{"id":9229,"date":"2024-03-23T00:20:11","date_gmt":"2024-03-22T16:20:11","guid":{"rendered":"\/?p=9229"},"modified":"2024-04-08T01:46:05","modified_gmt":"2024-04-07T17:46:05","slug":"%e6%89%8b%e6%90%93%e7%9a%84%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c-%e6%b7%b1%e5%85%a5%e6%b5%85%e5%87%ba%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e4%b8%8e%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"\/?p=9229","title":{"rendered":"\u624b\u6413\u7684\u795e\u7ecf\u7f51\u7edc-\u6df1\u5165\u6d45\u51fa\u795e\u7ecf\u7f51\u7edc\u4e0e\u6df1\u5ea6\u5b66\u4e60"},"content":{"rendered":"

\"image-20240323001648036\"<\/p>\n

\"image-20240323001842064\"<\/p>\n

network.py<\/h2>\n
import random\n\n# Third-party libraries\nimport numpy as np\n\nclass Network(object):\n    def __init__(self, sizes):\n        self.num_layers = len(sizes)\n        self.size = sizes\n        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]\n        self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])]\n\n    def feedforward(self, a):\n        """\u82e5a\u4e3a\u8f93\u5165\uff0c\u5219\u8fd4\u56de\u8f93\u51fa"""\n        for b, w in zip(self.biases, self.weights):\n            a = sigmoid(np.dot(w, a) + b)\n        return a\n\n    def SGD(self, training_data, epochs, mini_batch_size, eta,\n            test_data=None):\n        """\n        \u4f7f\u7528\u5c0f\u6279\u91cf\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u3002training_data \u662f\u7531\u8bad\u7ec3\u8f93\u5165\u548c\u76ee\u6807\u8f93\u51fa\u7684\u5143\u7ec4(x, y)\n        \u7ec4\u6210\u7684\u5217\u8868\u3002\u5176\u4ed6\u975e\u53ef\u9009\u53c2\u6570\u5bb9\u6613\u7406\u89e3\u3002\u5982\u679c\u63d0\u4f9b\u4e86 test_data\uff0c\u90a3\u4e48\u795e\u7ecf\u7f51\u7edc\u4f1a\u5728\u6bcf\u8f6e\u8bad\u7ec3\u7ed3\u675f\u540e\u7528\n        \u6d4b\u8bd5\u6570\u636e\u8fdb\u884c\u8bc4\u4f30\uff0c\u5e76\u8f93\u51fa\u90e8\u5206\u8fdb\u5ea6\u4fe1\u606f\u3002\u8fd9\u5bf9\u4e8e\u8ffd\u8e2a\u8fdb\u5ea6\u5f88\u6709\u7528\uff0c\u4e0d\u8fc7\u4f1a\u5ef6\u957f\u6574\u4f53\u5904\u7406\u65f6\u95f4\u3002\n        :param training_data:\n        :param epochs:\u8bad\u7ec3\u8f6e\u6570,\u6574\u4e2a\u8bad\u7ec3\u6570\u636e\u96c6\u88ab\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5b8c\u6574\u5730\u8fed\u4ee3\u8bad\u7ec3\u7684\u6b21\u6570\n        :param mini_batch_size:\u91c7\u6837\u7684\u5c0f\u6279\u91cf\u6570\u636e\u7684\u5927\u5c0f\n        :param eta:"eta" \u901a\u5e38\u6307\u5b66\u4e60\u7387\u03b7\n        :param test_data:\n        :return:\n        """\n        if test_data: \n            n_test = len(test_data)\n        n = len(training_data)\n        for j in range(epochs):\n            random.shuffle(training_data)\n            mini_batches = [\n                training_data[k:k + mini_batch_size] for k in range(0, n, mini_batch_size)\n            ]\n            for mini_batch in mini_batches:\n                self.update_mini_batch(mini_batch, eta)\n            if test_data:\n                # \u6bcf\u4e00\u8f6e\u7684\u8bad\u7ec3\u8fc7\u7a0b\/\u7ed3\u679c\n                print("Epoch {0}: {1} \/ {2}".format(j, self.evaluate(test_data), n_test))\n            else:\n                print("Epoch {0} complete".format(j))\n    def update_mini_batch(self, mini_batch, eta):\n        """\u5bf9\u4e00\u4e2a\u5c0f\u6279\u91cf\u5e94\u7528\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u548c\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u6765\u66f4\u65b0\u795e\u7ecf\u7f51\u7edc\u7684\u6743\u91cd\u548c\u504f\u7f6e\u3002mini_batch \u662f\u7531\u82e5\u5e72\n        \u5143\u7ec4(x, y)\u7ec4\u6210\u7684\u5217\u8868\uff0ceta \u662f\u5b66\u4e60\u7387\u3002"""\n        nabla_b = [np.zeros(b.shape) for b in self.biases]\n        nabla_w = [np.zeros(w.shape) for w in self.weights]\n        for x, y in mini_batch:\n            delta_nabla_b, delta_nabla_w = self.backprop(x, y)\n            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]\n            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]\n        self.weights = [w-(eta\/len(mini_batch))*nw\n                        for w, nw in zip(self.weights, nabla_w)]\n        self.biases = [b-(eta\/len(mini_batch))*nb\n                       for b, nb in zip(self.biases, nabla_b)]\n    def backprop(self, x, y):\n        """\u8fd4\u56de\u4e00\u4e2a\u8868\u793a\u4ee3\u4ef7\u51fd\u6570 C_x \u68af\u5ea6\u7684\u5143\u7ec4(nabla_b, nabla_w)\u3002nabla_b \u548c nabla_w \u662f\u4e00\u5c42\u63a5\u4e00\u5c42\u7684\n        numpy \u6570\u7ec4\u7684\u5217\u8868\uff0c\u7c7b\u4f3c\u4e8e self.biases \u548c self.weights\u3002"""\n        nabla_b = [np.zeros(b.shape) for b in self.biases]\n        nabla_w = [np.zeros(w.shape) for w in self.weights]\n        # \u524d\u9988\n        activation = x\n        activations = [x] # \u4e00\u5c42\u63a5\u4e00\u5c42\u5730\u5b58\u653e\u6240\u6709\u6fc0\u6d3b\u503c\n        zs = [] #  \u4e00\u5c42\u63a5\u4e00\u5c42\u5730\u5b58\u653e\u6240\u6709 z \u5411\u91cf\n        for b, w in zip(self.biases, self.weights):\n            z = np.dot(w, activation)+b\n            zs.append(z)\n            activation = sigmoid(z)\n            activations.append(activation)\n        # \u53cd\u5411\u4f20\u64ad\n        delta = self.cost_derivative(activations[-1], y) * \\\n            sigmoid_prime(zs[-1])\n        nabla_b[-1] = delta\n        nabla_w[-1] = np.dot(delta, activations[-2].transpose())\n        """\u6ce8\u610f\uff0c\u4e0b\u9762\u5faa\u73af\u4e2d\u7684\u53d8\u91cf l \u548c\u7b2c 2 \u7ae0\u7684\u5f62\u5f0f\u7a0d\u6709\u4e0d\u540c\u3002\u8fd9\u91cc l = 1 \u8868\u793a\u6700\u540e\u4e00\u5c42\u795e\u7ecf\u5143\uff0cl = 2 \u5219\n        \u8868\u793a\u5012\u6570\u7b2c\u4e8c\u5c42\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\u8fd9\u662f\u5bf9\u4e66\u4e2d\u65b9\u5f0f\u7684\u91cd\u7f16\u53f7\uff0c\u65e8\u5728\u5229\u7528 Python \u5217\u8868\u7684\u8d1f\u7d22\u5f15\u529f\u80fd\u3002"""\n        for l in range(2, self.num_layers):\n            z = zs[-l]\n            sp = sigmoid_prime(z)\n            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp\n            nabla_b[-l] = delta\n            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())\n        return (nabla_b, nabla_w)\n\n    def evaluate(self, test_data):\n        """\u8fd4\u56de\u6d4b\u8bd5\u8f93\u5165\u4e2d\u795e\u7ecf\u7f51\u7edc\u8f93\u51fa\u6b63\u786e\u7ed3\u679c\u7684\u6570\u76ee\u3002\u6ce8\u610f\uff0c\u8fd9\u91cc\u5047\u8bbe\u795e\u7ecf\u7f51\u7edc\u8f93\u51fa\u7684\u662f\u6700\u540e\u4e00\u5c42\u6709\u7740\n        \u6700\u5927\u6fc0\u6d3b\u503c\u7684\u795e\u7ecf\u5143\u7684\u7d22\u5f15\u3002"""\n        test_results = [(np.argmax(self.feedforward(x)), y)\n                        for (x, y) in test_data]\n        return sum(int(x == y) for (x, y) in test_results)\n\n    def cost_derivative(self, output_activations, y):\n        """\u8fd4\u56de\u5173\u4e8e\u8f93\u51fa\u6fc0\u6d3b\u503c\u7684\u504f\u5bfc\u6570\u7684\u5411\u91cf\u3002"""\n        return (output_activations-y)\n\ndef sigmoid(z):\n    """sigmoid \u51fd\u6570"""\n    return 1 \/ (1 + np.exp(-z))\ndef sigmoid_prime(z):\n    """sigmoid \u51fd\u6570\u7684\u5bfc\u6570"""\n    return sigmoid(z)*(1-sigmoid(z))\nif __name__ == '__main__':\n    import mnist_loader\n    training_data, validation_data, test_data = mnist_loader.load_data_wrapper()\n    net = Network([784, 30, 10])\n    net.SGD(training_data, 30, 10, 3.0, test_data=test_data)<\/code><\/pre>\n
\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n
Epoch 0: 8285 \/ 10000\nEpoch 1: 8426 \/ 10000\nEpoch 2: 8465 \/ 10000\nEpoch 3: 8514 \/ 10000\nEpoch 4: 8508 \/ 10000\nEpoch 5: 8563 \/ 10000\nEpoch 6: 8549 \/ 10000\nEpoch 7: 8561 \/ 10000\nEpoch 8: 8565 \/ 10000\nEpoch 9: 8614 \/ 10000\nEpoch 10: 8580 \/ 10000\nEpoch 11: 8594 \/ 10000\nEpoch 12: 8612 \/ 10000\nEpoch 13: 8624 \/ 10000\nEpoch 14: 8597 \/ 10000\nEpoch 15: 8631 \/ 10000\nEpoch 16: 8619 \/ 10000\nEpoch 17: 8647 \/ 10000\nEpoch 18: 8631 \/ 10000\nEpoch 19: 8632 \/ 10000\nEpoch 20: 8634 \/ 10000\nEpoch 21: 8640 \/ 10000\nEpoch 22: 8627 \/ 10000\nEpoch 23: 8647 \/ 10000\nEpoch 24: 8637 \/ 10000\nEpoch 25: 8651 \/ 10000\nEpoch 26: 8626 \/ 10000\nEpoch 27: 8638 \/ 10000\nEpoch 28: 8657 \/ 10000\nEpoch 29: 8651 \/ 10000<\/code><\/pre>\n
mnist_loader.py<\/h2>\n
"""\nmnist_loader\n~~~~~~~~~~~~\n\u4e00\u4e2a\u52a0\u8f7d MNIST \u56fe\u50cf\u6570\u636e\u7684\u5e93\u3002\u5173\u4e8e\u8fd4\u56de\u7684\u6570\u636e\u7ed3\u6784\u7684\u7ec6\u8282\uff0c\u53c2\u89c1 load_data \u548c load_data_wrapper \u7684\u6587\u6863\u5b57\u7b26\n\u4e32\u3002\u5728\u5b9e\u8df5\u4e2d\uff0cload_data_wrapper \u901a\u5e38\u662f\u795e\u7ecf\u7f51\u7edc\u4ee3\u7801\u8c03\u7528\u7684\u51fd\u6570\u3002\n"""\n#### \u5e93\n# \u6807\u51c6\u5e93\nimport pickle as pk\nimport gzip\n# \u7b2c\u4e09\u65b9\u5e93\nimport numpy as np\n\ndef load_data():\n    """\u4ee5\u5143\u7ec4\u5f62\u5f0f\u8fd4\u56de MNIST \u6570\u636e\uff0c\u5305\u542b\u8bad\u7ec3\u6570\u636e\u3001\u9a8c\u8bc1\u6570\u636e\u548c\u6d4b\u8bd5\u6570\u636e\u3002\n    \u8fd4\u56de\u7684 training_data \u662f\u6709\u4e24\u9879\u7684\u5143\u7ec4\uff0c\u7b2c\u4e00\u9879\u5305\u542b\u5b9e\u9645\u7684\u8bad\u7ec3\u56fe\u50cf\uff0c\u662f\u4e00\u4e2a\u6709 50 000 \u9879\u7684 NumPy ndarray\u3002\n    \u6bcf\u4e00\u9879\u662f\u4e00\u4e2a\u6709\u7740 784 \u4e2a\u503c\u7684 NumPy ndarray\uff0c\u4ee3\u8868\u4e00\u5e45 MNIST \u56fe\u50cf\u4e2d\u7684 28\u00d728=784 \u50cf\u7d20\u3002\n    \u5143\u7ec4 training_data \u7684\u7b2c\u4e8c\u9879\u662f\u4e00\u4e2a\u5305\u542b 50 000 \u9879\u7684 NumPy ndarray\uff0c\u8fd9\u4e9b\u9879\u5bf9\u5e94\u4e8e\u5143\u7ec4\u7b2c\u4e00\u9879\u4e2d\u5305\u542b\u7684\n    \u56fe\u50cf\u6570\u5b57\uff080\uff5e9\uff09\u3002\n    validation_data \u548c test_data \u7c7b\u4f3c\uff0c\u4f46\u56fe\u50cf\u4ec5\u6709 10 000 \u5e45\u3002\n    \u8fd9\u79cd\u6570\u636e\u683c\u5f0f\u5f88\u597d\uff0c\u4f46\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u5bf9 training_data \u7684\u683c\u5f0f\u8fdb\u884c\u5fae\u8c03\u5f88\u6709\u7528\u3002\u8fd9\u901a\u8fc7\u5c01\u88c5\u51fd\u6570\n    load_data_wrapper()\u5b8c\u6210\uff0c\u53c2\u89c1\u4e0b\u9762\u7684\u4ee3\u7801\u3002"""\n    f = gzip.open(u'..\/data\/mnist.pkl.gz', 'rb')\n    training_data, validation_data, test_data = pk.load(f, encoding='latin1')\n    f.close()\n    return (training_data, validation_data, test_data)\ndef load_data_wrapper():\n    """\u8fd4\u56de\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b(training_data, validation_data, test_data)\u3002\u57fa\u4e8e load_data\uff0c\u4f46\u662f\u8fd9\u4e2a\u683c\u5f0f\u66f4\n    \u4fbf\u4e8e\u5b9e\u73b0\u795e\u7ecf\u7f51\u7edc\u3002\n    training_data \u662f\u4e00\u4e2a\u5305\u542b 50 000 \u4e2a\u4e8c\u5143\u7ec4(x, y)\u7684\u5217\u8868\uff0c\u5176\u4e2d x \u662f\u4e00\u4e2a 784 \u7ef4\u7684 NumPy ndarray\uff0c\u5bf9\u5e94\u8f93\u5165\n    \u56fe\u50cf\uff1by \u662f\u4e00\u4e2a 10 \u7ef4\u7684 NumPy ndarray\uff0c\u8868\u793a\u5bf9\u5e94 x \u6b63\u786e\u6570\u5b57\u7684\u5355\u4f4d\u5411\u91cf\u3002\n    validation_data \u548c test_data \u5404\u5305\u542b 10 000 \u4e2a\u4e8c\u5143\u7ec4(x, y)\uff0c\u5176\u4e2d x \u662f\u4e00\u4e2a\u5305\u542b\u8f93\u5165\u56fe\u50cf\u7684 784 \u7ef4\u7684 NumPy\n    ndarray\uff1by \u662f\u76f8\u5e94\u7684\u5206\u7c7b\uff0c\u5bf9\u5e94\u4e8e x \u7684\u503c\uff08\u6574\u6570\uff09\u3002\n    \u663e\u7136\uff0c\u8fd9\u610f\u5473\u7740\u8bad\u7ec3\u6570\u636e\u3001\u9a8c\u8bc1\u6570\u636e\u548c\u6d4b\u8bd5\u6570\u636e\u91c7\u7528\u4e0d\u540c\u7684\u683c\u5f0f\u3002\u8fd9\u4e9b\u683c\u5f0f\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\u4ee3\u7801\u6765\u8bf4\u662f\u6700\n    \u65b9\u4fbf\u7684\u3002"""\n    tr_d, va_d, te_d = load_data()\n    training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]\n    training_results = [vectorized_result(y) for y in tr_d[1]]\n    training_data = list(zip(training_inputs, training_results))\n    validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]\n    validation_data = list(zip(validation_inputs, va_d[1]))\n    test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]\n    test_data = list(zip(test_inputs, te_d[1]))\n    return (training_data, validation_data, test_data)\ndef vectorized_result(j):\n    """\u8fd4\u56de\u4e00\u4e2a 10 \u7ef4\u7684\u5355\u4f4d\u5411\u91cf\uff0c\u5728\u7b2c j \u4e2a\u4f4d\u7f6e\u4e3a 1.0\uff0c\u5176\u4f59\u5747\u4e3a 0\u3002\u8fd9\u53ef\u4ee5\u7528\u4e8e\u5c06\u4e00\u4e2a\u6570\u5b57\uff080\uff5e9\uff09\u8f6c\u6362\u6210\n    \u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u4e2a\u5bf9\u5e94\u7684\u76ee\u6807\u8f93\u51fa\u3002"""\n    e = np.zeros((10, 1))\n    e[j] = 1.0\n    return e<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
network.py import random # Third-party libraries import numpy as np    \u2026 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[254],"tags":[],"_links":{"self":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9229"}],"collection":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9229"}],"version-history":[{"count":3,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9229\/revisions"}],"predecessor-version":[{"id":9240,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9229\/revisions\/9240"}],"wp:attachment":[{"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9229"},{"taxonomy":"post_tag","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}