July 2018
Beginner to intermediate
432 pages
5h 58m
Japanese
Content preview from ゼロから作るDeep Learning ❷ ―自然言語処理編
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付録Asigmoid関数とtanh関数の微分
ニューラルネットワークでは活性化関数にさまざまな関数が使われます。ここでは、その代表格であるsigmoid関数とtanh関数を取り上げ、その2つの関数の微分を求める過程を異なる2つのアプローチで説明します。具体的には、sigmoid関数の微分は計算グラフを使い、tanhの微分は数式を展開して求めます。それぞれのアプローチを理解することで、微分の計算により親しくなれるでしょう。
A.1 sigmoid関数
sigmoid関数は次の式で表されます。
(A.1)
このとき、式(A.1)の計算グラフは図A-1のようになります。
図A-1 sigmoidレイヤの計算グラフ
図A-1では「×」と「+」ノードの他に、「exp」と「/」ノードがあります。expノードはy＝exp(x)の計算を行い、「/」ノードは、
の計算を行います。それでは計算グラフを使って、ひとつずつ確認しながら逆伝播を行ってみます。
- Step.1
- 「/」ノードはを表しますが、この微分は解析的に次の式によって表されます。 ...
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