{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "8f3ff90a", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import nnfs\n", "from nnfs.datasets import spiral_data\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "439ab0e4", "metadata": {}, "outputs": [], "source": [ "nnfs.init()" ] }, { "cell_type": "code", "execution_count": 39, "id": "2bc1bb6c", "metadata": {}, "outputs": [], "source": [ "class Linear():\n", " def __init__(self, in_features, out_features):\n", " self.weights = np.random.randn(in_features, out_features) * 0.1\n", " self.bias = np.zeros((1, out_features))\n", " def forward(self, inputs):\n", " self.outputs = np.dot(inputs, self.weights) + self.bias\n", " self.inputs = inputs\n", " def backward(self, dvalues):\n", " #计算权重的梯度\n", " self.dweights = np.dot(self.inputs.T, dvalues)\n", " #计算偏置的梯度\n", " self.dbiases = np.sum(dvalues, axis=0, keepdims=True)\n", " #计算输入的梯度\n", " self.dinputs = np.dot(dvalues, self.weights.T)\n", "class Relu():\n", " def forward(self, inputs):\n", " self.outputs = np.maximum(0, inputs)\n", " self.inputs = inputs\n", " def backward(self, dvalues):\n", " self.dinputs = dvalues.copy()\n", " self.dinputs[self.inputs <= 0] = 0\n", "class Softmax():\n", " def forward(self, inputs):\n", " exp_values = np.exp(inputs - np.max(inputs, axis=1, keepdims=True))\n", " self.outputs = exp_values / np.sum(exp_values, axis=1, keepdims=True)\n", " def backward(self, dvalues):\n", " self.dinputs = np.empty_like(dvalues)\n", " for index, (single_output, single_dvalues) in enumerate(zip(self.outputs, dvalues)):\n", " single_output = single_output.reshape(-1, 1)\n", " jacobian_matrix = np.diagflat(single_output) - np.dot(single_output, single_output.T)\n", " self.dinputs[index] = np.dot(jacobian_matrix, single_dvalues)\n", "class Loss():\n", " def calculate(self, outputs, y):\n", " sample_loss = self.forward(outputs, y)\n", " data_loss = np.mean(sample_loss)\n", " return data_loss\n", "\"\"\"交叉熵损失函数\"\"\"\n", "class CategoricalCrossEntropy(Loss):\n", " def one_hot(self, y_true):\n", " y_true = np.eye(max(y_true) + 1)[y_true]\n", " return y_true\n", " def forward(self, y_pred, y_true):\n", " y_pred_clipped = np.clip(y_pred, 1e-7, 1-1e-7)#截断，放置np.log溢出\n", " if len(y_true.shape) == 1:#标签不是独热码，通过one_hot函数转化\n", " y_true = self.one_hot(y_true)\n", " confidences = np.sum(y_pred_clipped * y_true, axis=1)\n", " negative_log_likehoods = -np.log(confidences)\n", " return negative_log_likehoods\n", " def backward(self, dvalues, y_true):\n", " samples = len(dvalues)\n", " if len(y_true.shape) == 1:#将标签转化为onehot\n", " y_true = self.one_hot(y_true)\n", " self.dinputs = -y_true / dvalues\n", " self.dinputs = self.dinputs /samples\n", "\"\"\"准确率\"\"\"\n", "class Accuracy():\n", " def forward(self, logits, y_true):\n", " predictions = np.argmax(logits, axis=1)#从激活输出选出最大值对应的下标即使标签\n", " if len(y_true.shape) == 2:#独热编码\n", " y_true = np.max(y_true, axis=1)\n", " accuracy = np.mean(predictions == y_true)\n", " return accuracy" ] }, { "cell_type": "code", "execution_count": 41, "id": "5f334df4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(300, 3)\n", "[[-0.00222222 0.00111111 0.00111111]\n", " [-0.00222225 0.00111109 0.00111116]\n", " [-0.00222228 0.00111107 0.00111121]\n", " [-0.0022223 0.00111105 0.00111125]\n", " [-0.00222237 0.001111 0.00111137]\n", " [-0.00222236 0.00111101 0.00111135]\n", " [-0.0022224 0.00111098 0.00111142]\n", " [-0.00222249 0.00111092 0.00111157]\n", " [-0.00222261 0.00111093 0.00111168]\n", " [-0.00222254 0.00111087 0.00111167]\n", " [-0.00222249 0.0011109 0.00111159]\n", " [-0.00222283 0.00111091 0.00111191]\n", " [-0.00222279 0.00111083 0.00111196]\n", " [-0.00222299 0.00111105 0.00111194]\n", " [-0.00222305 0.001111 0.00111206]\n", " [-0.00222307 0.00111088 0.0011122 ]\n", " [-0.00222317 0.00111096 0.00111221]\n", " [-0.00222318 0.00111083 0.00111235]\n", " [-0.00222208 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] } ], "source": [ "if \"__main__\" == __name__:\n", " #数据（3，4）（batch_size, in_features）\n", " X, y = spiral_data(100, 3)#每个类别100个数据，3个类别就是300\n", " layer1 = Linear(2, 5)\n", " layer2 = Linear(5, 3)\n", " layer1.forward(X)\n", " act1 = Relu()\n", " act1.forward(layer1.outputs)\n", " layer2.forward(act1.outputs)\n", " act2 = Softmax()\n", " act2.forward(layer2.outputs)\n", " loss = CategoricalCrossEntropy()\n", " dvalues = loss.forward(act2.outputs, y)\n", " loss.backward(act2.outputs, y)\n", " print(loss.dinputs.shape)\n", " act2.backward(loss.dinputs)\n", " print(act2.dinputs)\n", "# cost = loss.calculate(act2.outputs, y)\n", "# print(cost)\n", "# acc = Accuracy()\n", "# accuracy = acc.forward(act2.outputs, y)\n", "# print(accuracy)" ] }, { "cell_type": "code", "execution_count": null, "id": "c588b453", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 5 }