April 2020
Intermediate to advanced
552 pages
6h 13m
Japanese
Content preview from ゼロから作るDeep Learning ❸ ―フレームワーク編
![最適化問題に利用されるベンチマーク用の関数リスト（Wikipedia<a href="bib.xhtml#bib-wiki">[13]</a>より引用）](/api/v2/epubs/urn:orm:book:9784873119069/files/images/html/ch2/2-30.png)
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ステップ24複雑な関数の微分
私たちのDeZeroは、代表的な演算子（+、*、-、/、**）に対応しました。そのため、いつものPythonプログラミングのようにコーディングできます。その有り難さが分かるのは、複雑な数式をコーディングするときです。ここでは、これまでの成果として、複雑な数式の微分をいくつか求めてみます。
本ステップで取り上げる関数は、最適化問題でよく用いられるテスト関数です。最適化問題のテスト関数とは、様々な最適化手法の“良さ”を評価するために利用される関数です。言うなれば、「ベンチマーク」のための関数と言ったところです。そのような関数はいくつか候補があります。たとえばWikipedia[13]の「Test functions for optimization」というページには、図24-1のような表でまとめられています。
図24-1 最適化問題に利用されるベンチマーク用の関数リスト（Wikipedia[13]より引用）
ここでは、図24-1の中から3つの関数を選んで、その微分を実際に求めてみます。それによって、DeZeroの実力が分かるでしょう。まずはSphere関数という単純な関数から始めます。
24.1 Sphere関数
Sphere関数は、
という数式で表されます。入力変数を2乗して足すだけの単純な関数です。私たちの課題は、その微分―― ...
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