7. 오차역전파_(Backpropagation).ipynb

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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S9Db_VsP_m1S"
      },
      "source": [
        "## 오차역전파 (Backpropagation)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Vdi2PAG_3lW"
      },
      "source": [
        "### 오차역전파 알고리즘\n",
        "- 학습 데이터로 정방향(forward) 연산을 통해 손실함수 값(loss)을 구함\n",
        "\n",
        "- 각 layer별로 역전파학습을 위해 중간값을 저장\n",
        "\n",
        "- 손실함수를 학습 파라미터(가중치, 편향)로 미분하여  \n",
        "  마지막 layer로부터 앞으로 하나씩 연쇄법칙을 이용하여 미분\n",
        "  각 layer를 통과할 때마다 저장된 값을 이용\n",
        "\n",
        "- 오류(error)를 전달하면서 학습 파라미터를 조금씩 갱신\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-o545ezeUuSB"
      },
      "source": [
        "### 오차역전파 학습의 특징\n",
        "- 손실함수를 통한 평가를 한 번만 하고, 연쇄법칙을 이용한 미분을 활용하기 때문에  \n",
        "  학습 소요시간이 매우 단축!\n",
        "\n",
        "- 미분을 위한 중간값을 모두 저장하기 때문에 메모리를 많이 사용\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CFoTt-ds_w8C"
      },
      "source": [
        "### 신경망 학습에 있어서 미분가능의 중요성\n",
        "- 경사하강법(Gradient Descent)에서 손실 함수(cost function)의 최소값,  \n",
        "  즉, 최적값을 찾기 위한 방법으로 미분을 활용\n",
        "\n",
        "- 미분을 통해 손실 함수의 학습 매개변수(trainable parameter)를 갱신하여  \n",
        "  모델의 가중치의 최적값을 찾는 과정\n",
        "\n",
        "![](https://i.pinimg.com/originals/5d/13/20/5d1320c7b672710834e63b95a7c1037b.png)\n",
        "\n",
        "<sub>출처: https://www.pinterest.co.kr/pin/424816177350692379/</sub>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ilYRMqLeQf6Z"
      },
      "source": [
        "# 합성함수의 미분 (연쇄법칙, Chain Rule)\n",
        "\n",
        "---\n",
        "\n",
        "## 기본 공식\n",
        "\n",
        "$$\n",
        "\\frac{d}{dx} [f(g(x))] = f^\\prime(g(x))g^\\prime(x)\n",
        "$$\n",
        "\n",
        "---\n",
        "\n",
        "## 여러 개 연속적으로 사용하는 경우\n",
        "\n",
        "합성함수는 여러 개의 변수가 연속적으로 연결된 경우에도 적용할 수 있습니다.\n",
        "\n",
        "$$\n",
        "\\frac{\\partial f}{\\partial x} = \\frac{\\partial f}{\\partial u} \\times \\frac{\\partial u}{\\partial m} \\times \\frac{\\partial m}{\\partial n} \\times \\cdots \\times \\frac{\\partial k}{\\partial g} \\times \\frac{\\partial g}{\\partial x}\n",
        "$$\n",
        "\n",
        "---\n",
        "\n",
        "## 편미분 적용 가능\n",
        "\n",
        "각 변수에 대해 **편미분**을 적용해 필요한 부분만 계산할 수 있습니다. 이를 통해 복잡한 다변수 함수도 단계적으로 미분 가능합니다.\n",
        "\n",
        "---\n",
        "\n",
        "## 오차역전파의 직관적 이해\n",
        "\n",
        "**오차역전파**(Backpropagation)는 합성함수의 연쇄법칙을 기반으로, 신경망 학습에서 손실함수의 기울기를 각 가중치와 편향에 대해 계산하는 과정입니다.  \n",
        "\n",
        "- 손실함수의 변화량이 **가중치** 또는 **편향**에 얼마나 영향을 미치는지 계산합니다.\n",
        "- 이를 통해 **손실함수의 최소값(minimum)**을 찾도록 가중치를 조정합니다.\n",
        "\n",
        "---\n",
        "\n",
        "## 시각적 이해\n",
        "\n",
        "아래 그림은 **오차역전파**를 활용한 신경망 학습 과정에서 기울기를 계산하는 과정을 보여줍니다:\n",
        "\n",
        "![Backpropagation Example](https://cdn-media-1.freecodecamp.org/images/1*_KMMFvRP5X9kC59brI0ykw.png)  \n",
        "<sub>출처: [FreeCodeCamp](https://www.freecodecamp.org/news/demystifying-gradient-descent-and-backpropagation-via-logistic-regression-based-image-classification-9b5526c2ed46/)</sub>\n",
        "\n",
        "---\n",
        "\n",
        "# 핵심 요약\n",
        "\n",
        "1. **연쇄법칙**은 함수가 여러 단계로 연결된 경우, 각각의 기울기를 곱하여 전체 기울기를 계산합니다.\n",
        "2. **오차역전파**는 신경망 학습에서 연쇄법칙을 사용해 손실에 따른 기울기를 계산하는 과정입니다.\n",
        "3. 직관적으로, 손실함수는 **각 가중치와 편향**이 얼마나 영향을 미치는지를 기반으로 조정됩니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6NLF8CXiQkuL"
      },
      "source": [
        "#### 합성함수 미분 (chain rule) 예제\n",
        "\n",
        "![Chain Rule Example](https://miro.medium.com/max/1000/1*azqHvbrNsZ8AIZ7H75tbIQ.jpeg)\n",
        "\n",
        "<sub>출처: https://medium.com/spidernitt/breaking-down-neural-networks-an-intuitive-approach-to-backpropagation-3b2ff958794c</sub>\n",
        "\n",
        "### 조건:\n",
        "- $$ a = -1, \\ b = 3, \\ c = 4 $$\n",
        "- $$ x = a + b, \\ y = b + c, \\ f = x \\cdot y $$\n",
        "\n",
        "---\n",
        "\n",
        "### 계산 과정:\n",
        "\n",
        "1. $$\\frac{\\partial f}{\\partial x}$$\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial x} = y + x \\cdot \\frac{\\partial y}{\\partial x}\n",
        "   $$\n",
        "   계산:\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial x} = (b + c) + (a + b) \\cdot 0 = 7\n",
        "   $$\n",
        "\n",
        "2. $$\\frac{\\partial f}{\\partial y}$$\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial y} = x + \\frac{\\partial x}{\\partial y} \\cdot y\n",
        "   $$\n",
        "   계산:\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial y} = (a + b) + 0 \\cdot (b + c) = 2\n",
        "   $$\n",
        "\n",
        "3. $$\\frac{\\partial x}{\\partial a}$$\n",
        "   $$\n",
        "   \\frac{\\partial x}{\\partial a} = 1\n",
        "   $$\n",
        "\n",
        "4. $$\\frac{\\partial y}{\\partial c}$$\n",
        "   $$\n",
        "   \\frac{\\partial y}{\\partial c} = 1\n",
        "   $$\n",
        "\n",
        "5. $$\\frac{\\partial f}{\\partial a}$$\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial a} = \\frac{\\partial f}{\\partial x} \\cdot \\frac{\\partial x}{\\partial a} = y \\cdot 1 = 7\n",
        "   $$\n",
        "\n",
        "6. $$\\frac{\\partial f}{\\partial b}$$\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial b} = \\frac{\\partial x}{\\partial b} \\cdot y + x \\cdot \\frac{\\partial y}{\\partial b}\n",
        "   $$\n",
        "   계산:\n",
        "   $$\n",
        "   \\frac{\\partial f}{\\partial b} = 1 \\cdot 7 + 2 \\cdot 1 = 9\n",
        "   $$\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2PgmdJN0Qtdw"
      },
      "source": [
        "### 덧셈, 곱셈 계층의 역전파\n",
        "위 예제를 통해 아래 사항을 알 수 있음:\n",
        "\n",
        "#### 1. 덧셈 계층 (\\( z = x + y \\)):\n",
        "- $$ \\frac{\\partial z}{\\partial x} = 1, \\quad \\frac{\\partial z}{\\partial y} = 1 $$\n",
        "\n",
        "#### 2. 곱셈 계층 (\\( t = xy \\)):\n",
        "- $$ \\frac{\\partial t}{\\partial x} = y, \\quad \\frac{\\partial t}{\\partial y} = x $$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hShSxvW5WMqi"
      },
      "source": [
        "class Mul():\n",
        "\n",
        "  def __init__(self):\n",
        "    self.x = None\n",
        "    self.y = None\n",
        "\n",
        "  def forward(self, x, y):\n",
        "    self.x = x\n",
        "    self.y = y\n",
        "    result = x * y\n",
        "    return result\n",
        "\n",
        "  def backward(self, dresult):\n",
        "    dx = dresult * self.y\n",
        "    dy = dresult * self.x\n",
        "    return dx, dy\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1bovOx6UQvLP"
      },
      "source": [
        "class Add():\n",
        "\n",
        "  def __init__(self):\n",
        "    self.x = None\n",
        "    self.y = None\n",
        "\n",
        "  def forward(self, x, y):\n",
        "    self.x = x\n",
        "    self.y = y\n",
        "    result = x + y\n",
        "    return result\n",
        "\n",
        "  def backward(self, dresult):\n",
        "    dx = dresult * 1\n",
        "    dy = dresult * 1\n",
        "    return dx, dy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e3RawqlUQwp0"
      },
      "source": [
        "a, b, c = -1, 3, 4\n",
        "x = Add()\n",
        "y = Add()\n",
        "f = Mul()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "soyk-HWiSnwh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "600cf238-6a2e-43de-ee27-ca87a90ec3b7"
      },
      "source": [
        "x_result = x.forward(a, b)\n",
        "y_result = y.forward(b, c)\n",
        "\n",
        "print(x_result)\n",
        "print(y_result)\n",
        "print(f.forward(x_result, y_result))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2\n",
            "7\n",
            "14\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FhPPrFIqSpq1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "882f4976-9856-42c9-ab6b-5e9fd65b6aa2"
      },
      "source": [
        "dresult = 1\n",
        "dx_mul, dy_mul = f.backward(dresult)\n",
        "\n",
        "da_add, db_add_1 = x.backward(dx_mul)\n",
        "db_add_2, dc_add = y.backward(dy_mul)\n",
        "\n",
        "print(dx_mul, dy_mul)\n",
        "print(da_add)\n",
        "print(db_add_1 + db_add_2)\n",
        "print(dc_add)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7 2\n",
            "7\n",
            "9\n",
            "2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dMfl0J1uWgiY"
      },
      "source": [
        "![](https://miro.medium.com/max/2000/1*U3mVDYuvnaLhJzIFw_d5qQ.png)\n",
        "<sub>출처: https://medium.com/spidernitt/breaking-down-neural-networks-an-intuitive-approach-to-backpropagation-3b2ff958794c</sub>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "byODNRUF5fbv"
      },
      "source": [
        "### 활성화 함수(Activation)에서의 역전파"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OkRurUgm5hqn"
      },
      "source": [
        "#### 시그모이드(Sigmoid) 함수\n",
        "\n",
        "![Sigmoid Function Graph](https://media.geeksforgeeks.org/wp-content/uploads/20190911181329/Screenshot-2019-09-11-18.05.46.png)\n",
        "\n",
        "<sub>출처: [GeeksforGeeks](https://www.geeksforgeeks.org/implement-sigmoid-function-using-numpy/)</sub>\n",
        "\n",
        "---\n",
        "\n",
        "### **수식**\n",
        "\n",
        "1. Sigmoid 함수 정의:\n",
        "   $$ y = \\frac{1}{1 + e^{-x}} $$\n",
        "\n",
        "2. Sigmoid 함수의 도함수:\n",
        "   $$\n",
        "   \\begin{aligned}\n",
        "   y' &= \\left( \\frac{1}{1 + e^{-x}} \\right)' \\\\\n",
        "   &= \\frac{-1}{(1 + e^{-x})^2} \\cdot (-e^{-x}) \\\\\n",
        "   &= \\frac{1}{1 + e^{-x}} \\cdot \\frac{e^{-x}}{1 + e^{-x}} \\\\\n",
        "   &= \\frac{1}{1 + e^{-x}} \\cdot \\left( 1 - \\frac{1}{1 + e^{-x}} \\right) \\\\\n",
        "   &= y \\cdot (1 - y)\n",
        "   \\end{aligned}\n",
        "   $$\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNWIw7ElVhLK"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "class Sigmoid():\n",
        "\n",
        "  def __init__(self):\n",
        "    self.out = None\n",
        "\n",
        "  def forward(self, x):\n",
        "    out = 1 / (1 + np.exp(-x))\n",
        "    return out\n",
        "\n",
        "  def backward(self, dout):\n",
        "    dx = dout * (1.0 - self.out) * self.dout\n",
        "    return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QWZ247xo5mtv"
      },
      "source": [
        "#### ReLU 함수\n",
        "\n",
        "![ReLU Function Graph](https://machinelearningmastery.com/wp-content/uploads/2018/10/Line-Plot-of-Rectified-Linear-Activation-for-Negative-and-Positive-Inputs.png)\n",
        "\n",
        "<sub>출처: [Machine Learning Mastery](https://machinelearningmastery.com/rectified-linear-activation-function-for-deep-learning-neural-networks/)</sub>\n",
        "\n",
        "---\n",
        "\n",
        "### **수식**\n",
        "\n",
        "1. **ReLU 함수 정의**:\n",
        "   $$\n",
        "   y =\n",
        "   \\begin{cases}\n",
        "   x & (x \\geq 0)  \\\\\n",
        "   0 & (x < 0)\n",
        "   \\end{cases}\n",
        "   $$\n",
        "\n",
        "2. **ReLU 함수의 도함수**:\n",
        "   $$\n",
        "   \\frac{\\partial y}{\\partial x} =\n",
        "   \\begin{cases}\n",
        "   1 & (x \\geq 0)  \\\\\n",
        "   0 & (x < 0)\n",
        "   \\end{cases}\n",
        "   $$\n",
        "\n",
        "---\n",
        "\n",
        "### **설명**\n",
        "- **ReLU (Rectified Linear Unit)** 함수는 입력값 \\( x \\)가 0보다 작으면 0을 출력하고, 0 이상이면 입력값 그대로 출력합니다.\n",
        "- 도함수는 \\( x \\)가 0 이상일 때는 1이고, 0 미만일 때는 0입니다.\n",
        "- **ReLU의 특징**:\n",
        "  - 비선형 활성화 함수로 신경망에서 널리 사용됨.\n",
        "  - \\( x < 0 \\)에서 기울기가 0이 되어 \"Dead Neurons\" 문제가 발생할 수 있음.\n",
        "\n",
        "---\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hHcPmAzh5nOZ"
      },
      "source": [
        "class ReLU():\n",
        "\n",
        "  def __init__(self):\n",
        "    self.out = None\n",
        "\n",
        "  def forward(self, x):\n",
        "    self.mask = (x < 0)\n",
        "    out = x.copy()\n",
        "    out[x<0] = 0\n",
        "    return out\n",
        "\n",
        "  def backward(self, dout):\n",
        "    dout[self.mask] = 0\n",
        "    dx = dout\n",
        "    return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MH_kQzedJFfw"
      },
      "source": [
        "### 행렬 연산에 대한 역전파\n",
        "\n",
        "# $$\\qquad Y = X \\bullet W + B$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W-SedVrpJILw"
      },
      "source": [
        "#### 순전파(forward)\n",
        "  \n",
        "  - 형상(shape)을 맞춰줘야함\n",
        "  - 앞서 봤던 곱셈, 덧셈 계층을 합친 형태"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QKIO7EzSJGD1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ff65ab7a-59b1-45be-afb5-bfe2e4ae740b"
      },
      "source": [
        "X = np.random.rand(3)\n",
        "W = np.random.rand(3, 2)\n",
        "B = np.random.rand(2)\n",
        "\n",
        "print(X.shape)\n",
        "print(W.shape)\n",
        "print(B.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(3,)\n",
            "(3, 2)\n",
            "(2,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tqvl76fFJNfU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "89c0d11f-2781-4c56-94a0-23f21fefb526"
      },
      "source": [
        "Y = np.dot(X, W) + B\n",
        "print(Y.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(2,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vTjJIvg9JPMV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed5d2f04-32b3-4cfb-d3ff-2551d58a8acc"
      },
      "source": [
        "X = np.random.rand(3)\n",
        "W = np.random.rand(2, 2)\n",
        "B = np.random.rand(2)\n",
        "\n",
        "print(X.shape)\n",
        "print(W.shape)\n",
        "print(B.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(3,)\n",
            "(2, 2)\n",
            "(2,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QnB0hE6YJQuD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 219
        },
        "outputId": "bca718d5-7153-465e-b912-2c9a6806b043"
      },
      "source": [
        "Y = np.dot(X, W) + B\n",
        "print(Y.shape)\n",
        "# np.dot 함수는 두 배열의 내적을 계산한다.\n",
        "#내적을 계산하려면 첫 번째 배열의 열 수와 두 번째 배열의 행 수가 같아야 한다.\n",
        "# X의 열 수는 3이고 W의 행 수는 2이므로 shape이 일치하지 않는다. 따라서 ValueError가 발생 **"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "shapes (3,) and (2,2) not aligned: 3 (dim 0) != 2 (dim 0)",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-11-fc5b1d15b880>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mW\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# np.dot 함수는 두 배열의 내적을 계산한다.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m#내적을 계산하려면 첫 번째 배열의 열 수와 두 번째 배열의 행 수가 같아야 한다.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;31m# X의 열 수는 3이고 W의 행 수는 2이므로 shape이 일치하지 않는다. 따라서 ValueError가 발생 **\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: shapes (3,) and (2,2) not aligned: 3 (dim 0) != 2 (dim 0)"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "04GHZHAiJUGl"
      },
      "source": [
        "#### 역전파(1)\n",
        "\n",
        "##  $$\\  Y = X \\bullet W$$\n",
        "- $$X :\\ \\ (2,\\ )$$\n",
        "\n",
        "- $$W :\\ \\ (2,\\ 3)$$\n",
        "\n",
        "- $$X \\bullet W :\\ \\ (3,\\ )$$\n",
        "\n",
        "- $$\\frac{\\partial L}{\\partial Y} :\\ \\ (3,\\ )$$\n",
        "\n",
        "- $$\\frac{\\partial L}{\\partial X} = \\frac{\\partial L}{\\partial Y}\\bullet W^T ,\\ (2,\\ )$$\n",
        "\n",
        "- $$\\frac{\\partial L}{\\partial W} = X^T \\bullet \\frac{\\partial L}{\\partial Y} ,\\ (2,\\ 3)$$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DCruMHCGJSHK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "23619ad6-e289-466d-ffd4-dcf82a2bf9c0"
      },
      "source": [
        "X = np.random.randn(2)\n",
        "W = np.random.randn(2, 3)\n",
        "Y = np.dot(X, W)\n",
        "\n",
        "print(\"X\\n{}\".format(X))\n",
        "print(\"W\\n{}\".format(W))\n",
        "print(\"Y\\n{}\".format(Y))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X\n",
            "[-1.81607449 -0.23449418]\n",
            "W\n",
            "[[-0.88123562  2.8101045   1.66961195]\n",
            " [-0.73448874  1.65921975 -0.42002786]]\n",
            "Y\n",
            "[ 1.77262287 -5.49243649 -2.93364558]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TEvyFXedJWC7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d70c4b73-91c8-45ed-d511-715f0362e198"
      },
      "source": [
        "dL_dY = np.random.randn(3)\n",
        "dL_dX = np.dot(dL_dY, W.T)\n",
        "dL_dW = np.dot(X.reshape(-1, 1), dL_dY.reshape(1, -1))\n",
        "\n",
        "print(\"dL_dY\\n {}\".format(dL_dY))\n",
        "print(\"dL_dX\\n {}\".format(dL_dX))\n",
        "print(\"dL_dW\\n {}\".format(dL_dW))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dL_dY\n",
            " [-0.89762196  0.78350206  0.53540307]\n",
            "dL_dX\n",
            " [3.88665446 1.7344111 ]\n",
            "dL_dW\n",
            " [[ 1.63014834 -1.4228981  -0.97233186]\n",
            " [ 0.21048713 -0.18372667 -0.12554891]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uuOVqySWJauS"
      },
      "source": [
        "#### 역전파(2)\n",
        "\n",
        "## $$\\ (2)\\  Y = X \\bullet W + B$$\n",
        "- $$X, W는 위와 동일$$\n",
        "\n",
        "- $$B: \\ (3, )$$\n",
        "\n",
        "- $$\\frac{\\partial L}{\\partial B} = \\frac{\\partial L}{\\partial Y}, \\ (3,\\ )$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D_Jb9sY8JYGB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e803c69e-fdc4-465a-9059-2e864304ab8d"
      },
      "source": [
        "X = np.random.randn(2)\n",
        "W = np.random.randn(2, 3)\n",
        "B = np.random.randn(3)\n",
        "Y = np.dot(X, W) + B\n",
        "print(Y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-2.88333741 -1.03075617  3.48585346]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "frdvKz8oJcoZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7c5d3053-88ce-4df7-bc91-a00f2a96da16"
      },
      "source": [
        "dL_dY = np.random.randn(3)\n",
        "dL_dX = np.dot(dL_dY, W.T)\n",
        "dL_dW = np.dot(X.reshape(-1, 1), dL_dY.reshape(1, -1))\n",
        "dL_dB = dL_dY\n",
        "\n",
        "print(\"dL_dY\\n{}\".format(dL_dY))\n",
        "print(\"dL_dX\\n{}\".format(dL_dX))\n",
        "print(\"dL_dW\\n{}\".format(dL_dW))\n",
        "print(\"dL_dB\\n{}\".format(dL_dB))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dL_dY\n",
            "[ 0.80246208 -0.56634725  0.95726248]\n",
            "dL_dX\n",
            "[-0.24630116  0.29656935]\n",
            "dL_dW\n",
            "[[-1.72679255  1.21870457 -2.0599026 ]\n",
            " [ 1.36406496 -0.96270523  1.62720239]]\n",
            "dL_dB\n",
            "[ 0.80246208 -0.56634725  0.95726248]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0FrBSUsRJgFl"
      },
      "source": [
        "#### 배치용 행렬 내적 계층\n",
        "- N개의 데이터에 대해,  \n",
        "# $$\\qquad Y = X \\bullet W + B$$\n",
        "\n",
        "  - $$X : \\quad  (N,\\ 3)$$\n",
        "\n",
        "  - $$W : \\quad  (3,\\ 2)$$\n",
        "\n",
        "  - $$B : \\quad  (2,\\ )$$\n",
        "  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AoWx5fDnJd-2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "df4a5d05-acd7-4b91-cbbb-ed00ac7b0f15"
      },
      "source": [
        "X = np.random.rand(4, 3)\n",
        "W = np.random.rand(3, 2)\n",
        "B = np.random.rand(2)\n",
        "\n",
        "print(X.shape)\n",
        "print(W.shape)\n",
        "print(B.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(4, 3)\n",
            "(3, 2)\n",
            "(2,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EqhSX54BJmPQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c71356df-2493-45f4-a76a-a351ea2d24ce"
      },
      "source": [
        "print(\"X\\n{}\".format(X))\n",
        "print(\"W\\n{}\".format(W))\n",
        "print(\"B\\n{}\".format(B))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X\n",
            "[[0.48739056 0.82497807 0.83675992]\n",
            " [0.30337004 0.10025118 0.71253457]\n",
            " [0.25474385 0.11815561 0.13114815]\n",
            " [0.36809993 0.0124405  0.00779342]]\n",
            "W\n",
            "[[0.10110915 0.05591815]\n",
            " [0.43012451 0.81402718]\n",
            " [0.64932872 0.33070778]]\n",
            "B\n",
            "[0.06173016 0.28855886]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_1IOOfhuJqF-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "795d35c4-9649-46a2-fb27-ba1486fcce19"
      },
      "source": [
        "Y = np.dot(X, W) + B\n",
        "\n",
        "print(\"Y\\n{}\".format(Y))\n",
        "print(\"Y.shape: \", Y.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Y\n",
            "[[1.00918533 1.26409042]\n",
            " [0.5981933  0.62277066]\n",
            " [0.22346697 0.44235725]\n",
            " [0.10935989 0.32184658]]\n",
            "Y.shape:  (4, 2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TOKsN2NHJrqT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "59e536c2-c43e-4f73-8d9b-87fad2607aef"
      },
      "source": [
        "dL_dY = np.random.randn(4, 2)\n",
        "dL_dX = np.dot(dL_dY, W.T)\n",
        "dL_dW = np.dot(X.T, dL_dY)\n",
        "dL_dB = np.sum(dL_dY, axis=0)\n",
        "\n",
        "print(\"dL_dY\\n{}\".format(dL_dY))\n",
        "print(\"dL_dX\\n{}\".format(dL_dX))\n",
        "print(\"dL_dW\\n{}\".format(dL_dW))\n",
        "print(\"dL_dB\\n{}\".format(dL_dB))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dL_dY\n",
            "[[-0.36649488 -0.91535652]\n",
            " [ 0.47149517  1.44678334]\n",
            " [-1.01701251 -1.8083023 ]\n",
            " [-1.15521765 -0.69691125]]\n",
            "dL_dX\n",
            "[[-0.08824103 -0.90276351 -0.54069117]\n",
            " [ 0.12857393  1.38052258  0.78461786]\n",
            " [-0.2039462  -1.90944922 -1.25839507]\n",
            " [-0.15577307 -1.06419212 -0.98058997]]\n",
            "dL_dW\n",
            "[[-0.71990185 -0.72441227]\n",
            " [-0.38961951 -0.8324383 ]\n",
            " [-0.11309403  0.02236268]]\n",
            "dL_dB\n",
            "[-2.06722987 -1.97378672]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YjIYrXGaJtEz"
      },
      "source": [
        "class Layer():\n",
        "\n",
        "  def __init__(self):\n",
        "    self.W = np.random.randn(3, 2)\n",
        "    self.b = np.random.randn(2)\n",
        "    self.x = None\n",
        "    self.dW =None\n",
        "    self.db = None\n",
        "\n",
        "  def forward(self, x):\n",
        "    self.x = x\n",
        "    out = np.dot(x, self.W) + self.b\n",
        "    return out\n",
        "\n",
        "  def backward(self, dout):\n",
        "    dx = np.dot(dout, self.W.T)\n",
        "    self.dW = np.dot(self.x.T, dout)\n",
        "    self.db = np.sum(dout, axis=0)\n",
        "    return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "twG43EylJvC-"
      },
      "source": [
        "np.random.seed(111)\n",
        "\n",
        "layer =Layer()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CrCDxHw5Jw3S",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eb2b6359-909a-4df6-854d-1ba67f6db40b"
      },
      "source": [
        "X = np.random.rand(2, 3)\n",
        "Y = layer.forward(X)\n",
        "\n",
        "print(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.23868214 0.33765619 0.99071246]\n",
            " [0.23772645 0.08119266 0.66960024]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "boKm8OIgJyJy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "824ff863-c3fe-4e44-a1a9-75b18aee23a0"
      },
      "source": [
        "dout = np.random.rand(2, 2)\n",
        "dout_dx = layer.backward(dout)\n",
        "\n",
        "print(dout_dx)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.59898814  0.83225859 -0.61525238]\n",
            " [-0.48312871  0.65565961 -0.42154775]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bz-0zFPpJ3Jz"
      },
      "source": [
        "### MNIST 분류 with 역전파\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eW3InPxBJ6qo"
      },
      "source": [
        "#### Modules Import"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZKtAhkm4J2Z3"
      },
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('seaborn-v0_8-whitegrid')\n",
        "from collections import OrderedDict"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F1_2_jGMKGiT"
      },
      "source": [
        "#### 데이터 로드"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S3SQq80sJ8mR"
      },
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "# 데이터 로드 및 전처리\n",
        "mnist = tf.keras.datasets.mnist\n",
        "(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
        "\n",
        "num_classes = 10"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mv_pjKdxKKIy"
      },
      "source": [
        "#### 데이터 전처리"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B95lI86tKIyY"
      },
      "source": [
        "X_train = X_train.reshape(-1, 28 * 28).astype(np.float32)\n",
        "X_test = X_test.reshape(-1, 28 * 28).astype(np.float32)\n",
        "\n",
        "\n",
        "X_train /= 255\n",
        "X_test /= 255"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ar7DZIlMKLjJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0eefc35a-93b6-4171-87a9-75113f4bd58e"
      },
      "source": [
        "print(X_train.shape)\n",
        "print(y_train.shape)\n",
        "print(X_test.shape)\n",
        "print(y_test.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(60000, 784)\n",
            "(60000,)\n",
            "(10000, 784)\n",
            "(10000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oye4pC82KPbg"
      },
      "source": [
        "#### Hyper Parameters"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rFeXORJjKM7s"
      },
      "source": [
        "epochs = 1000\n",
        "learning_rate = 1e-3\n",
        "batch_size = 100\n",
        "train_size = X_train.shape[0]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cIdzuyRDKSm0"
      },
      "source": [
        "#### Util Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8E2_fN1dKRzv"
      },
      "source": [
        "def softmax(x):\n",
        "    if x.ndim == 2:\n",
        "        x = x.T\n",
        "        x = x - np.max(x, axis=0)\n",
        "        y = np.exp(x) / np.sum(np.exp(x), axis=0)\n",
        "        return y.T\n",
        "\n",
        "    x = x - np.max(x)\n",
        "    return np.exp(x) / np.sum(np.exp(x))\n",
        "\n",
        "def mean_squared_error(pred_y, true_y):\n",
        "  return 0.5 * np.sum((pred_y - true_y) ** 2)\n",
        "\n",
        "def cross_entropy_error(pred_y, true_y):\n",
        "    if pred_y.ndim == 1:\n",
        "        true_y = true_y.reshape(1, true_y.size)\n",
        "        pred_y = pred_y.reshape(1, pred_y.size)\n",
        "\n",
        "    if true_y.size == pred_y.size:\n",
        "        true_y = true_y.argmax(axis=1)\n",
        "\n",
        "    batch_size = pred_y.shape[0]\n",
        "    return -np.sum(np.log(pred_y[np.arange(batch_size), true_y]+1e-7)) / batch_size\n",
        "\n",
        "def softmax_loss(X, true_y):\n",
        "  pred_y = softmax(X)\n",
        "  return cross_entropy_error(pred_y, true_y)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SBvWUNh-KY2R"
      },
      "source": [
        "#### Util Classes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rc0sLXWJs8Dq"
      },
      "source": [
        "##### ReLU"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ej2m6Robs-uJ"
      },
      "source": [
        "class ReLU:\n",
        "    def __init__(self):\n",
        "        self.mask = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        self.mask = (x <= 0)\n",
        "        out = x.copy()\n",
        "        out[self.mask] = 0\n",
        "        return out\n",
        "\n",
        "    def backward(self, dout):\n",
        "        dout[self.mask] = 0\n",
        "        return dout"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RucLfG0EtYcf"
      },
      "source": [
        "##### Sigmoid"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TWoPmtpNtZ__"
      },
      "source": [
        "class Sigmoid:\n",
        "    def __init__(self):\n",
        "        self.out = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        out = 1 / (1 + np.exp(-x))\n",
        "        self.out = out\n",
        "        return out\n",
        "\n",
        "    def backward(self, dout):\n",
        "        dx = dout * (1.0 - self.out) * self.out\n",
        "        return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IZZeNtd-tuM5"
      },
      "source": [
        "##### Layer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NEcCZ4bFtzgq"
      },
      "source": [
        "class Layer:\n",
        "    def __init__(self, W, b):\n",
        "        self.W = W\n",
        "        self.b = b\n",
        "        self.x = None\n",
        "        self.dL_dW = None  # 수정: dl_dW -> dL_dW (일관성)\n",
        "        self.dL_db = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        self.x = x\n",
        "        return np.dot(x, self.W) + self.b\n",
        "\n",
        "    def backward(self, dout):\n",
        "        self.dL_dW = np.dot(self.x.T, dout)\n",
        "        self.dL_db = np.sum(dout, axis=0)\n",
        "        dx = np.dot(dout, self.W.T)\n",
        "        return dx\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s1Yqp7kVvOoD"
      },
      "source": [
        "#### Softmax"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0RXBVEMdvP9r"
      },
      "source": [
        "class Softmax:\n",
        "    def __init__(self):\n",
        "        self.loss = None\n",
        "        self.y = None\n",
        "        self.t = None\n",
        "\n",
        "    def forward(self, x, t):\n",
        "        self.t = t\n",
        "        self.y = softmax(x)\n",
        "        self.loss = cross_entropy_error(self.y, self.t)\n",
        "        return self.loss\n",
        "\n",
        "    def backward(self, dout=1):\n",
        "        batch_size = self.t.shape[0]\n",
        "        if self.t.size == self.y.size:\n",
        "            dx = (self.y - self.t) / batch_size\n",
        "        else:\n",
        "            dx = self.y.copy()\n",
        "            dx[np.arange(batch_size), self.t] -= 1\n",
        "            dx = dx / batch_size\n",
        "        return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sX4I-bKfuRaq"
      },
      "source": [
        "class MyModel:\n",
        "    def __init__(self, input_size, hidden_size_list, output_size, activation='relu'):\n",
        "        self.input_size = input_size\n",
        "        self.output_size = output_size\n",
        "        self.hidden_size_list = hidden_size_list\n",
        "        self.hidden_layer_num = len(hidden_size_list)\n",
        "        self.params = {}\n",
        "\n",
        "        self.__init_weights(activation)\n",
        "\n",
        "        activation_layer = {'sigmoid': Sigmoid, 'relu': ReLU}\n",
        "        self.layers = OrderedDict()\n",
        "\n",
        "        for idx in range(1, self.hidden_layer_num + 1):\n",
        "            self.layers['Layer' + str(idx)] = Layer(self.params['W' + str(idx)],\n",
        "                                                  self.params['b' + str(idx)])\n",
        "            self.layers['Activation_function' + str(idx)] = activation_layer[activation]()\n",
        "\n",
        "        idx = self.hidden_layer_num + 1\n",
        "        self.layers['Layer' + str(idx)] = Layer(self.params['W' + str(idx)],\n",
        "                                              self.params['b' + str(idx)])\n",
        "\n",
        "        self.last_layer = Softmax()\n",
        "\n",
        "    def __init_weights(self, activation):\n",
        "        all_size_list = [self.input_size] + self.hidden_size_list + [self.output_size]\n",
        "        for idx in range(1, len(all_size_list)):\n",
        "            if activation.lower() == 'relu':\n",
        "                weight_std = np.sqrt(2.0 / all_size_list[idx-1])\n",
        "            elif activation.lower() == 'sigmoid':\n",
        "                weight_std = np.sqrt(1.0 / all_size_list[idx-1])\n",
        "\n",
        "            self.params['W' + str(idx)] = weight_std * np.random.randn(all_size_list[idx-1], all_size_list[idx])\n",
        "            self.params['b' + str(idx)] = np.zeros(all_size_list[idx])  # 수정: random -> zeros\n",
        "\n",
        "    def predict(self, x):\n",
        "        for layer in self.layers.values():\n",
        "            x = layer.forward(x)\n",
        "        return x\n",
        "\n",
        "    def loss(self, x, true_y):\n",
        "        pred_y = self.predict(x)\n",
        "        return self.last_layer.forward(pred_y, true_y)\n",
        "\n",
        "    def accuracy(self, x, true_y):\n",
        "        pred_y = self.predict(x)\n",
        "        pred_y = np.argmax(pred_y, axis=1)\n",
        "\n",
        "        if true_y.ndim != 1:\n",
        "            true_y = np.argmax(true_y, axis=1)\n",
        "\n",
        "        accuracy = np.sum(pred_y == true_y) / float(x.shape[0])\n",
        "        return accuracy\n",
        "\n",
        "    def gradient(self, x, t):\n",
        "        # Forward\n",
        "        self.loss(x, t)\n",
        "\n",
        "        # Backward\n",
        "        dout = 1\n",
        "        dout = self.last_layer.backward(dout)\n",
        "\n",
        "        layers = list(self.layers.values())\n",
        "        layers.reverse()\n",
        "        for layer in layers:\n",
        "            dout = layer.backward(dout)\n",
        "\n",
        "        # 기울기 저장\n",
        "        grads = {}\n",
        "        for idx in range(1, self.hidden_layer_num + 2):\n",
        "            grads['W' + str(idx)] = self.layers['Layer' + str(idx)].dL_dW\n",
        "            grads['b' + str(idx)] = self.layers['Layer' + str(idx)].dL_db\n",
        "\n",
        "        return grads"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LwyNo3TsyDZR"
      },
      "source": [
        "#### 모델 생성 및 학습"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Du5naLufxMvv"
      },
      "source": [
        "model = MyModel(784, [100, 64, 32], 10, activation='relu')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rb0HhW9x0mrN"
      },
      "source": [
        "train_loss_list = []\n",
        "train_acc_list = []\n",
        "test_acc_list = []"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VV5PciwAxM6s",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "350dbee3-77a6-436d-92b5-8462b8164085"
      },
      "source": [
        "for epoch in range(epochs):\n",
        "    batch_mask = np.random.choice(train_size, batch_size)\n",
        "    x_batch = X_train[batch_mask]\n",
        "    y_batch = y_train[batch_mask]\n",
        "\n",
        "    grad = model.gradient(x_batch, y_batch)\n",
        "\n",
        "    # 가중치 업데이트\n",
        "    for key in model.params.keys():\n",
        "        model.params[key] -= learning_rate * grad[key]\n",
        "\n",
        "    loss = model.loss(x_batch, y_batch)\n",
        "    train_loss_list.append(loss)\n",
        "\n",
        "    if epoch % 50 == 0:\n",
        "        train_acc = model.accuracy(X_train, y_train)\n",
        "        test_acc = model.accuracy(X_test, y_test)\n",
        "        train_acc_list.append(train_acc)\n",
        "        test_acc_list.append(test_acc)\n",
        "        print(f\"Epoch: {epoch+1}, Train_acc: {train_acc:.4f}, Test_acc: {test_acc:.4f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch: 1, Train_acc: 0.1290, Test_acc: 0.1251\n",
            "Epoch: 51, Train_acc: 0.1419, Test_acc: 0.1373\n",
            "Epoch: 101, Train_acc: 0.1549, Test_acc: 0.1497\n",
            "Epoch: 151, Train_acc: 0.1702, Test_acc: 0.1643\n",
            "Epoch: 201, Train_acc: 0.1914, Test_acc: 0.1854\n",
            "Epoch: 251, Train_acc: 0.2162, Test_acc: 0.2150\n",
            "Epoch: 301, Train_acc: 0.2414, Test_acc: 0.2427\n",
            "Epoch: 351, Train_acc: 0.2617, Test_acc: 0.2657\n",
            "Epoch: 401, Train_acc: 0.2791, Test_acc: 0.2843\n",
            "Epoch: 451, Train_acc: 0.2994, Test_acc: 0.3033\n",
            "Epoch: 501, Train_acc: 0.3150, Test_acc: 0.3200\n",
            "Epoch: 551, Train_acc: 0.3332, Test_acc: 0.3382\n",
            "Epoch: 601, Train_acc: 0.3483, Test_acc: 0.3551\n",
            "Epoch: 651, Train_acc: 0.3643, Test_acc: 0.3717\n",
            "Epoch: 701, Train_acc: 0.3829, Test_acc: 0.3896\n",
            "Epoch: 751, Train_acc: 0.3989, Test_acc: 0.4032\n",
            "Epoch: 801, Train_acc: 0.4167, Test_acc: 0.4205\n",
            "Epoch: 851, Train_acc: 0.4385, Test_acc: 0.4447\n",
            "Epoch: 901, Train_acc: 0.4584, Test_acc: 0.4655\n",
            "Epoch: 951, Train_acc: 0.4770, Test_acc: 0.4830\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.arange(1000/50), train_acc_list, 'r--', label='trian_acc')\n",
        "plt.plot(np.arange(1000/50), test_acc_list, 'b', label='test_acc')\n",
        "\n",
        "plt.title('Result')\n",
        "plt.xlabel('Epochs')\n",
        "plt.legend(loc=5)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "y1aLlIVcRN-b",
        "outputId": "b085651e-d63d-49cf-b57c-f90014d042a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 모델 성능 개선해보기\n",
        "1. 단순 255로 나누는 대신 평균을 빼고 표준편차로 나누어 정규화\n",
        "- 데이터를 평균 0, 표준편차1로 정규화하면 모든 특성이 동일한 스케일을 가지게 해서 데이터의 분포를 균일하게 만들면 경사하강법의 수렴을 더 안정적이고 빠르게 만들기 때문\n",
        "\n",
        "2. 모델 구조 개선 - 히든 레이어 더 넓게 설정, He초기화 사용\n",
        "- 히든 레이어\n",
        "  - 더 많은 뉴런으로 복잡한 패턴 학습, 중간 레이어도 충분한 표현력을 가지게 하기 위함\n",
        "- He 초기화\n",
        "  - ReLU 활성화 함수와 함께 사용하면 효과적, 기울기 소실/초과 문제를 완화\n",
        "3. 옵티마이저 개선\n",
        "- 모멘텀 SGD 구현 및 적용\n",
        "  - 일반 SGD보다 local minima회피에 효과적\n",
        "- 학습률을 0.01로 증가\n",
        "  - 초기에는 큰 학습률로 빠르게 학습하고 점진적으로 줄여서 미세 조정을 가능하게 하기 위함\n",
        "- 200에포크마다 학습률을 절반으로 감소\n",
        "4. 학습 과정 개선\n",
        "- 배치 사이즈를 256으로 증가\n",
        "  - 더 안정적인 그래디언트 추정, 너무 작은 배치는 노이즈가 많고, 너무 크면 일반화가 약화됨\n"
      ],
      "metadata": {
        "id": "ttNdmJf9R8A_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 정규화 개선\n",
        "\n",
        "X_train = (X_train - np.mean(X_train)) / np.std(X_train)\n",
        "X_test = (X_test - np.mean(X_test)) / np.std(X_test)\n",
        "\n",
        "y_train = np.eye(num_classes)[y_train]"
      ],
      "metadata": {
        "id": "ldEbkgqiSYY-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# 하이퍼 파라미터 수정\n",
        "epochs = 1000\n",
        "learning_rate = 0.01 # 학습률 증가\n",
        "batch_size = 256 # 배치사이즈 증가\n",
        "train_size = X_train.shape[0]"
      ],
      "metadata": {
        "id": "L4aSxetiSxYa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### SGD 추가**"
      ],
      "metadata": {
        "id": "xB25wwLwTZQT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 모멘텀 SGD추가\n",
        "class MomentumSGD:\n",
        "    def __init__(self, lr=0.01, momentum=0.9):\n",
        "        self.lr = lr\n",
        "        self.momentum = momentum\n",
        "        self.v = None\n",
        "\n",
        "    def update(self, params, grads):\n",
        "        if self.v is None:\n",
        "            self.v = {}\n",
        "            for key, val in params.items():\n",
        "                self.v[key] = np.zeros_like(val)\n",
        "\n",
        "        for key in params.keys():\n",
        "            self.v[key] = self.momentum * self.v[key] - self.lr * grads[key]\n",
        "            params[key] += self.v[key]"
      ],
      "metadata": {
        "id": "RD--sWDcS7gn"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WuVn3YI3TXx2"
      },
      "source": [
        "##### ReLU"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iywiu_sITXx3"
      },
      "source": [
        "class ReLU:\n",
        "    def __init__(self):\n",
        "        self.mask = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        self.mask = (x <= 0)\n",
        "        out = x.copy()\n",
        "        out[self.mask] = 0\n",
        "        return out\n",
        "\n",
        "    def backward(self, dout):\n",
        "        dout[self.mask] = 0\n",
        "        return dout"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AZpXdR4zTXx3"
      },
      "source": [
        "##### Sigmoid"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JzeplYJaTXx3"
      },
      "source": [
        "class Sigmoid:\n",
        "    def __init__(self):\n",
        "        self.out = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        out = 1 / (1 + np.exp(-x))\n",
        "        self.out = out\n",
        "        return out\n",
        "\n",
        "    def backward(self, dout):\n",
        "        dx = dout * (1.0 - self.out) * self.out\n",
        "        return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z8qkdGZJTXx3"
      },
      "source": [
        "##### Layer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qpny032RTXx3"
      },
      "source": [
        "class Layer:\n",
        "    def __init__(self, W, b):\n",
        "        self.W = W\n",
        "        self.b = b\n",
        "        self.x = None\n",
        "        self.dL_dW = None  # 수정: dl_dW -> dL_dW (일관성)\n",
        "        self.dL_db = None\n",
        "\n",
        "    def forward(self, x):\n",
        "        self.x = x\n",
        "        return np.dot(x, self.W) + self.b\n",
        "\n",
        "    def backward(self, dout):\n",
        "        self.dL_dW = np.dot(self.x.T, dout)\n",
        "        self.dL_db = np.sum(dout, axis=0)\n",
        "        dx = np.dot(dout, self.W.T)\n",
        "        return dx\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BjJbhfDvTXx4"
      },
      "source": [
        "#### Softmax"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4SykdsCYTXx4"
      },
      "source": [
        "class Softmax:\n",
        "    def __init__(self):\n",
        "        self.loss = None\n",
        "        self.y = None\n",
        "        self.t = None\n",
        "\n",
        "    def forward(self, x, t):\n",
        "        self.t = t\n",
        "        self.y = softmax(x)\n",
        "        self.loss = cross_entropy_error(self.y, self.t)\n",
        "        return self.loss\n",
        "\n",
        "    def backward(self, dout=1):\n",
        "        batch_size = self.t.shape[0]\n",
        "        if self.t.size == self.y.size:\n",
        "            dx = (self.y - self.t) / batch_size\n",
        "        else:\n",
        "            dx = self.y.copy()\n",
        "            dx[np.arange(batch_size), self.t] -= 1\n",
        "            dx = dx / batch_size\n",
        "        return dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class MyModel:\n",
        "    def __init__(self, input_size, hidden_size_list, output_size, activation='relu'):\n",
        "        self.input_size = input_size\n",
        "        self.output_size = output_size\n",
        "        self.hidden_size_list = hidden_size_list\n",
        "        self.hidden_layer_num = len(hidden_size_list)\n",
        "        self.params = {}\n",
        "        self.optimizer = MomentumSGD()\n",
        "\n",
        "        self.__init_weights(activation)\n",
        "\n",
        "        activation_layer = {'sigmoid': Sigmoid, 'relu': ReLU}\n",
        "        self.layers = OrderedDict()\n",
        "\n",
        "        for idx in range(1, self.hidden_layer_num + 1):\n",
        "            self.layers['Layer' + str(idx)] = Layer(self.params['W' + str(idx)],\n",
        "                                                  self.params['b' + str(idx)])\n",
        "            self.layers['Activation_function' + str(idx)] = activation_layer[activation]()\n",
        "\n",
        "        idx = self.hidden_layer_num + 1\n",
        "        self.layers['Layer' + str(idx)] = Layer(self.params['W' + str(idx)],\n",
        "                                              self.params['b' + str(idx)])\n",
        "\n",
        "        self.last_layer = Softmax()\n",
        "\n",
        "    def __init_weights(self, activation):\n",
        "        all_size_list = [self.input_size] + self.hidden_size_list + [self.output_size]\n",
        "        for idx in range(1, len(all_size_list)):\n",
        "            scale = np.sqrt(2.0 / all_size_list[idx-1])  # He 초기화\n",
        "            self.params['W' + str(idx)] = scale * np.random.randn(all_size_list[idx-1], all_size_list[idx])\n",
        "            self.params['b' + str(idx)] = np.zeros(all_size_list[idx])\n",
        "\n",
        "    def predict(self, x):\n",
        "        for layer in self.layers.values():\n",
        "            x = layer.forward(x)\n",
        "        return x\n",
        "\n",
        "    def loss(self, x, true_y):\n",
        "        pred_y = self.predict(x)\n",
        "        return self.last_layer.forward(pred_y, true_y)\n",
        "\n",
        "    def accuracy(self, x, true_y):\n",
        "        pred_y = self.predict(x)\n",
        "        pred_y = np.argmax(pred_y, axis=1)\n",
        "\n",
        "        if true_y.ndim != 1:\n",
        "            true_y = np.argmax(true_y, axis=1)\n",
        "\n",
        "        accuracy = np.sum(pred_y == true_y) / float(x.shape[0])\n",
        "        return accuracy\n",
        "\n",
        "    def gradient(self, x, t):\n",
        "        # Forward\n",
        "        self.loss(x, t)\n",
        "\n",
        "        # Backward\n",
        "        dout = 1\n",
        "        dout = self.last_layer.backward(dout)\n",
        "\n",
        "        layers = list(self.layers.values())\n",
        "        layers.reverse()\n",
        "\n",
        "        for layer in layers:\n",
        "            dout = layer.backward(dout)\n",
        "\n",
        "        # 기울기 저장\n",
        "        grads = {}\n",
        "        for idx in range(1, self.hidden_layer_num + 2):\n",
        "            grads['W' + str(idx)] = self.layers['Layer' + str(idx)].dL_dW\n",
        "            grads['b' + str(idx)] = self.layers['Layer' + str(idx)].dL_db\n",
        "\n",
        "        return grads\n",
        "\n",
        "    def update(self, grad):\n",
        "        self.optimizer.update(self.params, grad)"
      ],
      "metadata": {
        "id": "BKtrQNsMTdBg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# 모델 생성 (더 큰 네트워크)\n",
        "model = MyModel(784, [256, 256, 128], 10, activation='relu')  # 더 넓은 히든 레이어\n",
        "\n",
        "train_loss_list = []\n",
        "train_acc_list = []\n",
        "test_acc_list = []"
      ],
      "metadata": {
        "id": "CPLhOdLaTk8k"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for epoch in range(epochs):\n",
        "    # 학습률 감소\n",
        "    if epoch % 200 == 0 and epoch != 0:\n",
        "        model.optimizer.lr *= 0.5\n",
        "\n",
        "    batch_mask = np.random.choice(train_size, batch_size)\n",
        "    x_batch = X_train[batch_mask]\n",
        "    y_batch = y_train[batch_mask]\n",
        "\n",
        "    grad = model.gradient(x_batch, y_batch)\n",
        "    model.update(grad)\n",
        "\n",
        "    loss = model.loss(x_batch, y_batch)\n",
        "    train_loss_list.append(loss)\n",
        "\n",
        "    if epoch % 50 == 0:\n",
        "        train_acc = model.accuracy(X_train, y_train)\n",
        "        test_acc = model.accuracy(X_test, y_test)\n",
        "        train_acc_list.append(train_acc)\n",
        "        test_acc_list.append(test_acc)\n",
        "        print(f\"Epoch: {epoch+1}, Train_acc: {train_acc:.4f}, Test_acc: {test_acc:.4f}, Loss: {loss:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wW7MMITeTlns",
        "outputId": "949310ed-e076-497c-b213-444109c925ea"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch: 1, Train_acc: 0.0848, Test_acc: 0.0849, Loss: 2.6137\n",
            "Epoch: 51, Train_acc: 0.9017, Test_acc: 0.9043, Loss: 0.3018\n",
            "Epoch: 101, Train_acc: 0.9322, Test_acc: 0.9348, Loss: 0.1959\n",
            "Epoch: 151, Train_acc: 0.9429, Test_acc: 0.9448, Loss: 0.1321\n",
            "Epoch: 201, Train_acc: 0.9504, Test_acc: 0.9496, Loss: 0.1060\n",
            "Epoch: 251, Train_acc: 0.9545, Test_acc: 0.9531, Loss: 0.1278\n",
            "Epoch: 301, Train_acc: 0.9587, Test_acc: 0.9549, Loss: 0.0932\n",
            "Epoch: 351, Train_acc: 0.9600, Test_acc: 0.9576, Loss: 0.1410\n",
            "Epoch: 401, Train_acc: 0.9633, Test_acc: 0.9603, Loss: 0.1060\n",
            "Epoch: 451, Train_acc: 0.9642, Test_acc: 0.9603, Loss: 0.1149\n",
            "Epoch: 501, Train_acc: 0.9660, Test_acc: 0.9609, Loss: 0.1491\n",
            "Epoch: 551, Train_acc: 0.9660, Test_acc: 0.9606, Loss: 0.1325\n",
            "Epoch: 601, Train_acc: 0.9672, Test_acc: 0.9621, Loss: 0.1278\n",
            "Epoch: 651, Train_acc: 0.9684, Test_acc: 0.9631, Loss: 0.0848\n",
            "Epoch: 701, Train_acc: 0.9686, Test_acc: 0.9637, Loss: 0.0811\n",
            "Epoch: 751, Train_acc: 0.9687, Test_acc: 0.9627, Loss: 0.0681\n",
            "Epoch: 801, Train_acc: 0.9696, Test_acc: 0.9633, Loss: 0.0781\n",
            "Epoch: 851, Train_acc: 0.9697, Test_acc: 0.9632, Loss: 0.1032\n",
            "Epoch: 901, Train_acc: 0.9696, Test_acc: 0.9634, Loss: 0.0949\n",
            "Epoch: 951, Train_acc: 0.9700, Test_acc: 0.9646, Loss: 0.1611\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# epochs가 1000이고 50마다 기록했으므로 총 20개의 데이터 포인트가 있음\n",
        "x = np.arange(len(train_acc_list))  # [0, 1, 2, ..., 19]\n",
        "epochs_points = x * 50  # [0, 50, 100, ..., 950]\n",
        "\n",
        "plt.figure(figsize=(10, 6))  # 그래프 크기 설정\n",
        "plt.plot(epochs_points, train_acc_list, 'r--', label='train_acc', linewidth=2)\n",
        "plt.plot(epochs_points, test_acc_list, 'b-', label='test_acc', linewidth=2)\n",
        "\n",
        "plt.title('Training Progress', fontsize=14)\n",
        "plt.xlabel('Epochs', fontsize=12)\n",
        "plt.ylabel('Accuracy', fontsize=12)\n",
        "plt.legend(loc='lower right')  # loc=5와 동일하지만 더 명시적\n",
        "plt.grid(True)\n",
        "plt.xlim([0, 1000])  # x축 범위 명시적 설정\n",
        "plt.ylim([0, 1.0])   # y축 범위를 0~1로 설정\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 559
        },
        "id": "_pbKMy0xVWdJ",
        "outputId": "4921e506-eb99-4d4c-b588-90970b0474af"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10, 6))  # 그래프 크기 설정\n",
        "plt.plot(np.arange(1000), train_loss_list, color='green', label='train_loss', alpha=0.8, linewidth=1)\n",
        "\n",
        "# 이동 평균을 추가하여 트렌드를 더 잘 볼 수 있게 함\n",
        "window_size = 50\n",
        "moving_avg = np.convolve(train_loss_list, np.ones(window_size)/window_size, mode='valid')\n",
        "plt.plot(np.arange(len(moving_avg)), moving_avg, color='red', label='moving average', linewidth=2)\n",
        "\n",
        "plt.title('Training Loss over Epochs', fontsize=14)\n",
        "plt.xlabel('Epochs', fontsize=12)\n",
        "plt.ylabel('Loss', fontsize=12)\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "\n",
        "# y축 범위 설정 (loss가 너무 크면 조정 필요)\n",
        "plt.ylim(bottom=0)  # 최소값을 0으로 설정\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 559
        },
        "id": "61CV3SE7Vq8c",
        "outputId": "8c0fca29-5f44-4545-9451-ab41297f6f74"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}