{"id":356,"date":"2024-10-23T09:03:53","date_gmt":"2024-10-23T01:03:53","guid":{"rendered":"https:\/\/www.bertzzz-horizon.xyz\/?p=356"},"modified":"2024-10-23T09:51:00","modified_gmt":"2024-10-23T01:51:00","slug":"%e7%ae%80%e7%ae%80%e5%8f%88%e5%8d%95%e5%8d%95%e7%9a%84%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%ef%bc%881%ef%bc%89-%e5%8f%8d%e5%90%91%e4%bc%a0%e6%92%ad","status":"publish","type":"post","link":"https:\/\/www.bertzzz-horizon.xyz\/?p=356","title":{"rendered":"\u7b80\u7b80\u53c8\u5355\u5355\u7684\u795e\u7ecf\u7f51\u7edc\uff081\uff09-\u53cd\u5411\u4f20\u64ad"},"content":{"rendered":"\n

<\/p>\n\n\n\n

\u65e2\u7136\u6709\u53cd\u5411\u4f20\u64ad\uff0c\u5c31\u8981\u5148\u6765\u8bf4\u8bf4\u524d\u5411\u4f20\u64ad\uff1b\u6211\u4eec\u53ef\u4ee5\u7528\u5982\u4e0b\u5f0f\u5b50\u8868\u793a\u3002<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[y = \sigma(Wx + b)\]\"<\/p><\/p>\n\n\n\n

\u5176\u4e2d\"W\"\u662f\u6743\u91cd\u77e9\u9635\uff1b\"x\"\u662f\u8f93\u5165\u5411\u91cf\uff1b\"b\"\u662f\u504f\u7f6e\u5411\u91cf\uff1b\"\sigma\"\u662f\u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n\n\n\n

\u5176\u6b21\uff0c\u4e3a\u4e86\u68c0\u67e5\u6a21\u578b\u7684\u8868\u73b0\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u635f\u5931\u51fd\u6570\u6765\u8ba1\u7b97\u635f\u5931\uff0c\u6bd4\u5982\u5229\u7528MSE\uff1a<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\text{Loss} = \frac{1}{n} \sum_{i=1}^{n} (y_{true}^{(i)} - y_{pred}^{(i)})^2\]\"<\/p><\/p>\n\n\n\n

\u6709\u4e86\u8fd9\u4e9b\uff0c\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u6765\u8bf4\u8bf4\u53cd\u5411\u4f20\u64ad\u4e86\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u4ec0\u4e48\u662f\u53cd\u5411\u4f20\u64ad\uff1f<\/p>\n\n\n\n

\u6211\u4eec\u8981\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5173\u4e8e\u6743\u91cd\u4e0e\u504f\u5dee\u7684\u68af\u5ea6\uff0c\u6765\u5141\u8bb8\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u8fdb\u884c\u66f4\u65b0\u3002\u542c\u8d77\u6765\u5f88\u5947\u602a\u7684\u8bdd\u6ca1\u5173\u7cfb\uff0c\u7ee7\u7eed\u770b\u4e0b\u9762\u7684\u5f0f\u5b50\u5427\u3002<\/p>\n\n\n\n

\u8ba1\u7b97\u635f\u5931\u68af\u5ea6\uff1a<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\frac{\partial \text{Loss}}{\partial y} = -\frac{2}{n}(y_{true} - y_{pred})\]\"<\/p><\/p>\n\n\n\n

\u76f8\u5bf9\u4e8e\u6743\u91cd\u7684\u68af\u5ea6\uff1a<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\frac{\partial y}{\partial W} = \frac{\partial y}{\partial z} \cdot \frac{\partial z}{\partial W}\]\"<\/p><\/p>\n\n\n\n

\u5176\u4e2d\"z = Wx + b\"\uff0c\u4e14<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\frac{\partial y}{\partial z} = \sigma'(z) = \sigma(z)(1 - \sigma(z))\]\"<\/p><\/p>\n\n\n\n

\u4ee5\u53ca<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\frac{\partial z}{\partial W} = x\]\"<\/p><\/p>\n\n\n\n

\u8fdb\u884c\u4e86\u8fd9\u4e9b\u8ba1\u7b97\u4e4b\u540e\uff0c\u6700\u7ec8\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6743\u91cd\u8fdb\u884c\u66f4\u65b0\uff08\"\eta\"\u662f\u5b66\u4e60\u7387\uff09\uff1a<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[W_{\text{new}} = W - \eta \frac{\partial \text{Loss}}{\partial W}\]\"<\/p><\/p>\n\n\n\n

\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u5b8c\u6210\u4e86\u53cd\u5411\u4f20\u64ad\u3002\u539f\u7406\u5f88\u7b80\u5355\uff0c\u4e00\u53e5\u8bdd\u6982\u62ec\u5c31\u662f\u201c\u4ece\u9519\u8bef\u4e2d\u5b66\u4e60\u5e76\u6539\u8fdb\u201d\u3002\u65e2\u7136\u7406\u8bba\u5b58\u5728\uff0c\u90a3\u4e48\u5b9e\u8df5\u5f00\u59cb\uff0c\u8ba9\u6211\u4eec\u624b\u6413\u4e00\u4e2a\u53cd\u5411\u4f20\u64ad\u5427\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u5b9a\u4e49\u4e00\u4e2aTensor\u7c7b\u3002<\/p>\n\n\n\n

class Tensor:\n    def __init__(self, data, requires_grad=False):\n        self.data = np.array(data)\n        self.requires_grad = requires_grad\n        self.grad = None\n        self._backward = None\n\n    def backward(self):\n        if self._backward is not None:\n            self._backward()\n\n    def zero_grad(self):\n        self.grad = None<\/code><\/pre>\n\n\n\n
\u7136\u540e\uff0c\u5b9a\u4e49\"\text{Sigmoid}\"\u51fd\u6570\u4ee5\u53ca\u5b83\u7684\u5bfc\u6570\uff08\u7b80\u5316\u5f62\u5f0f\uff09\uff08\"\text{Sigmoid}\"\u51fd\u6570\u5c31\u662f\u6211\u4eec\u4e0a\u9762\u63d0\u5230\u7684\u6fc0\u6d3b\u51fd\u6570\uff09\u3002<\/p>\n\n\n\n
def sigmoid(x):\n    return 1 \/ (1 + np.exp(-x))\n\ndef sigmoid_derivative(x):\n    return x * (1 - x)<\/code><\/pre>\n\n\n\n
\u4e4b\u540e\uff0c\u5b9a\u4e49Layer\u7c7b\uff0c\u6211\u4eec\u5728\u91cc\u9762\u5c01\u88c5\u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u4e2a\u5c42\u7684\u529f\u80fd\u3002<\/p>\n\n\n\n
class Layer:\n\n    # \u968f\u673a\u521d\u59cb\u5316\u5c42\u7684\u6743\u91cd\u4e0e\u504f\u5dee\n    def __init__(self, input_size, output_size):\n        self.weights = np.random.rand(input_size, output_size)\n        self.bias = np.random.rand(output_size)\n\n    def forward(self, input_tensor):\n        self.input = input_tensor.data\n        self.output = sigmoid(np.dot(self.input, self.weights) + self.bias)\n\n        # \u4fdd\u5b58\u53cd\u5411\u51fd\u6570\n        def backward():\n            self.grad_input = np.dot(self.output * (1 - self.output), self.weights.T) * input_tensor.grad\n            self.grad_weights = np.dot(self.input.T, self.output * (1 - self.output))\n            self.grad_bias = np.sum(self.output * (1 - self.output), axis=0)\n\n            if input_tensor.requires_grad:\n                input_tensor.grad = self.grad_input\n\n        self._backward = backward\n        return Tensor(self.output, requires_grad=False)\n<\/code><\/pre>\n\n\n\n
\u5176\u4e2d\u7684\u4e09\u4e2a\u68af\u5ea6\uff1a<\/p>\n\n\n\n
grad_input\u662f\u8f93\u5165\u68af\u5ea6\uff0c\u8ba1\u7b97\u8f93\u5165\u5bf9\u8f93\u51fa\u7684\u5f71\u54cd\uff0c\u7528\u4e8e\u524d\u4e00\u5c42\u7684\u53cd\u5411\u4f20\u64ad\uff1bgrad_weights\u662f\u6743\u91cd\u68af\u5ea6\uff0c\u8ba1\u7b97\u6bcf\u4e2a\u6743\u91cd\u5e94\u6839\u636e\u8f93\u51fa\u7684\u8bef\u5dee\u6539\u53d8\u591a\u5c11\uff1b\u5728grad_bias\u5c06\u504f\u5dee\u7684\u68af\u5ea6\u76f8\u52a0\u3002\u5982\u679cinput_tensor\u9700\u8981\u68af\u5ea6\uff0c\u5c31\u4f1a\u76f8\u5e94\u5730\u66f4\u65b0\u3002<\/p>\n\n\n\n
\u6700\u540e\uff0c\u5b9a\u4e49NeuralNetwork\u7c7b\u3002<\/p>\n\n\n\n
class NeuralNetwork:\n    def __init__(self, input_size, output_size):\n        self.layer = Layer(input_size, output_size)\n\n    def forward(self, x):\n        return self.layer.forward(x)\n\n    def backward(self, loss):\n        loss.backward()\n        # \u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0\u6743\u91cd\u4e0e\u504f\u5dee\n        self.layer.weights -= 0.1 * self.layer.grad_weights\n        self.layer.bias -= 0.1 * self.layer.grad_bias\n<\/code><\/pre>\n\n\n\n
\u5230\u6b64\u4e3a\u6b62\uff0c\u6211\u4eec\u5c31\u5b8c\u6210\u4e86\u6240\u6709\u7684\u5de5\u4f5c\u4e86\u3002\u603b\u7ed3\u4e00\u4e0b\u5c31\u662f\uff0c\u6211\u4eec\u7528\u524d\u5411\u4f20\u9012\u8f93\u5165\u6570\u636e\uff0c\u6d41\u7ecf\u795e\u7ecf\u7f51\u7edc\uff0c\u4f7f\u7528\u5c42\u548c\u6fc0\u6d3b\u51fd\u6570\"\text{Sigmoid}\"\u4ea7\u751f\u8f93\u51fa\uff1b\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u635f\u5931\u5e76\u901a\u8fc7\u7f51\u7edc\u53cd\u5411\u4f20\u64ad\uff0c\u518d\u6839\u636e\u8ba1\u7b97\u51fa\u7684\u68af\u5ea6\u66f4\u65b0\u6743\u91cd\u548c\u504f\u5dee\uff0c\u6765\u5c3d\u53ef\u80fd\u51cf\u5c11\u9884\u6d4b\u7684\u8bef\u5dee\u3002\u8fd9\u79cd\u8fed\u4ee3\u5bf9\u4e8e\u6a21\u578b\u7684\u8bad\u7ec3\u81f3\u5173\u91cd\u8981\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u65e2\u7136\u6709\u53cd\u5411\u4f20\u64ad\uff0c\u5c31\u8981\u5148\u6765\u8bf4\u8bf4\u524d\u5411\u4f20\u64ad\uff1b\u6211\u4eec\u53ef\u4ee5\u7528\u5982\u4e0b\u5f0f\u5b50\u8868\u793a\u3002     \u5176\u4e2d\u662f\u6743\u91cd\u77e9\u9635\uff1b\u662f […]<\/p>\n","protected":false},"author":1,"featured_media":375,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[9],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.bertzzz-horizon.xyz\/wordpress\/wp-content\/uploads\/2024\/10\/Switch_Launch_NA_eShop_ESRB.jpg","_links":{"self":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/356"}],"collection":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=356"}],"version-history":[{"count":12,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/356\/revisions"}],"predecessor-version":[{"id":376,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/356\/revisions\/376"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/media\/375"}],"wp:attachment":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}