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  2. File:Prox function for both L2 and L1 norm.pdf - Wikipedia

    en.wikipedia.org/wiki/File:Prox_function_for...

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  3. Normalization (machine learning) - Wikipedia

    en.wikipedia.org/wiki/Normalization_(machine...

    The FixNorm method divides the output vectors from a transformer by their L2 norms, then multiplies by a learned parameter . The ScaleNorm replaces all LayerNorms inside a transformer by division with L2 norm, then multiplying by a learned parameter g ′ {\displaystyle g'} (shared by all ScaleNorm modules of a transformer).

  4. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.

  5. Regularization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Regularization_(mathematics)

    When learning a linear function , characterized by an unknown vector such that () =, one can add the -norm of the vector to the loss expression in order to prefer solutions with smaller norms. Tikhonov regularization is one of the most common forms.

  6. Dual norm - Wikipedia

    en.wikipedia.org/wiki/Dual_norm

    The Frobenius norm defined by ‖ ‖ = = = | | = ⁡ = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...

  7. Reproducing kernel Hilbert space - Wikipedia

    en.wikipedia.org/wiki/Reproducing_kernel_Hilbert...

    However, there are RKHSs in which the norm is an L 2-norm, such as the space of band-limited functions (see the example below). An RKHS is associated with a kernel that reproduces every function in the space in the sense that for every x {\displaystyle x} in the set on which the functions are defined, "evaluation at x {\displaystyle x} " can be ...

  8. Statistical learning theory - Wikipedia

    en.wikipedia.org/wiki/Statistical_learning_theory

    The most common loss function for regression is the square loss function (also known as the L2-norm). This familiar loss function is used in Ordinary Least Squares regression. The form is: ((),) = (()) The absolute value loss (also known as the L1-norm) is also sometimes used: ((),) = | |

  9. Operator norm - Wikipedia

    en.wikipedia.org/wiki/Operator_norm

    In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces .