9_梯度与激活函数.ipynb

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      "name": "9_梯度与激活函数.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mengcius/pytorch-learn/blob/master/9_%E6%A2%AF%E5%BA%A6%E4%B8%8E%E6%BF%80%E6%B4%BB%E5%87%BD%E6%95%B0.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0B3pohZOrrWx",
        "colab_type": "text"
      },
      "source": [
        "## 9_梯度与激活函数"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wZFUKBXZrjdf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bm1OQiwULdqD",
        "colab_type": "text"
      },
      "source": [
        "### sigmoid\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uf_ldhFk3u1t",
        "colab_type": "code",
        "outputId": "f2b823a0-9a71-48bd-a260-7d547e1d072b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "x=torch.linspace(-100,100,10) #线性等分向量\n",
        "x"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-100.0000,  -77.7778,  -55.5556,  -33.3333,  -11.1111,   11.1111,\n",
              "          33.3333,   55.5555,   77.7778,  100.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rrY8ZWtLEcec",
        "colab_type": "code",
        "outputId": "d3e1a36a-57a9-4997-e121-855d030b190b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "torch.sigmoid(x)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.0000e+00, 1.6655e-34, 7.4564e-25, 3.3382e-15, 1.4945e-05, 9.9999e-01,\n",
              "        1.0000e+00, 1.0000e+00, 1.0000e+00, 1.0000e+00])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rCtDHb66EcUx",
        "colab_type": "code",
        "outputId": "e1239b00-1984-4958-8758-8d446bb3f477",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "F.sigmoid(x) #不建议用torch.nn.functional中的sigmoid"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/torch/nn/functional.py:1386: UserWarning: nn.functional.sigmoid is deprecated. Use torch.sigmoid instead.\n",
            "  warnings.warn(\"nn.functional.sigmoid is deprecated. Use torch.sigmoid instead.\")\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.0000e+00, 1.6655e-34, 7.4564e-25, 3.3382e-15, 1.4945e-05, 9.9999e-01,\n",
              "        1.0000e+00, 1.0000e+00, 1.0000e+00, 1.0000e+00])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JGYQ5fNzNXwz",
        "colab_type": "text"
      },
      "source": [
        "### tanh"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "trUjOTgaEcNd",
        "colab_type": "code",
        "outputId": "85edf4f8-9c8d-4c03-8454-3a2c96bc73fa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "x=torch.linspace(-10,10,10)\n",
        "x"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-10.0000,  -7.7778,  -5.5556,  -3.3333,  -1.1111,   1.1111,   3.3333,\n",
              "          5.5556,   7.7778,  10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3IULqXLEEcFK",
        "colab_type": "code",
        "outputId": "bd8746b4-5e0d-462c-e797-3692d78beee8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "torch.tanh(x)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-1.0000, -1.0000, -1.0000, -0.9975, -0.8045,  0.8045,  0.9975,  1.0000,\n",
              "         1.0000,  1.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oo0rQukbPXao",
        "colab_type": "text"
      },
      "source": [
        "### relu"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5_isHKT-N9V6",
        "colab_type": "code",
        "outputId": "16c2c9a9-ecc0-48e3-d93a-51213354d2d3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "x=torch.linspace(-10,10,10)\n",
        "x"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-10.0000,  -7.7778,  -5.5556,  -3.3333,  -1.1111,   1.1111,   3.3333,\n",
              "          5.5556,   7.7778,  10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mC4yJcXePcIV",
        "colab_type": "code",
        "outputId": "b973525a-4146-4a53-df17-c9164a9e4c32",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "torch.relu(x)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
              "         7.7778, 10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6y7SMs-EPet9",
        "colab_type": "code",
        "outputId": "321b6f6b-da1d-45d6-93f3-5c7e7cfc45eb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "F.relu(x)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
              "         7.7778, 10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "up1JOCwGUtnL",
        "colab_type": "text"
      },
      "source": [
        "### autograd.grad求mse_loss的梯度\n",
        "\n",
        "torch.nn.functional.mse_loss() 计算均方差损失\n",
        "\n",
        "torch.autograd.grad(loss, [w1, w2,...]) 求导，返回[w1 grad, w2 grad...]\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EdLjq0pcPiKp",
        "colab_type": "code",
        "outputId": "c9e200d9-2f3c-406c-d7e4-8b066cea155a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "x=torch.ones(1)\n",
        "w=torch.full([1],2) #预测为y^=x*w，w=torch.full([1],2,requires_grad=True)\n",
        "x,w"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([1.]), tensor([2.]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qNvxS2AEWtIp",
        "colab_type": "code",
        "outputId": "1c6d2ae7-9f66-4e8e-c55f-e532cce299ff",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "mse=F.mse_loss(torch.ones(1),x*w) #均方差，实际值y-预测值y^的平方和\n",
        "mse"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LO0_Z4FnYW4w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "torch.autograd.grad(mse,[w]) #让mse损失对w求导\n",
        "#报错w无需求导，要将w标注为可求导的\n",
        "#RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E1CeiE-cYuV5",
        "colab_type": "code",
        "outputId": "66251550-ceeb-4a24-9e74-676ce03725e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "w.requires_grad_() #标注w是需要梯度信息的，或在一开始就w=torch.full([1],2,requires_grad=True)\n",
        "#因为torch是动态图，在w更新后，要再计算一次mse，重新更新图\n",
        "mse=F.mse_loss(torch.ones(1),x*w)\n",
        "torch.autograd.grad(mse,[w]) #让mse损失对w求导，返回w的梯度"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([2.]),)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tAb2oEsocvcE",
        "colab_type": "text"
      },
      "source": [
        "### backward求mse_loss的梯度\n",
        "\n",
        "xloss.backward() 反向传播，无返回，但附在了w1.grad，w2.grad\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dhHC6vlnbAQP",
        "colab_type": "code",
        "outputId": "749c62af-cff2-4c49-f7a8-032029d839d3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "x=torch.ones(1)\n",
        "w=torch.full([1],2,requires_grad=True) #预测为y^=x*w\n",
        "x,w"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([1.]), tensor([2.], requires_grad=True))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZnCbG7vkc8su",
        "colab_type": "code",
        "outputId": "540d5793-a129-498a-8460-ed211a441bb0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "mse=F.mse_loss(torch.ones(1),x*w) #均方差\n",
        "mse.backward() #反向传播，会计算出图中需要计算的梯度，不返回值，会把各自的梯度附在grad成员变量上\n",
        "w.grad"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2w1kJ--0ehfL",
        "colab_type": "code",
        "outputId": "1cb35111-d038-4647-d402-d0aeaebf38ae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "w.grad.norm() "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(2.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bVAdHSYwj04E",
        "colab_type": "text"
      },
      "source": [
        "### Softmax激活函数及其梯度\n",
        "\n",
        "F.softmax(a,dim=0) 求softmax\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wQ-4PIrwelMH",
        "colab_type": "code",
        "outputId": "8d8c2566-2d69-4199-eab3-9807a74f5a08",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "a=torch.rand(3)\n",
        "a.requires_grad_()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.6954, 0.7282, 0.5982], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yq4dZDxYonk6",
        "colab_type": "code",
        "outputId": "9c705cc7-182d-4b5a-d29e-2828a80f8d3f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "p=F.softmax(a,dim=0) #求softmax激活后的值，可以指定维度，以便跳过batch那维\n",
        "p"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.3400, 0.3514, 0.3086], grad_fn=<SoftmaxBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rTDaZ7eOo5Qe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "p.backward() #有问题？之前执行了一次，再次执行需要保持图retain_graph=True ？\n",
        "#RuntimeError: grad can be implicitly created only for scalar outputs"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lv4gn8GqpIIW",
        "colab_type": "code",
        "outputId": "9e50dd52-b6be-4d86-a647-1a986162ecc7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "#求softmax对参数a的梯度\n",
        "torch.autograd.grad(p[1],[a],retain_graph=True) #p只能是长度为1的[1]或标量，[a]长度不限制"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([-0.1195,  0.2279, -0.1084]),)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EFbUk380tPzP",
        "colab_type": "code",
        "outputId": "54b3d013-38ee-4c02-d425-409f61eee696",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "torch.autograd.grad(p[0],[a]) #当输入和输出的节点序号相同时，它的梯度才为正"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([ 0.2244, -0.1195, -0.1049]),)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ANwwFKWTLR3I",
        "colab_type": "text"
      },
      "source": [
        "### 单一输出感知机"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M3uglBuVbm5e",
        "colab_type": "code",
        "outputId": "5342f3bd-5573-494b-a821-b9a0dc3cdec9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "x=torch.randn(1,10)\n",
        "w=torch.randn(1,10,requires_grad=True)\n",
        "w"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.4849, -0.3153, -0.3720,  0.8757,  0.4986,  0.7716,  0.7317,  1.0519,\n",
              "         -2.2420,  0.3338]], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MGufmwoptocd",
        "colab_type": "code",
        "outputId": "40395ed6-0765-4e3c-ec7e-c99c152bf2a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "o=torch.sigmoid(x@w.t()) #sigmoid激活函数，压缩到了[0,1]\n",
        "o,o.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0.0064]], grad_fn=<SigmoidBackward>), torch.Size([1, 1]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gFPJiL6gYxXA",
        "colab_type": "code",
        "outputId": "83e64751-9d05-4999-d48e-683b154bab09",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "loss=F.mse_loss(torch.ones(1,1),o) #均方差损失,返回标量\n",
        "loss,loss.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.9872, grad_fn=<MeanBackward0>), torch.Size([]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ezNF5kdndFka",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "loss.backward()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XJJucKModGFE",
        "colab_type": "code",
        "outputId": "f9e9dcf0-b604-4433-a4ca-6f8be553f784",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "w.grad #梯度有10个，loss对w中[1,10]每个元素求导\n",
        "#后面就可以看哪个梯度小就往哪里更新w，不断优化，是loss趋近于0，预测值接近真实值"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.0688e-03,  8.7082e-05, -1.3061e-03,  1.5318e-02,  1.9848e-02,\n",
              "         -5.8090e-03, -1.3079e-02,  2.7386e-02, -1.1368e-02, -1.2993e-03]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UDat8uYpk3qA",
        "colab_type": "text"
      },
      "source": [
        "### 多输出感知机"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jcjQyuYTda3g",
        "colab_type": "code",
        "outputId": "04c61558-7ba6-4d99-beea-73238e06d0d1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "x=torch.randn(1,10)\n",
        "w=torch.randn(2,10,requires_grad=True)\n",
        "w"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.0605, -0.1957, -0.4953, -1.4759, -0.1880,  1.5185, -2.5982,  0.1016,\n",
              "         -0.3507, -0.5002],\n",
              "        [ 0.8593, -0.4353,  0.1071,  0.3676,  0.0844,  0.1094, -0.9263,  1.0166,\n",
              "         -0.2961,  1.4854]], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ji5A0ZP3lA09",
        "colab_type": "code",
        "outputId": "a92975bf-f102-4c96-ad37-a0a57de695b6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "o=torch.sigmoid(x@w.t()) #sigmoid激活函数，2维的\n",
        "o,o.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0.9988, 0.2463]], grad_fn=<SigmoidBackward>), torch.Size([1, 2]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tA1h07pulN7F",
        "colab_type": "code",
        "outputId": "567bfcd4-c530-4bdc-e880-54743cb6690d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "loss=F.mse_loss(torch.ones(1,2),o) #均方差损失,实际值也是2维的，要对每个激活函数元素比较\n",
        "loss,loss.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.2840, grad_fn=<MeanBackward0>), torch.Size([]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FbWGx1iKleHu",
        "colab_type": "code",
        "outputId": "081b8942-a023-4369-ac3a-1c38500575f8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "source": [
        "torch.ones(1,2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IQRJCxr9lmNo",
        "colab_type": "code",
        "outputId": "d8ed58b8-0deb-464f-ff68-04cfedcb3cd9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "loss.backward()\n",
        "w.grad #梯度有[2,10]，shape和w一样"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 7.2703e-07,  1.6904e-06,  4.6854e-07, -1.0084e-06,  4.4634e-07,\n",
              "         -2.0258e-06,  2.6752e-06,  1.7831e-06, -1.0550e-06,  1.7076e-06],\n",
              "        [ 7.2562e-02,  1.6871e-01,  4.6763e-02, -1.0064e-01,  4.4548e-02,\n",
              "         -2.0219e-01,  2.6700e-01,  1.7797e-01, -1.0530e-01,  1.7043e-01]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-de0YmzzCBbX",
        "colab_type": "text"
      },
      "source": [
        "### 链式法则"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_egSvhETl9MQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x=torch.tensor(1.)\n",
        "w1=torch.tensor(2.,requires_grad=True)\n",
        "b1=torch.tensor(1.)\n",
        "w2=torch.tensor(2.,requires_grad=True)\n",
        "b2=torch.tensor(1.)\n",
        "\n",
        "y1=x*w1+b1\n",
        "y2=y1*w2+b2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7LSRiYK4KJ_t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "26272d3b-9a8f-49ef-f90a-b6c0fbc3c511"
      },
      "source": [
        "dy2_dy1=torch.autograd.grad(y2,[y1],retain_graph=True)[0] #y2对y1求导，等于w2\n",
        "dy1_dw1=torch.autograd.grad(y1,[w1],retain_graph=True)[0] #y1对w1求导，等于x\n",
        "dy2_dy1,dy1_dw1"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(2.), tensor(1.))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7CR-65LSMS93",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "32de49af-53d6-4935-8592-c529f3bb2fbb"
      },
      "source": [
        "dy2_dy1*dy1_dw1 #链式法则求出y2对w1的导数，结果和下面的一样"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(2.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sOnVPs-lLGn9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "aed5fa6e-c55e-4a0d-b209-e48298255f77"
      },
      "source": [
        "dy2_dw1=torch.autograd.grad(y2,[w1],retain_graph=True)[0] #直接用torch功能使y2对w1求导\n",
        "dy2_dw1"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(2.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "690nXmJZPCJD",
        "colab_type": "text"
      },
      "source": [
        "### 2D函数优化实例"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y5UTsE1NeLKA",
        "colab_type": "text"
      },
      "source": [
        "可视化函数："
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G2Ur9GXEfrEs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from mpl_toolkits import mplot3d"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3GodGyDoMllX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def himmelblau(x): #定义himmelblau函数\n",
        "    return (x[0]**2+x[1]-11)**2 + (x[0]+x[1]**2-7)**2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cpS9Ya9PQDrA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        },
        "outputId": "531a88bd-5fd3-4ab4-a095-6703df441e63"
      },
      "source": [
        "x=np.arange(-6,6,0.1) #值范围-6到6，间隔0.1\n",
        "y=np.arange(-6,6,0.1)\n",
        "print('x,y range',x.shape,y.shape)\n",
        "X,Y=np.meshgrid(x,y) #meshgrid将x,y设为X,Y轴\n",
        "print('X,Y maps',X.shape,Y.shape)\n",
        "Z=himmelblau([X,Y]) #Z轴为函数值"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "x,y range (120,) (120,)\n",
            "X,Y maps (120, 120) (120, 120)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tGtNe1Ubf2Ps",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "369a2781-bbc2-4e1b-e455-5b07c169c92f"
      },
      "source": [
        "fig=plt.figure('himmelblau')\n",
        "ax=fig.gca(projection='3d')\n",
        "ax.plot_surface(X,Y,Z)\n",
        "ax.view_init(60,-30)\n",
        "ax.set_xlabel('x')\n",
        "ax.set_ylabel('y')\n",
        "plt.show()"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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agUJOgjqXhVHdLma8NlCsDEfnAeWVZmfgZ6bcVlTbo+9Rq91BJN0Pmv/opIy/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\nSwuC3sT/AVBCTKJBjEOUAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C_WIKioZjGk2",
        "colab_type": "text"
      },
      "source": [
        "随机梯度下降求解最小值：\n",
        "\n",
        "反向传播求解梯度，优化器adam更新参数"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bisfDYO0huJ2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 184
        },
        "outputId": "f8e40475-8ae2-4631-c920-260a4885c634"
      },
      "source": [
        "x=torch.tensor([4,0.],requires_grad=True) #x是优化目标，不同x初始值结果不一样[1.,0.],[-4,0.],[4,0.]\n",
        "optimizer=torch.optim.Adam([x],lr=1e-3) #Adam优化器，优化的是[x]，学习率是lr\n",
        "\n",
        "for step in range(20000): \n",
        "    pred=himmelblau(x) #计算himmelblau函数的预测值\n",
        "    optimizer.zero_grad() #优化器使梯度清零\n",
        "    pred.backward() #反向传播法计算出pred对x的梯度\n",
        "    optimizer.step() #优化器使参数x（x,y轴）更新一次，x=x-lr*x'，x[0]和x[1]是x,y轴\n",
        "\n",
        "    if step%2000==0:\n",
        "        print('step{}:x={},f(x)={}'.format(step,x.tolist(),pred.item()))  \n",
        "#最终找到最好的x[0]和x[1]使himmelblau函数达到最小值0，这模拟了优化损失函数的核心步骤      "
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "step0:x=[3.999000072479248, -0.0009999999310821295],f(x)=34.0\n",
            "step2000:x=[3.5741987228393555, -1.7641836404800415],f(x)=0.09904662519693375\n",
            "step4000:x=[3.5844225883483887, -1.8481197357177734],f(x)=2.1100277081131935e-09\n",
            "step6000:x=[3.5844264030456543, -1.8481241464614868],f(x)=2.41016095969826e-10\n",
            "step8000:x=[3.58442759513855, -1.848125696182251],f(x)=2.9103830456733704e-11\n",
            "step10000:x=[3.584428310394287, -1.8481262922286987],f(x)=9.094947017729282e-13\n",
            "step12000:x=[3.584428310394287, -1.8481265306472778],f(x)=0.0\n",
            "step14000:x=[3.584428310394287, -1.8481265306472778],f(x)=0.0\n",
            "step16000:x=[3.584428310394287, -1.8481265306472778],f(x)=0.0\n",
            "step18000:x=[3.584428310394287, -1.8481265306472778],f(x)=0.0\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}