Translations:Neural Networks/18/en: Difference between revisions

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    Latest revision as of 23:34, 27 April 2026

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    Message definition (Neural Networks)
    {| class="wikitable"
    |-
    ! Function !! Formula !! Range !! Notes
    |-
    | '''Sigmoid''' || <math>\sigma(z) = \frac{1}{1+e^{-z}}</math> || (0, 1) || Historically popular; suffers from vanishing gradients
    |-
    | '''Tanh''' || <math>\tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}</math> || (−1, 1) || Zero-centred; still saturates for large inputs
    |-
    | '''ReLU''' || <math>\max(0, z)</math> || [0, ∞) || Default choice in modern networks; can cause "dead neurons"
    |-
    | '''Leaky ReLU''' || <math>\max(\alpha z, z)</math> for small <math>\alpha > 0</math> || (−∞, ∞) || Addresses the dead-neuron problem
    |-
    | '''{{Term|softmax}}''' || <math>\frac{e^{z_i}}{\sum_j e^{z_j}}</math> || (0, 1) || Used in output layer for multi-class classification
    |}
    Function Formula Range Notes
    Sigmoid $ \sigma(z) = \frac{1}{1+e^{-z}} $ (0, 1) Historically popular; suffers from vanishing gradients
    Tanh $ \tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}} $ (−1, 1) Zero-centred; still saturates for large inputs
    ReLU $ \max(0, z) $ [0, ∞) Default choice in modern networks; can cause "dead neurons"
    Leaky ReLU $ \max(\alpha z, z) $ for small $ \alpha > 0 $ (−∞, ∞) Addresses the dead-neuron problem
    softmax $ \frac{e^{z_i}}{\sum_j e^{z_j}} $ (0, 1) Used in output layer for multi-class classification
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