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ゼロから作るDeep Learning Java編 第2章 パーセプトロン

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目次

2.3 パーセプトロンの実装

2.3.1 簡単な実装

パーセプトロンは関数(静的メソッド)として実装できます。

public static int AND(int x1, int x2) {
    double w1 = 0.5, w2 = 0.5, theta = 0.7;
    double tmp = x1 * w1 + x2 * w2;
    if (tmp <= theta)
        return 0;
    else
        return 1;
}
assertEquals(0, AND(0, 0));
assertEquals(0, AND(1, 0));
assertEquals(0, AND(0, 1));
assertEquals(1, AND(1, 1));

2.3.2 重みとバイアスの導入

ND4Jを使うと以下のようになります。

INDArray x = Nd4j.create(new double[] {0, 1});
INDArray w = Nd4j.create(new double[] {0.5, 0.5});
double b = -0.7;
assertEquals("[0.00,0.50]", Util.string(w.mul(x)));
assertEquals(0.5, w.mul(x).sumNumber().doubleValue(), 0.000005);
assertEquals(-0.19999999999999996, w.mul(x).sumNumber().doubleValue() + b, 0.000005);

2.3.3 重みとバイアスによる実装

「重みとバイアスによる方式」を用いれば、AND、NDND、ORゲートは次のように実装できます。

public static int AND2(int x1, int x2) {
    INDArray x = Nd4j.create(new double[] {x1, x2});
    INDArray w = Nd4j.create(new double[] {0.5, 0.5});
    double b = -0.7;
    double tmp = w.mul(x).sumNumber().doubleValue() + b;
    return tmp <= 0 ? 0 : 1;
}

public static int NAND(int x1, int x2) {
    INDArray x = Nd4j.create(new double[] {x1, x2});
    INDArray w = Nd4j.create(new double[] {-0.5, -0.5});
    double b = 0.7;
    double tmp = w.mul(x).sumNumber().doubleValue() + b;
    return tmp <= 0 ? 0 : 1;
}

public static int OR(int x1, int x2) {
    INDArray x = Nd4j.create(new double [] {x1, x2});
    INDArray w = Nd4j.create(new double[] {0.5, 0.5});
    double b = -0.2;
    double tmp = w.mul(x).sumNumber().doubleValue() + b;
    return tmp <= 0 ? 0 : 1;
}
assertEquals(0, AND2(0, 0));
assertEquals(0, AND2(1, 0));
assertEquals(0, AND2(0, 1));
assertEquals(1, AND2(1, 1));
assertEquals(1, NAND(0, 0));
assertEquals(1, NAND(1, 0));
assertEquals(1, NAND(0, 1));
assertEquals(0, NAND(1, 1));
assertEquals(0, OR(0, 0));
assertEquals(1, OR(1, 0));
assertEquals(1, OR(0, 1));
assertEquals(1, OR(1, 1));

2.5 多層パーセプトロン

2.5.2 XORゲートの実装

パーセプトロンを多層にするとXORゲートが実装できます。

public static int XOR(int x1, int x2) {
    int s1 = NAND(x1, x2);
    int s2 = OR(x1, x2);
    int y = AND2(s1, s2);
    return y;
}
assertEquals(0, XOR(0, 0));
assertEquals(1, XOR(1, 0));
assertEquals(1, XOR(0, 1));
assertEquals(0, XOR(1, 1));
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