea2af14633ebac53ecfae5de8c","datavalue":{"value":{"entity-type":"item","numeric-id":147,"id":"Q147"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q156$80638920-0B3A-45F3-A24C-612B2F778099","rank":"normal"}],"P29":[{"mainsnak":{"snaktype":"value","property":"P29","hash":"436f15ef86d1b51a3dce331542152ae2664cf420","datavalue":{"value":{"entity-type":"item","numeric-id":5,"id":"Q5"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q156$A255F3F9-3BFF-4E0F-858E-63FCAB216044","rank":"normal"}]},"sitelinks":{}}}}