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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Softmax function ： ウィキペディア英語版 Softmax function In mathematics, in particular probability theory and related fields, the softmax function, or normalized exponential,〔 is a generalization of the logistic function that "squashes" a -dimensional vector $\backslash mathbf$ of arbitrary real values to a -dimensional vector $\backslash sigma(\backslash mathbf)$ of real values in the range (0, 1) that add up to 1. The function is given by :$\backslash sigma(\backslash mathbf)\_j\; =\; \backslash frac^K\; e^\}$    for ''j'' = 1, ..., ''K''. The softmax function is the gradient-log-normalizer of the categorical probability distribution. For this reason, the softmax function is used in various probabilistic multiclass classification methods including multinomial logistic regression, multiclass linear discriminant analysis, naive Bayes classifiers and artificial neural networks.〔ai-faq (What is a softmax activation function? )〕 Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of distinct linear functions, and the predicted probability for the 'th class given a sample vector is: :$P(y=j|\backslash mathbf)\; =\; \backslash frac\backslash mathbf\_j\}\}^\backslash mathsf\backslash mathbf\_k\}\}$ This can be seen as the composition of linear functions $\backslash mathbf\; \backslash mapsto\; \backslash mathbf^\backslash mathsf\backslash mathbf\_1,\; \backslash ldots,\; \backslash mathbf\; \backslash mapsto\; \backslash mathbf^\backslash mathsf\backslash mathbf\_K$ and the softmax function (where $\backslash mathbf^\backslash mathsf\backslash mathbf$ denotes the inner product of $\backslash mathbf$ and $\backslash mathbf$). == Artificial neural networks == In neural network simulations, the softmax function is often implemented at the final layer of a network used for classification. Such networks are then trained under a log loss (or cross-entropy) regime, giving a non-linear variant of multinomial logistic regression. Since the function maps a vector and a specific index ''i'' to a real value, the derivative needs to take the index into account: :$\backslash frac\backslash sigma(\backslash textbf,\; i)\; =\; \backslash dots\; =\; \backslash sigma(\backslash textbf,\; i)(\backslash delta\_\; -\; \backslash sigma(\backslash textbf,\; k))$ Here, the Kronecker delta is used for simplicity (cf. the derivative of a sigmoid function, being expressed via the function itself). See Multinomial logit for a probability model which uses the softmax activation function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Softmax function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.