{"id":2375,"date":"2026-07-30T16:59:22","date_gmt":"2026-07-30T08:59:22","guid":{"rendered":"http:\/\/fnos:8192\/?p=2375"},"modified":"2026-07-31T00:51:08","modified_gmt":"2026-07-30T16:51:08","slug":"%e8%b7%9f%e7%9d%80-andrej-karpathy-%e9%9b%b6%e5%9f%ba%e7%a1%80%e5%ad%a6%e4%b9%a0%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c-%e5%8f%8d%e5%90%91%e4%bc%a0%e6%92%ad-%e5%ad%a6%e4%b9%a0%e7%ac%94%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/blog.zjml.life\/?p=2375","title":{"rendered":"\u8ddf\u7740 Andrej Karpathy \u96f6\u57fa\u7840\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc \u53cd\u5411\u4f20\u64ad \u5b66\u4e60\u7b14\u8bb0"},"content":{"rendered":"\n

\u7b14\u8005\u6700\u8fd1\u8ddf\u7740Andrej Karpathy \u96f6\u57fa\u7840\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u7684\u89c6\u9891\u8bfe\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u987a\u4fbf\u628a\u5b66\u4e60\u7b14\u8bb0\u53d1\u5728\u8fd9\u91cc\u3002Andrej Karpathy\u662f\u795e\u7ecf\u7f51\u7edc\u9886\u57df\u7684\u5927\u4f6c\uff0c\u4ed6\u5bf9Python\u7684\u4f7f\u7528\u4e86\u5982\u6307\u638c\uff0c\u4f46\u662f\u7b14\u8005\u5176\u5b9e\u5bf9Python\u7684\u638c\u63e1\u4e0d\u662f\u7279\u522b\u7684\u719f\u7ec3\u3002\u867d\u7136\u8bf4\u4e4b\u524d\u4e5f\u5199\u8fc7\u4e00\u4e9b\u722c\u866b\uff0c\u4f46\u662f\u7b14\u8005\u6700\u8fd1\u4e24\u5e74\u90fd\u662f\u5728\u505aJava\u5f00\u53d1\u3002\u56e0\u6b64\u7b14\u8005\u5199\u7684\u4ee3\u7801\u53ef\u80fd\u66f4\u901a\u4fd7\u6613\u61c2\u4e00\u4e9b\u3002\u4e5f\u4e0d\u4f1a\u50cfAndrej Karpathy\u4e00\u6837\u4f7f\u7528\u5f88\u591a\u7684\u4ee3\u7801\u4e0a\u7684\u7b80\u5199\uff0c\u53ef\u80fd\u4e5f\u66f4\u901a\u4fd7\u4e00\u4e9b\u5427\u3002\u53e6\u5916Andrej Karpathy\u53d1\u5728GitHub\u4e0a\u7684\u4ee3\u7801\u6ca1\u6709\u751f\u6210\u56fe\u793a\u7684\u76f8\u5173\u4ee3\u7801\uff0c\u7b14\u8005\u5728\u8fd9\u91cc\u8865\u4e0a\u4e86\u3002<\/p>\n\n\n\n

\u51c6\u5907\u5de5\u4f5c<\/h2><\/div>\n\n\n\n

\u5b89\u88c5Python
\u5b89\u88c5Graphviz<\/a>\uff08\u751f\u6210\u56fe\u8868\uff09
\u89c2\u770b\u89c6\u9891\u8bfe\u7a0b<\/a><\/p>\n\n\n\n

\u6b63\u5f0f\u5f00\u59cb\u7f16\u5199\u4ee3\u7801<\/h2><\/div>\n\n\n\n

\u7f16\u5199\u7ed8\u5236\u56fe\u8868\u7684draw_dot.py<\/h3><\/div>\n\n\n\n

\u8fd9\u4e2a\u811a\u672c\u63d0\u4f9b\u4e86draw_dot(root)\u65b9\u6cd5\uff0c\u5c06\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u7f16\u5199\u7684\u81ea\u5b9a\u4e49\u7c7bValue\u8f93\u5165\u4e4b\u540e\uff0c\u5b83\u53ef\u4ee5\u751f\u6210\u7ed3\u6784\u56fe\u6587\u4ef6<\/p>\n\n\n\n

from graphviz import Digraph\nimport os\nos.environ['PATH'] += os.pathsep + r'C:\\Program Files\\Graphviz\\bin'\ndef trace(root):\n    nodes, edges = set(), set()\n    def build(v):\n        if v not in nodes:\n            nodes.add(v)\n            for child in v._prev:\n                edges.add((child, v))\n                build(child)\n    build(root)\n    return nodes, edges\n\ndef draw_dot(root):\n    dot = Digraph(format=\"png\", graph_attr={\"rankdir\":\"LR\",\"dpi\": \"300\"})\n\n    nodes, edges = trace(root)\n    for node in nodes:\n        uid = str(id(node))\n        dot.node(name = uid, label = \"{ %s | data %.4f | grad %.4f }\" % (node.label, node.data, node.grad), shape='record')\n        if node._op:\n            dot.node(name = uid + node._op, label = node._op)\n            dot.edge(uid + node._op, uid)\n\n    for node1, node2 in edges:\n        dot.edge(str(id(node1)), str(id(node2)) + node2._op)\n\n    dot.render('complex_graph', view=True)\n    return dot\n<\/code><\/pre>\n\n\n\n
\u81ea\u5b9a\u4e49Value\u7c7b<\/h3><\/div>\n\n\n\n
\u6211\u4eec\u9700\u8981\u7f16\u5199\u4e00\u4e2a\u81ea\u5b9a\u4e49Value\u7c7b\u5e76\u4e14\u4e3a\u5b83\u63d0\u4f9b\u53cd\u5411\u4f20\u64ad\u7684\u65b9\u6cd5\u3002\u5bf9\u4e8e\u4e0d\u540c\u7684\u8fd0\u7b97\uff0c\u9700\u8981\u6839\u636e\u5176\u6c42\u5bfc\u516c\u5f0f\u5b9e\u73b0\u4e0d\u540c\u7684\u53cd\u5411\u4f20\u64ad\u65b9\u6cd5\u3002\u8fd9\u4e2aValue\u7c7b\u7528\u4e8e\u7ec4\u5efa\u795e\u7ecf\u5143\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u8fd8\u4f1a\u7f16\u5199\u795e\u7ecf\u5143\u3002<\/p>\n\n\n\n
import random\n\nclass Value:\n    def __init__(self, data, _children=(), _op=\"\", label=\"\"):\n        self.data = data\n        self.grad = 0 # \u68af\u5ea6\n        self._backward = lambda : None # \u53cd\u5411\u4f20\u64ad\u51fd\u6570\uff0c\u9ed8\u8ba4\u4e3a\u7a7a\uff0c\u8fd0\u7b97\u4f1a\u8fdb\u884c\u66ff\u6362\n        self._prev = set(_children) # \u5176\u5b69\u5b50\u8282\u70b9\n        self._op = _op # \u8fd0\u7b97\u7b26\n        self.label = label # \u8282\u70b9\u540d\u79f0\n\n    # \u52a0\u6cd5\n    def __add__(self, other):\n        if not isinstance(other, Value):\n            other = Value(other)\n        out = Value(self.data + other.data, (self, other), \"+\")\n\n        def _backward():\n            self.grad += out.grad\n            other.grad += out.grad\n\n        out._backward = _backward\n        return out\n    # \u4e58\u6cd5\n    def __mul__(self, other):\n        other = other if isinstance(other, Value) else Value(other)\n        out = Value(self.data * other.data, (self, other), \"*\")\n\n        def _backward():\n            self.grad += other.data * out.grad\n            other.grad += self.data * out.grad\n        out._backward = _backward\n        return out\n\n    # \u5e42\u8fd0\u7b97\n    def __pow__(self, other):\n        # \u53ea\u652f\u6301int float \u5e42\u6307\u6570\n        assert isinstance(other, (int, float))\n        out = Value(self.data**other, (self,), f\"**{other}\")\n\n        def _backward():\n            self.grad += ( other * self.data ** (other -1)) * out.grad\n\n        out._backward = _backward\n        return out\n\n    def relu(self):\n        out = Value(0 if self.data < 0 else self.data, (self,),\"ReLU\")\n        def _backward():\n            if out.data > 0:\n                self.grad = self.grad + out.grad\n            else:\n                self.grad = self.grad\n\n        out._backward = _backward\n        return out\n\n    # \u53cd\u5411\u4f20\u64ad\u5165\u53e3\u51fd\u6570\n    def backward(self):\n        \"\"\"\n        \u6267\u884c\u6d41\u7a0b\u793a\u4f8b\uff1a\n        \u5047\u8bbe\u8ba1\u7b97\u56fe\uff1aa \u2192 b \u2192 c \u2192 out\n        \u62d3\u6251\u6392\u5e8f\u540e\uff1atopo = [a, b, c, out]\n        \u53cd\u5411\u4f20\u64ad\u987a\u5e8f\uff1areversed(topo) = [out, c, b, a]\n        \"\"\"\n        # \u5148\u62d3\u6251\u6392\u5e8f\n        topo = []\n        visited = set()\n\n        def build_top(v):\n            if v not in visited:\n                visited.add(v)\n                for child in v._prev:\n                    build_top(child)\n                topo.append(v)\n\n        build_top(self)\n\n        # \u6839\u636e\u62d3\u6251\u6392\u5e8f\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\n        self.grad = 1 # \u6839\u8282\u70b9\u8bbe\u7f6e\u4e3a1\n        for v in reversed(topo):\n            v._backward()\n\n    # \u53d6\u8d1f\u6570\u8fd0\u7b97\n    def __neg__(self):\n        return self * -1\n\n    # \u53cd\u5411\u52a0\u6cd5 other + self\n    def __radd__(self, other):\n        return self + other\n\n    # \u51cf\u6cd5\n    def __sub__(self, other):\n        return self + (-other)\n\n    # \u53cd\u5411\u51cf\u6cd5 other - self\n    def __rsub__(self, other):\n        return other + (-self)\n\n    # \u53cd\u5411\u4e58\u6cd5 other * self\n    def __rmul__(self, other):\n        return self * other\n\n    # \u9664\u6cd5 self \/ other = self * (other ^ -1 )\n    def __truediv__(self, other):\n        return self * other ** -1\n\n    # \u53cd\u5411\u9664\u6cd5 other \/ self = other * (self ^ -1)\n    def __rtruediv__(self, other):\n        return other * self ** -1\n\n    # \u8c03\u8bd5\u8f93\u51fa\n    def __repr__(self):\n        return f\"Value{self.data}, grad={self.grad}\"<\/code><\/pre>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u5199\u4e00\u4e2amain.py\u6765\u9a8c\u8bc1\u4e00\u4e0b\uff1a<\/p>\n\n\n\n
from value import Value\nfrom draw_dot import draw_dot\n\na = Value(2, label=\"a\")\nb = Value(3, label=\"b\")\nc = a * b + a ** 2\nc.label = \"c\"\n# \u7528\u53cd\u5411\u4f20\u64ad\u65b9\u6cd5\u8ba1\u7b97\u68af\u5ea6\nc.backward()\ndraw_dot(c)<\/code><\/pre>\n\n\n\n
\u8fd0\u884c\u540e\u7ed3\u6784\u56fe\u5982\u4e0b\uff0c\u7b26\u5408\u9884\u671f\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u4fee\u6539\u4e00\u4e0bmain.py\uff0c\u6211\u60f3\u770b\u770bReLU\u7684\u4f5c\u7528\uff1a<\/p>\n\n\n\n
from value import Value\nfrom draw_dot import draw_dot\n\nx = Value(-2.0, label=\"x\")\ny = x.relu()\ny.backward()\ndraw_dot(y)<\/code><\/pre>\n\n\n\n
\u8fd0\u884c\u4e00\u4e0b\uff0c\u53ef\u4ee5\u770b\u5230\uff0c\u5f53X\u7684\u503c\u662f\u8d1f\u6570\u7684\u65f6\u5019\uff0c\u5b83\u5f80\u540e\u4f20\u7684data\u4f1a\u5f52\u96f6\u3002\u56e0\u6b64\uff0c\u5f53\u5b83\u7684data\u4e3a\u8d1f\u6570\u65f6\uff0c\u5b83\u7684\u68af\u5ea6\u662f0\uff0c\u56e0\u4e3a\u5b83\u5728\u6b63\u5411\u4f20\u64ad\u4e2d\u65e0\u6cd5\u5bf9\u540e\u7eed\u7684\u8282\u70b9\u4ea7\u751f\u4f5c\u7528\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u6211\u4eec\u4fee\u6539\u4e00\u4e0bmain.py\uff0c\u770b\u770bx\u4e3a\u6b63\u6570\u7684\u60c5\u51b5\uff1a<\/p>\n\n\n\n
from value import Value\nfrom draw_dot import draw_dot\n\nx = Value(2.0, label=\"x\")\ny = x.relu()\ny.backward()\ndraw_dot(y)<\/code><\/pre>\n\n\n\n
\u8fd0\u884c\u4e00\u4e0b\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u5f88\u660e\u663e\uff0c\u5f53X\u7684\u503c\u4e3a\u6b63\u6570\u7684\u65f6\u5019\uff0cReLU\u4e0d\u4f1a\u5bf9\u5176\u4ea7\u751f\u4efb\u4f55\u5f71\u54cd\u3002<\/p>\n\n\n\n
\u81ea\u5b9a\u4e49\u57fa\u7c7b\u4e0e\u795e\u7ecf\u5143<\/h3><\/div>\n\n\n\n
\u6211\u4eec\u5148\u8981\u5236\u5b9a\u4e00\u4e2a\u57fa\u7c7b\uff0c\u7136\u540e\u81ea\u5b9a\u4e49\u795e\u7ecf\u5143\uff0c\u8ba9\u6211\u4eec\u5f00\u59cb\u5199nn.py\uff1a<\/p>\n\n\n\n
\"\"\"\nModule (\u57fa\u7c7b)\n    \u2502\n    \u251c\u2500\u2500 Neuron(nin)      # \u5355\u795e\u7ecf\u5143: y = ReLU(w\u00b7x + b)\n    \u2502       \u2514\u2500\u2500 \u53c2\u6570: nin \u4e2a\u6743\u91cd + 1 \u4e2a\u504f\u7f6e\n    \u2502\n    \u251c\u2500\u2500 Layer(nin, nout) # \u5168\u8fde\u63a5\u5c42: nout \u4e2a\u795e\u7ecf\u5143\u5e76\u884c\n    \u2502       \u2514\u2500\u2500 \u53c2\u6570: nin\u00d7nout \u4e2a\u6743\u91cd + nout \u4e2a\u504f\u7f6e\n    \u2502\n    \u2514\u2500\u2500 MLP(nin, nouts)  # \u591a\u5c42\u611f\u77e5\u673a: \u591a\u4e2a Layer \u5806\u53e0\n            \u2514\u2500\u2500 \u53c2\u6570: \u6240\u6709 Layer \u53c2\u6570\u4e4b\u548c\n\"\"\"\nimport random\nfrom value import Value\n\n# \u57fa\u7c7b\nclass Module:\n    # \u8fd4\u56de\u6240\u6709\u53ef\u5b66\u4e60\u53c2\u6570\n    def parameters(self):\n        return []\n\n    # \u6e05\u9664\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\uff0c\u6bcf\u6b21\u8bad\u7ec3\u4e4b\u524d\u90fd\u9700\u8981\u5c06\u68af\u5ea6\u6e05\u96f6\uff0c\u7136\u540e\u518d\u53cd\u5411\u4f20\u64ad\uff0c\u83b7\u5f97\u68af\u5ea6\uff0c\u6700\u540e\u518d\u66f4\u65b0\u53c2\u6570\n    def zero_grad(self):\n        for p in self.parameters():\n            p.grad = 0\n\n# \u795e\u7ecf\u5143\nclass Neuron(Module):\n    def __init__(self, nin, nonlin=True):\n        \"\"\"\n        :param nin: \u8f93\u5165\u7279\u5f81\u7684\u7ef4\u5ea6\u3002\u8fd9\u4e2a\u5730\u65b9\u662f\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u91cd\u70b9\uff0c\n        \u5176\u524d\u4e00\u5c42\u6709\u51e0\u4e2a\u795e\u7ecf\u5143\uff0c\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u90fd\u8981\u8ddf\u540e\u4e00\u5c42\u7684\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u8fdb\u884c\u8fd0\u7b97\u3002\n        \u5047\u8bbe\u7b2c\u4e00\u5c42\u67095\u4e2a\u795e\u7ecf\u5143\uff0c\u90a3\u4e48\u5b83\u4eec\u5c31\u4f1a\u67095\u4e2a\u8f93\u51fa\uff0c\u8fd95\u4e2a\u8f93\u51fa\u8981\u8ddf\u7b2c\u4e8c\u5c42\u7684\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u4e2d\u7684\u53c2\u6570\u8fdb\u884c\u76f8\u4e58\u7684\u8fd0\u7b97\uff0c\u90a3\u4e48\u7b2c\u4e8c\u5c42\u7684\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u90fd\u9700\u8981\u67095\u4e2a\u53c2\u6570\u624d\u80fd\u5b9e\u73b0\u8fd0\u7b97\u3002\n        \u7b2c\u4e8c\u5c42\u7684\u795e\u7ecf\u5143\u76845\u4e2a\u53c2\u6570\u4e0e\u524d\u4e00\u5c42\u76845\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u5206\u522b\u76f8\u4e58\uff0c\u4e4b\u540e\uff0c\u518d\u52a0\u4e0a\u4e00\u4e2a\u504f\u7f6e\u503cb\uff0c\u5c31\u662f\u7b2c\u4e8c\u5c42\u7684\u8fd9\u4e00\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u51fa\n        :param nonlin: \u662f\u5426\u5f00\u542fReLU\n        \"\"\"\n        # \u6839\u636e\u524d\u4e00\u5c42\u7684\u8f93\u51fa\u91cf\u4e3a\u5f53\u524d\u795e\u7ecf\u5143\u521d\u59cb\u5316\u76f8\u540c\u6570\u91cf\u7684\u53c2\u6570\n        self.w = []\n        for i in range(nin):\n            self.w.append(Value(random.uniform(-1, 1),label = f\"x{i}\"))\n\n        # \u521d\u59cb\u5316\u504f\u7f6e\uff0c\u9ed8\u8ba4\u4e3a0\n        self.b = Value(0,label=\"b\")\n\n        # \u662f\u5426\u6fc0\u6d3bReLU\n        self.nonlin = nonlin\n\n    # \u524d\u5411\u4f20\u64ad\u8ba1\u7b97\uff0c\u4e5f\u5c31\u662f\u8ba1\u7b97\u5f53\u524d\u795e\u7ecf\u5143\u7684\u8f93\u51fa\uff0c\u8fd9\u4e2a\u8f93\u51fa\u5f53\u7136\u662f\u4e00\u4e2a\u503c\n    def __call__(self, x):\n        \"\"\"\n        :param x: \u8f93\u5165\u5411\u91cf\uff0c\u4e5f\u5c31\u662f\u5176\u8f93\u5165\u7684\u5bf9\u5e94\u7684\u503c\uff0c\u5176\u957f\u5ea6\u5e94\u8be5\u662fnin\n        :return: \u795e\u7ecf\u5143\u8f93\u51fa\uff0c\u5e94\u8be5\u662f\u4e00\u4e2a\u503c\n        \u8ba1\u7b97\u65b9\u5f0f\uff1a\u5047\u8bbe\u5176\u4e0a\u4e00\u5c42\u67095\u4e2a\u795e\u7ecf\u5143\uff0c\u5206\u522b\u8f93\u51fa\u4e86[1,2,3,4,5]\uff0c\u90a3\u4e48\uff0c\u5728\u5f53\u524d\u795e\u7ecf\u5143\u5e94\u5148\u521d\u59cb\u5316\u4e94\u4e2a\u53c2\u6570[Value(6),Value(7),Value(8),Value(9),Value(10)]\u548c\u504f\u7f6eb\n        \u7ed3\u679c = 1 * Value(6) + 2 * Value(7) + 3 * Value(8) + 4 * Value(9) + 5 * Value(10) + b\n        \"\"\"\n        act = Value(0)\n        for i in range(len(x)):\n            act += x[i] * self.w[i]\n\n        # \u52a0\u4e0a\u504f\u7f6e\u503c\n        act += self.b\n\n        # \u5982\u679c\u542f\u7528ReLU\uff0c\u5219\u8c03\u7528ReLU\u7684\u65b9\u6cd5\n        if self.nonlin:\n            act = act.relu()\n\n        return act\n\n    # \u8fd4\u56de\u8be5\u795e\u7ecf\u5143\u6240\u6709\u53ef\u5b66\u4e60\u53c2\u6570\n    def parameters(self):\n        \"\"\"\n        \u65e0\u975e\u5c31\u662f\u8fd4\u56de\u8fd9\u4e2a\u795e\u7ecf\u5143\u521d\u59cb\u5316\u521b\u5efa\u7684\u6240\u6709\u7684\u53c2\u6570\uff0c\u5176\u6570\u91cf\u5e94\u8be5\u8ddf\u5176\u8f93\u5165\u503c\u662f\u4e00\u6837\u7684\uff0c\u53e6\u5916\u8fd8\u8981\u52a0\u4e0a\u5b83\u7684\u504f\u7f6e\u503c\n        \"\"\"\n        return self.w + [self.b]\n\n    # \u5b57\u7b26\u4e32\u8868\u793a\uff0c\u7528\u4e8e\u8c03\u8bd5\u548c\u6253\u5370\n    def __repr__(self):\n        return f\"{'ReLU' if self.nonlin else 'Linear'}Neuron({len(self.w)})\"<\/code><\/pre>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u6539\u4e00\u4e0bmain.py\uff0c\u770b\u770b\u6211\u4eec\u5199\u7684\u8fd9\u4e2a\u795e\u7ecf\u5143\u5de5\u4f5c\u6b63\u4e0d\u6b63\u5e38\uff1a<\/p>\n\n\n\n
from value import Value\nfrom draw_dot import draw_dot\nfrom nn import Neuron\n\nn = Neuron(5)\nx = [1,2,3,4,5]\ny = n.__call__(x)\ny.backward()\ndraw_dot(y)<\/code><\/pre>\n\n\n\n
\u7531\u4e8e\u8fd9\u4e2a\u795e\u7ecf\u5143\uff0c\u6700\u7ec8\u8fd4\u56de\u7684\u4e5f\u662f\u4e00\u4e2aValue\u7c7b\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5bf9\u8fd9\u4e2a\u6700\u7ec8\u8fd4\u56de\u7684Value\u7c7b\u8fdb\u884c\u4e00\u6b21\u53cd\u5411\u4f20\u64ad\uff0c\u5c31\u53ef\u4ee5\u770b\u5230\u6240\u6709\u53c2\u6570\u5bf9\u5e94\u7684\u68af\u5ea6\uff0c\u8ba9\u6211\u4eec\u8fd0\u884c\u4e00\u4e0b\uff0c\u770b\u770b\u6548\u679c\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u4e00\u6b21\u7531\u4e8e\u8fd9\u4e2a\u795e\u7ecf\u5143\u6700\u7ec8\u8f93\u51fa\u7684\u662f\u4e2a\u8d1f\u6570\uff0c\u800c\u53c8\u6253\u5f00\u4e86ReLU\uff0c\u8fd9\u5bfc\u81f4\u8fd9\u4e2a\u795e\u7ecf\u5143\u5728\u5f53\u524d\u7684\u8f93\u51fa\u662f0\uff0c\u5e76\u4e14\u5176\u6240\u6709\u7684\u53c2\u6570\u68af\u5ea6\u90fd\u662f0\u3002\u8ba9\u6211\u4eec\u518d\u8fd0\u884c\u4e00\u6b21\u770b\u770b\u5176\u4ed6\u60c5\u51b5\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u4e00\u6b21\u7531\u4e8e\u5176\u6700\u7ec8\u8f93\u51fa\u662f\u4e00\u4e2a\u6b63\u6570\uff0c\u6240\u4ee5\u5404\u4e2a\u53c2\u6570\u7684\u68af\u5ea6\u90fd\u662f\u6b63\u5e38\u663e\u793a\u7684\u3002<\/p>\n\n\n\n
\u89c2\u5bdf\u4ed4\u7ec6\u7684\u670b\u53cb\u53ef\u80fd\u770b\u5230\uff0c\u5728\u7b2c\u4e8c\u5217\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u8282\u70b9\uff0cdata=0\uff0cgrad=1\u3002\u8fd9\u4e2a\u5b9e\u9645\u4e0a\u662f\u56e0\u4e3a\u6211\u4eec\u5728\u5199\u795e\u7ecf\u5143\u7684\u4ee3\u7801\u65f6\uff0c\u5728\u5199__call__()<\/code>\u65b9\u6cd5\u65f6\uff0c\u901a\u8fc7act = Value(0)<\/code>\u5b9a\u4e49\u4e86\u521d\u59cb\u7684\u4e00\u4e2a\u8282\u70b9\uff0c\u4f46\u7531\u4e8e\u4e4b\u540e\u6211\u4eec\u5199\u8fd9\u4e2a\u795e\u7ecf\u5143\u8fd4\u56de\u8be5\u795e\u7ecf\u5143\u6240\u6709\u53ef\u5b66\u4e60\u53c2\u6570\u7684\u4ee3\u7801\u4e2d\uff0c\u5e76\u6ca1\u6709\u8fd4\u56de\u8fd9\u4e2a\u8282\u70b9\uff0c\u56e0\u6b64\u5b83\u4e0d\u4f1a\u5f71\u54cd\u5230\u6211\u4eec\u4e4b\u540e\u5199\u795e\u7ecf\u7f51\u7edcLayer\u548cMLP\u4e4b\u540e\u7684\u4ee3\u7801\uff0c\u56e0\u4e3a\u5b83\u4e0d\u5728\u53ef\u5b66\u4e60\u53c2\u6570\u4e4b\u5217\uff0c\u6240\u4ee5\u5728\u672a\u6765\u6211\u4eec\u8fdb\u884c\u53cd\u5411\u4f20\u64ad\u7684\u65f6\u5019\uff0c\u4e5f\u4e0d\u4f1a\u5bf9\u8fd9\u4e2a\u53c2\u6570\u505a\u4efb\u4f55\u5fae\u8c03\u3002<\/p>\n\n\n\n
\u81ea\u5b9a\u4e49\u5168\u8fde\u63a5\u5c42<\/h3><\/div>\n\n\n\n
\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u5b9e\u73b0\u5168\u8fde\u63a5\u5c42\u3002\u4e00\u4e2a\u5168\u8fde\u63a5\u5c42\u5e94\u8be5\u7531\u591a\u4e2a\u795e\u7ecf\u5143\u7ec4\u6210\uff0c\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u72ec\u7acb\u5730\u63a5\u6536\u6240\u6709\u7684\u8f93\u5165\uff0c\u5e76\u4e14\u4ea7\u751f\u4e00\u4e2a\u8f93\u51fa\u3002\u8fd9\u4e00\u5c42\u6709\u591a\u5c11\u4e2a\u795e\u7ecf\u5143\uff0c\u5b83\u5c31\u5e94\u8be5\u4ea7\u751f\u591a\u5c11\u4e2a\u8f93\u51fa\uff0c\u4e0a\u4e00\u5c42\u6709\u591a\u5c11\u4e2a\u795e\u7ecf\u5143\uff0c\u5c31\u51b3\u5b9a\u4e86\u4e0b\u4e00\u5c42\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u5165\u4e2a\u6570\u3002<\/p>\n\n\n\n
# \u5168\u8fde\u63a5\u5c42\uff0c\u7531\u591a\u4e2a\u795e\u7ecf\u5143\u7ec4\u6210\uff0c\u6bcf\u4e2a\u795e\u7ecf\u5143\u72ec\u7acb\u5904\u7406\u76f8\u540c\u7684\u8f93\u5165\uff0c\u4ea7\u751f\u4e00\u4e2a\u8f93\u51fa\nclass Layer(Module):\n    def __init__(self, nin, nout, **kwargs):\n        \"\"\"\n        :param nin: \u8f93\u5165\u7684\u7279\u5f81\u7ef4\u6570\uff0c\u4e5f\u5c31\u662f\u6709\u591a\u5c11\u4e2a\u8f93\u5165\u503c\uff0c\u4e5f\u5c31\u662f\u4e0a\u4e00\u5c42\u6709\u591a\u5c11\u4e2a\u795e\u7ecf\u5143\n        :param nout: \u8f93\u51fa\u7684\u795e\u7ecf\u5143\u4e2a\u6570\uff0c\u4e5f\u5c31\u662f\u5f53\u524d\u8fd9\u4e00\u5c42\u6709\u591a\u5c11\u4e2a\u795e\u7ecf\u5143\n        :param kwargs: \u4f20\u9012\u7ed9\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u7684\u989d\u5916\u53c2\u6570\uff0c\u5982 nonlin=False\n        \"\"\"\n        # \u521b\u5efa nout\u4e2a\u795e\u7ecf\u5143\n        self.neurons = []\n        for _ in range(nout):\n            self.neurons.append(Neuron(nin, **kwargs))\n\n    # \u524d\u5411\u4f20\u64ad\u65b9\u6cd5\uff0c\u7531\u4e8e\u6bcf\u4e00\u4e2a\u795e\u7ecf\u5143\u90fd\u662f\u72ec\u7acb\u5904\u7406\u76f8\u540c\u7684\u8f93\u5165\uff0c\u4ea7\u751f\u4e00\u4e2a\u8f93\u51fa\uff0c\u56e0\u6b64\u53ef\u4ee5\u5e76\u884c\u8ba1\u7b97\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u3002\u5f53\u7136\uff0c\u6211\u8bf4\u7684\u662f\u5b9e\u9645\u5de5\u4e1a\u4e0a\u7684\u4f7f\u7528\u60c5\u51b5\uff0c\u5728\u8fd9\u91cc\u4f7f\u7528\u4e00\u4e2afor\u5faa\u73af\u662f\u4e0d\u53ef\u80fd\u8fdb\u884c\u5e76\u884c\u8fd0\u7b97\u7684\n    def __call__(self, x):\n        \"\"\"\n        :param x: \u8f93\u5165\u5411\u91cf\uff0c\u4e5f\u5c31\u662f\u5176\u8f93\u5165\u7684\u5bf9\u5e94\u7684\u503c\uff0c\u5176\u957f\u5ea6\u5e94\u8be5\u662fnin\n        :return: \u5982\u679c\u53ea\u6709\u4e00\u4e2a\u795e\u7ecf\u5143\uff0c\u8fd4\u56de\u5355\u4e2aValue\uff0c\u5982\u679c\u8fd9\u4e00\u5c42\u6709\u591a\u4e2a\u795e\u7ecf\u5143\uff0c\u5219\u8fd4\u56de\u5217\u8868\n        \"\"\"\n        out = []\n        for n in self.neurons:\n            out.append(n(x))\n\n        # \u5982\u679c\u53ea\u6709\u4e00\u4e2a\u795e\u7ecf\u5143\uff0c\u8fd4\u56de\u5355\u4e2aValue\uff0c\u5982\u679c\u8fd9\u4e00\u5c42\u6709\u591a\u4e2a\u795e\u7ecf\u5143\uff0c\u5219\u8fd4\u56de\u5217\u8868\n        if len(out) == 1:\n            return out[0]\n        else:\n            return out\n\n    # \u8fd4\u56de\u8be5\u5c42\u6240\u6709\u795e\u7ecf\u5143\u7684\u6240\u6709\u53ef\u5b66\u4e60\u53c2\u6570\n    def parameters(self):\n        ret = []\n        for n in self.neurons:\n            # \u8fd9\u91cc\u4e0d\u80fd\u7528append\uff0c\u800c\u662f\u5e94\u8be5\u7528extend\uff0c\u8fd9\u6837\u53ef\u4ee5\u628a\u6bcf\u4e00\u4e2a\u5143\u7d20\u7684\u5c55\u5f00\u653e\u5230\u5217\u8868\u4e2d\n            ret.extend(n.parameters())\n        return ret\n\n    # \u5b57\u7b26\u4e32\u8868\u793a\uff0c\u7528\u4e8e\u8c03\u8bd5\u548c\u6253\u5370\n    def __repr__(self):\n        return f\"Layer of [{', '.join(str(n) for n in self.neurons)}]\"<\/code><\/pre>\n\n\n\n
\u6211\u4eec\u73b0\u5728\u4e3adraw_dot.py\u65b0\u589e\u4e00\u4e2a\u65b9\u6cd5\uff0c\u5141\u8bb8\u5176\u8f93\u5165Value\u5217\u8868\uff0c\u5e76\u4e14\u5c06\u7ed3\u6784\u6253\u5370\u5728\u540c\u4e00\u5f20\u56fe\u4e0a\u3002\u56e0\u4e3a\u5168\u8fde\u63a5\u5c42\uff0c\u9664\u975e\u662f\u6700\u540e\u4e00\u5c42\uff0c\u5426\u5219\u5e94\u8be5\u6709\u591a\u4e2a\u8f93\u51fa\uff0c\u6211\u5e0c\u671b\u628a\u5b83\u653e\u5728\u540c\u4e00\u5f20\u56fe\u4e0a\u5c55\u793a\uff1a<\/p>\n\n\n\n
def draw_dot_list(roots, filename='multi_graph', view=True):\n    \"\"\"\u4f20\u5165 Value \u5217\u8868\uff0c\u5c06\u591a\u4e2a\u8ba1\u7b97\u6839\u8282\u70b9\u7684\u56fe\u5408\u5e76\u7ed8\u5236\u4e3a\u4e00\u4e2a\u56fe\u3002\n\n    :param roots: Value \u5bf9\u8c61\u7684\u5217\u8868\uff0c\u5982 [y1, y2, y3]\n    :param filename: \u8f93\u51fa\u6587\u4ef6\u540d\uff08\u4e0d\u542b\u6269\u5c55\u540d\uff09\n    :param view: \u662f\u5426\u81ea\u52a8\u6253\u5f00\u56fe\u7247\n    :return: Digraph \u5bf9\u8c61\n    \"\"\"\n    # 1. \u5408\u5e76\u6240\u6709\u6839\u8282\u70b9\u7684\u8282\u70b9\u548c\u8fb9\uff08\u53d6\u5e76\u96c6\uff09\n    all_nodes = set()\n    all_edges = set()\n\n    def trace(root):\n        nodes, edges = set(), set()\n        def build(v):\n            if v not in nodes:\n                nodes.add(v)\n                for child in v._prev:\n                    edges.add((child, v))\n                    build(child)\n        build(root)\n        return nodes, edges\n\n    for root in roots:\n        n, e = trace(root)\n        all_nodes |= n\n        all_edges |= e\n\n    dot = Digraph(format=\"png\", graph_attr={\"rankdir\": \"LR\", \"dpi\": \"300\"})\n\n    for node in all_nodes:\n        uid = str(id(node))\n        dot.node(name=uid, label=\"{ %s | data %.4f | grad %.4f }\" % (node.label, node.data, node.grad), shape='record')\n        if node._op:\n            dot.node(name=uid + node._op, label=node._op)\n            dot.edge(uid + node._op, uid)\n\n    for node1, node2 in all_edges:\n        dot.edge(str(id(node1)), str(id(node2)) + node2._op)\n\n    dot.render(filename, view=view)\n    return dot<\/code><\/pre>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u91cd\u65b0\u5199\u4e00\u4e0bmain.py\uff0c\u6765\u9a8c\u8bc1\u4e00\u4e0b\u6211\u4eec\u7684\u5168\u8fde\u63a5\u5c42\u662f\u5426\u6b63\u786e\uff1a<\/p>\n\n\n\n
from draw_dot import draw_dot_list\nfrom nn import Layer\n\nn = Layer(5, 2, nonlin=False)\nx = [1,2,3,4,5]\ny = n.__call__(x)       # \u8fd4\u56de\u4e24\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u5217\u8868\nfor out in y:\n    out.backward()\ndraw_dot_list(y)<\/code><\/pre>\n\n\n\n
\u7531\u4e8e\u8fd9\u4e00\u5c42\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e24\u4e2a\u795e\u7ecf\u5143\uff0c\u56e0\u6b64\u6211\u4eec\u62ff\u5230\u7684\u8f93\u51fa\u540e\u8981\u5bf9\u8fd9\u4e24\u4e2a\u795e\u7ecf\u5143\u6267\u884c\u53cd\u5411\u4f20\u64ad\u7684\u65b9\u6cd5\uff0c\u4ee5\u66f4\u65b0\u6240\u6709\u7684\u68af\u5ea6\u503c\uff0c\u73b0\u5728\u6211\u4eec\u6765\u8fd0\u884c\u4e00\u4e0b\uff1a<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u53ef\u4ee5\u770b\u5230\uff0c\u968f\u7740\u6211\u4eec\u7ed3\u6784\u7684\u6108\u52a0\u5b8c\u5584\uff0c\u5176\u56fe\u8868\u4e5f\u53d8\u5f97\u6108\u52a0\u590d\u6742\uff0c\u4f46\u662f\u6574\u4f53\u4e0a\u8fd8\u662f\u7b26\u5408\u6211\u4eec\u7684\u9884\u671f\u7684\uff0c\u975e\u5e38\u4e0d\u9519\uff01<\/p>\n\n\n\n
\u81ea\u5b9a\u4e49\u591a\u5c42\u611f\u77e5\u673aMLP<\/h3><\/div>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u628a\u5404\u4e2a\u5c42\u4e32\u5230\u4e00\u8d77\uff0c\u5f62\u6210\u4e00\u4e2a\u591a\u5c42\u611f\u77e5\u673aMLP<\/p>\n\n\n\n
# \u591a\u5c42\u611f\u77e5\u673a\uff0c\u7531\u591a\u4e2a\u5168\u8fde\u63a5\u5c42\u5806\u780c\u800c\u6210\nclass MLP(Module):\n    \"\"\"\n    \u9664\u6700\u540e\u4e00\u5c42\u5916\u6bcf\u5c42\u90fd\u4f7f\u7528 ReLU \u6fc0\u6d3b\u3002\n\n    \u7f51\u7edc\u7ed3\u6784\u793a\u4f8b\uff1a\n        MLP(2, [8, 4, 1])\n            \u8f93\u5165\u5c42 (2)\n                \u2193\n            Layer 1 (2\u21928) + ReLU\n                \u2193\n            Layer 2 (8\u21924) + ReLU\n                \u2193\n            Layer 3 (4\u21921) + Linear (\u8f93\u51fa\u5c42)\n                \u2193\n            \u8f93\u51fa (1)\n    \u53c2\u6570\u6570\u91cf\u8ba1\u7b97\uff1a\n    Layer 1: 2\u00d78 + 8 = 24\n    Layer 2: 8\u00d74 + 4 = 36\n    Layer 3: 4\u00d71 + 1 = 5\n    \u603b\u8ba1: 65 \u4e2a\u53c2\u6570\n\n    \u4e2d\u95f4\u5c42\u6709\u591a\u5c11\u4e2a\u795e\u7ecf\u5143\u662f\u53ef\u4ee5\u8c03\u8282\u7684\n    \"\"\"\n    def __init__(self, nin, nout):\n        \"\"\"\n        :param nin:\u8f93\u5165\u5c42\u7ef4\u5ea6\uff0c\u4e5f\u5c31\u662f\u521d\u59cb\u5230\u5e95\u6709\u591a\u5c11\u4e2a\u8f93\u5165\u503c\n        :param nout:\u5404\u5c42\u7684\u8f93\u51fa\u7ef4\u5ea6\u5217\u8868\uff0c\u5982[8 , 4 , 1]\n        \"\"\"\n        self.layers = []\n        # \u6784\u5efa\u5b8c\u6574\u7684\u7ef4\u5ea6\u94fe\uff1a[\u8f93\u5165, \u9690\u85cf1, \u9690\u85cf2, ..., \u8f93\u51fa]\n        dims = [nin] + nout\n        # \u521b\u5efa\u4e2d\u95f4\u5c42\uff0c\u9664\u6700\u540e\u4e00\u5c42\u5916\u6bcf\u5c42\u90fd\u4f7f\u7528 ReLU \u6fc0\u6d3b\u3002\n        for i in range(len(nout)):\n            if i == len(nout) - 1:\n                # \u9664\u6700\u540e\u4e00\u5c42\u5916\u6bcf\u5c42\u90fd\u4f7f\u7528 ReLU \u6fc0\u6d3b\u3002\n                layer = Layer(dims[i], dims[i + 1], nonlin=False)\n            else:\n                layer = Layer(dims[i], dims[i + 1], nonlin=True)\n\n            self.layers.append(layer)\n\n    # \u524d\u5411\u4f20\u64ad\n    def __call__(self, x):\n        # \u7531\u4e8e\u6bcf\u4e00\u5c42\u7684\u8f93\u51fa\u90fd\u662f\u4e0b\u4e00\u5c42\u7684\u8f93\u5165\uff0c\u6240\u4ee5\u6211\u4eec\u5e94\u8be5\u4ece\u7b2c\u4e00\u5c42\u5f00\u59cb\uff0c\u7ed9\u7b2c\u4e00\u5c42\u4f20\u5165\u6574\u4e2a\u6a21\u578b\u7684\u8f93\u5165\u503c\uff0c\u7136\u540e\u83b7\u53d6\u7b2c\u4e00\u5c42\u7684\u8f93\u51fa\uff0c\u518d\u4f20\u9012\u7ed9\u7b2c\u4e8c\u5c42\uff0c\u4ee5\u6b64\u7c7b\u63a8\n        for layer in self.layers:\n            x = layer(x)\n        return x\n\n    # \u8fd4\u56de\u6240\u6709\u53ef\u5b66\u4e60\u53c2\u6570\n    def parameters(self):\n        # \u4e5f\u5c31\u662f\u6309\u5c42\u5c55\u5f00\u3002\u6240\u6709\u5c42\u7684\u53c2\u6570\n        ret = []\n        for layer in self.layers:\n            # \u8fd9\u91cc\u4e0d\u80fd\u7528append\uff0c\u800c\u662f\u5e94\u8be5\u7528extend\uff0c\u8fd9\u6837\u53ef\u4ee5\u628a\u6bcf\u4e00\u4e2a\u5143\u7d20\u7684\u5c55\u5f00\u653e\u5230\u5217\u8868\u4e2d\n            ret.extend(layer.parameters())\n        return ret\n\n    # \u5b57\u7b26\u4e32\u8868\u793a\uff0c\u7528\u4e8e\u8c03\u8bd5\u548c\u6253\u5370\n    def __repr__(self):\n        return f\"MLP of [{', '.join(str(layer) for layer in self.layers)}]\"<\/code><\/pre>\n\n\n\n
\u73b0\u5728\u6211\u4eec\u4fee\u6539\u4e00\u4e0bmain.py\uff0c\u6765\u9a8c\u8bc1\u4e00\u4e0b\u6211\u4eec\u7684\u591a\u5c42\u611f\u77e5\u673a\u662f\u5426\u6b63\u786e\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u591a\u5c42\u611f\u77e5\u673a\uff0c\u5176\u6700\u540e\u8fd4\u56de\u7684\u80af\u5b9a\u662f\u4e00\u4e2aValue\u7c7b\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u7528draw_dot()<\/code>\u65b9\u6cd5\u6765\u7ed8\u5236\u5c31\u884c\u4e86\uff1a<\/p>\n\n\n\n
from draw_dot import draw_dot\nfrom nn import MLP\n\nn = MLP(5, [8 , 4 , 1])\nx = [1,2,3,4,5]\ny = n.__call__(x)       \ny.backward()\ndraw_dot(y)<\/code><\/pre>\n\n\n\n
\u6211\u4eec\u8fd9\u91cc\u5b9a\u4e49\u7684\u662f\u4e00\u4e2a\u4e2d\u95f4\u5c42\u4e3a[8 , 4 , 1]\u7684\u591a\u5c42\u611f\u77e5\u673a\uff0c\u8fd0\u884c\u4e00\u4e0b\u770b\u770b\u6548\u679c\uff1a<\/p>\n\n\n\n
\"\"\/<\/div><\/figure>\n\n\n\n
\u53ef\u4ee5\u770b\u5230\uff0c\u753165\u4e2a\u53c2\u6570\u7ec4\u6210\u7684\u795e\u7ecf\u7f51\u7edc\u5df2\u7ecf\u5927\u5f97\u5413\u4eba\u4e86\uff0c\u5e76\u4e14\u9664\u4e86\u6700\u540e\u4e00\u5c42\u6ca1\u6709ReLU\uff0c\u5176\u4ed6\u5c42\u90fd\u662f\u5f00\u542f\u4e86ReLU\u7684\u3002\u8fd9\u4e00\u4e2a\u56fe\u4e0d\u592a\u5177\u6709\u53ef\u8bfb\u6027\u4e86\uff0c\u4f46\u662f\u6211\u4eec\u5df2\u7ecf\u521d\u6b65\u5b8c\u6210\u4e86\u4e00\u4e2a\u591a\u5c42\u611f\u77e5\u673a\uff0c\u4e3a\u4e86\u4fbf\u4e8e\u8c03\u8bd5\u4ee5\u53ca\u89c2\u5bdf\uff0c\u6211\u4eec\u73b0\u5728\u628a\u968f\u673a\u79cd\u5b50\u8bbe\u7f6e\u4e3a42\uff0c\u8fd9\u6837\u6bcf\u4e00\u6b21\u7684\u968f\u673a\u503c\u90fd\u662f\u4e00\u5b9a\u7684\u3002\u6211\u73b0\u5728\u53ea\u60f3\u77e5\u9053\u5f53\u524d\u6a21\u578b\u5bf9\u4e8e\u8fd9\u4e00\u4e2a\u8f93\u5165\uff0c\u5176\u6700\u7ec8\u7684\u8f93\u51fa\u662f\u4ec0\u4e48\uff1a<\/p>\n\n\n\n
from nn import MLP\nimport random\nrandom.seed(42)\n\nn = MLP(5, [8 , 4 , 1])\nx = [1,2,3,4,5]\ny = n.__call__(x)\ny.backward()\nprint(y)<\/code><\/pre>\n\n\n\n
\u8fd0\u884c\u4e00\u4e0b\uff0c\u770b\u770b\u7ed3\u679c\uff1a<\/p>\n\n\n\n
D:\\Data\\Anacondea\\envs\\lora\\python.exe D:\\Data\\Python\\Class_1\\main.py \nValue0.5775760457072401, grad=1<\/code><\/pre>\n\n\n\n
\u65e0\u8bba\u8fd0\u884c\u591a\u5c11\u6b21\uff0c\u76ee\u524d\u6700\u540e\u7684\u7ed3\u679c\u90fd\u662f\u4e00\u5b9a\u7684\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u6a21\u578b\uff0c\u6211\u4eec\u8fdb\u884c\u76f8\u540c\u7684\u8f93\u5165\uff0c\u5176\u7ed3\u679c\u4e3a0.57\u5de6\u53f3\uff0c\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u635f\u5931\u503c\u3002<\/p>\n\n\n\n
\u8fd9\u4e2a\u6a21\u578b\u76ee\u524d\u7684\u8f93\u5165\u4e0e\u6211\u4eec\u9884\u8ba1\u7684\u8f93\u5165\u7684\u533a\u522b\uff0c\u5c31\u662f\u635f\u5931\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u7528\u635f\u5931\u503c\u6765\u8861\u91cf\u5f53\u524d\u6a21\u578b\u7684\u8f93\u51fa\u4e0e\u6211\u4eec\u6240\u671f\u671b\u7684\u8f93\u51fa\u7684\u5dee\u989d\u3002\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u5bf9\u4e8e[1,2,3,4,5]<\/code>\u8fd9\u4e2a\u8f93\u5165\uff0c\u6211\u4eec\u671f\u671b\u5176\u8f93\u51fa1\uff0c\u6211\u4eec\u7528\u4e00\u4e2a\u5f88\u7b80\u5355\u7684\u65b9\u6cd5\u8ba1\u7b97\u635f\u5931\uff0c\u5373\u7528\u5f53\u524d\u6a21\u578b\u5f97\u5230\u7684\u7ed3\u679c\u4e0e\u6211\u4eec\u9884\u671f\u7684\u7ed3\u679c\u76f8\u51cf\u4e4b\u540e\u4e58\u4ee5\u4e00\u4e2a\u5e73\u65b9\uff0c\u8fd9\u6837\u80fd\u786e\u4fdd\u635f\u5931\u6c38\u8fdc\u662f\u6b63\u6570\uff1a<\/p>\n\n\n\n
\u6211\u4eec\u73b0\u5728\u91cd\u65b0\u5199\u4e00\u4e0bmain.py\uff0c\u5e76\u4e14\u6839\u636e\u6211\u4eec\u7684\u903b\u8f91\u6765\u5b9e\u73b0\u4e00\u6b65\u7684\u5fae\u8c03\uff1a<\/p>\n\n\n\n
from nn import *\nimport random\nrandom.seed(42)\n\nn = MLP(5, [8 , 4 , 1])\nx = [1,2,3,4,5]\n\n# \u6b63\u5411\u4f20\u64ad\uff0c\u5f97\u5230\u6a21\u578b\u5f53\u524d\u5bf9\u4e8e\u8f93\u5165\u5411\u91cf\u7684\u8f93\u51fa\ny = n(x) # \u4e0e y = n.__call__(x)\u76f8\u540c\n\n# \u8fd9\u91cc\u5b9a\u4e49\u6211\u4eec\u7684\u9884\u671f\u503c\ny_true = Value(1)\n\n# \u8ba1\u7b97\u635f\u5931\uff0c\u4e58\u4ee5\u4e00\u4e2a\u5e73\u65b9\uff0c\u786e\u4fdd\u635f\u5931\u6c38\u8fdc\u4e3a\u6b63\u6570\nloss = (y_true - y) ** 2\nprint(loss)\n\n# \u5c06\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\u6e05\u7a7a\nn.zero_grad()\n\n# \u8ba1\u7b97\u635f\u5931\u7684\u53cd\u5411\u4f20\u64ad\nloss.backward()\n\n# \u5c06\u5404\u4e2a\u53c2\u6570\u7684\u503c\u6839\u636e\u5176\u68af\u5ea6\u8fdb\u884c\u5fae\u8c03\nfor p in n.parameters():\n    p.data += -0.01 * p.grad\n\n# \u518d\u6b21\u6b63\u5411\u4f20\u64ad\uff0c\u770b\u770b\u5f53\u524d\u66f4\u65b0\u540e\u6a21\u578b\u5bf9\u4e8e\u540c\u6837\u7684\u8f93\u5165\uff0c\u5f97\u5230\u4e86\u4ec0\u4e48\u8f93\u51fa\ny = n(x)\n\nloss = (y_true - y) ** 2\nprint(loss)<\/code><\/pre>\n\n\n\n
\u6211\u4eec\u8fd0\u884c\u4e00\u4e0b\u770b\u770b\uff1a<\/p>\n\n\n\n
D:\\Data\\Anacondea\\envs\\lora\\python.exe D:\\Data\\Python\\Class_1\\main.py \nValue0.1784419971603317, grad=0\nValue0.017774538128664325, grad=0<\/code><\/pre>\n\n\n\n
\u53ef\u4ee5\u5f88\u660e\u663e\u770b\u5230\uff0c\u6211\u4eec\u7684\u635f\u5931\u662f\u4ece0.17\u53d8\u6210\u4e860.017\uff0c\u73b0\u5728\u6211\u4eec\u4fee\u6539\u4ee3\u7801\uff0c\u8ba9\u6a21\u578b\u5faa\u73af\u5fae\u8c0310\u6b21\uff1a<\/p>\n\n\n\n
from nn import *\nimport random\nrandom.seed(42)\n\nn = MLP(5, [8 , 4 , 1])\nx = [1,2,3,4,5]\n\n# \u6b63\u5411\u4f20\u64ad\uff0c\u5f97\u5230\u6a21\u578b\u5f53\u524d\u5bf9\u4e8e\u8f93\u5165\u5411\u91cf\u7684\u8f93\u51fa\ny = n(x) # \u4e0e y = n.__call__(x)\u76f8\u540c\n\n# \u8fd9\u91cc\u5b9a\u4e49\u6211\u4eec\u7684\u9884\u671f\u503c\ny_true = Value(1)\n\n# \u8ba1\u7b97\u635f\u5931\uff0c\u4e58\u4ee5\u4e00\u4e2a\u5e73\u65b9\uff0c\u786e\u4fdd\u635f\u5931\u6c38\u8fdc\u4e3a\u6b63\u6570\nloss = (y_true - y) ** 2\nprint(loss)\n\nfor _ in range(10):\n    # \u5c06\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\u6e05\u7a7a\n    n.zero_grad()\n\n    # \u8ba1\u7b97\u635f\u5931\u7684\u53cd\u5411\u4f20\u64ad\n    loss.backward()\n\n    # \u5c06\u5404\u4e2a\u53c2\u6570\u7684\u503c\u6839\u636e\u5176\u68af\u5ea6\u8fdb\u884c\u5fae\u8c03\n    for p in n.parameters():\n        p.data += -0.01 * p.grad\n\n    # \u518d\u6b21\u6b63\u5411\u4f20\u64ad\uff0c\u770b\u770b\u5f53\u524d\u66f4\u65b0\u540e\u6a21\u578b\u5bf9\u4e8e\u540c\u6837\u7684\u8f93\u5165\uff0c\u5f97\u5230\u4e86\u4ec0\u4e48\u8f93\u51fa\n    y = n(x)\n\n    loss = (y_true - y) ** 2\n    print(loss)<\/code><\/pre>\n\n\n\n
\u8fd0\u884c\u4e00\u4e0b\uff1a<\/p>\n\n\n\n
D:\\Data\\Anacondea\\envs\\lora\\python.exe D:\\Data\\Python\\Class_1\\main.py \nValue0.1784419971603317, grad=0\nValue0.017774538128664325, grad=0\nValue0.0025305873910934284, grad=0\nValue0.00031141530032524655, grad=0\nValue4.034746486335811e-05, grad=0\nValue5.131459834284199e-06, grad=0\nValue6.569582290880621e-07, grad=0\nValue8.390869140101244e-08, grad=0\nValue1.0726138625601893e-08, grad=0\nValue1.3707193806979307e-09, grad=0\nValue1.751865023724053e-10, grad=0\n<\/code><\/pre>\n\n\n\n
\u53ef\u4ee5\u770b\u5230\uff0c\u6211\u4eec\u7684\u635f\u5931\u503c\u662f\u8d8a\u6765\u8d8a\u5c0f\u7684\uff0c\u76f4\u5230\u6700\u540e\u53ef\u4ee5\u5ffd\u7565\u4e0d\u8ba1\u3002\u73b0\u5728\u6211\u4eec\u518d\u6539\u9020\u4e00\u4e0bmain.py\uff0c\u63d0\u4f9b\u591a\u5bf9\u8f93\u5165\u548c\u9884\u671f\u8f93\u51fa\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4fee\u6539\u4e00\u4e0b\u8ba1\u7b97\u635f\u5931\u65f6\u7684\u65b9\u6cd5\uff0c\u56e0\u4e3a\u6211\u4eec\u8fd9\u91cc\u7684\u6837\u672c\u662f\u4f7f\u7528\u4e86\u4e00\u4e2a\u771f\u5b9e\u7684\u6570\u5b66\u51fd\u6570\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4e3a\u5b83\u63d0\u4f9b\u4e00\u4e2a\u9a8c\u8bc1\u6837\u672c\uff0c\u4e0d\u65ad\u7684\u67e5\u770b\u5f53\u524d\u6a21\u578b\u7684\u8f93\u51fa\u8ddf\u6211\u4eec\u7684\u9a8c\u8bc1\u6837\u672c\u7ed3\u679c\u7684\u5dee\u503c\uff1a<\/p>\n\n\n\n
from nn import *\nimport random\nrandom.seed(42)\n\nn = MLP(5, [8 , 4 , 1])\n\n# y = 2*x1 - 1.5*x2 + 0.5*x3 - 3*x4 + 1*x5 + 0.5\ndef true_func(x):\n    return 2.0*x[0] - 1.5*x[1] + 0.5*x[2] - 3.0*x[3] + 1.0*x[4] + 0.5\n\n# \u8bad\u7ec3\u6837\u672c\nxs = [\n    [2.0, 3.0, -1.0, 0.5, 1.0],\n    [1.0, -2.0, 4.0, 2.0, 0.0],\n    [-1.0, 2.0, 3.0, 1.0, 1.0],\n    [0.0, 1.0, -2.0, -1.0, 3.0],\n    [4.0, -3.0, 2.0, 0.5, 2.0],\n    [-2.0, -1.0, 5.0, 3.0, 0.5],\n    [1.5, 0.0, 0.5, 2.0, 1.0],\n    [0.5, 4.0, -3.0, -0.5, 2.0],\n    [-0.5, 5.0, 1.0, 1.5, 0.0],\n    [3.0, -1.0, -2.0, 1.0, 4.0],\n    [-3.0, 2.0, 5.0, 0.5, -1.0],\n    [2.5, 1.0, -4.0, -2.0, 3.0],\n    [-1.5, -3.0, 0.0, 1.5, -2.0],\n    [0.5, 0.5, 0.5, 0.5, 0.5],\n    [3.0, 3.0, 3.0, -1.0, -1.0],\n    [-2.0, 4.0, -1.0, 2.0, 0.0],\n    [1.0, 1.0, 1.0, 1.0, 1.0],\n    [5.0, -5.0, 2.0, -2.0, 2.0],\n    [-4.0, 0.0, -3.0, 0.0, 5.0],\n    [0.0, -2.0, 1.0, 3.0, -3.0],\n]\n\n# \u7528\u7ebf\u6027\u516c\u5f0f\u8ba1\u7b97\u5bf9\u5e94\u7684 y \u503c\nys = [true_func(x) for x in xs]\n\n# \u9a8c\u8bc1\u6837\u672c\nxs_val = [1.0, -2.5, 0.5, 2.0, 1.5]\nys_val = true_func(xs_val)\n\nfor _ in range(10000):\n    # \u5c06\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\u6e05\u7a7a\n    n.zero_grad()\n\n    # \u9010\u4e2a\u6b63\u5411\u4f20\u64ad\uff0c\u62ff\u5230\u5f53\u524d\u6a21\u578b\u5bf9\u4e8e\u5404\u4e2a\u8f93\u5165\u7684\u8f93\u51fa\u503c\n    y_preds = [n(x) for x in xs]\n\n    # \u8ba1\u7b97\u635f\u5931\u503c\n    loss = 0\n    for y, y_pred in zip(ys, y_preds):\n        loss += (y_pred - y) ** 2\n\n    # \u9664\u4ee5\u6837\u672c\u6570\u91cf\uff0c\u9632\u6b62\u635f\u5931\u503c\u968f\u7740\u6837\u672c\u6570\u91cf\u7684\u589e\u52a0\u800c\u65e0\u9650\u589e\u957f\n    loss = loss \/ len(ys)\n\n    # \u8ba1\u7b97\u9a8c\u8bc1\u6837\u672c\n    y_pred = n(xs_val)\n    if _ % 200 == 0:\n        print(f\"epoch {_} \u5f53\u524d\u635f\u5931\u503c\uff1a{loss.data:.4f}\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a{y_pred.data:.4f}\uff0c\u76ee\u6807\uff1a{ys_val}\")\n\n    # \u8ba1\u7b97\u635f\u5931\u7684\u53cd\u5411\u4f20\u64ad\n    loss.backward()\n\n    # \u5c06\u5404\u4e2a\u53c2\u6570\u7684\u503c\u6839\u636e\u5176\u68af\u5ea6\u8fdb\u884c\u5fae\u8c03\n    for p in n.parameters():\n        p.data += -0.0005 * p.grad<\/code><\/pre>\n\n\n\n
\u6211\u4eec\u6765\u8fd0\u884c\u4e00\u4e0b\uff0c\u7531\u4e8e\u8fd9\u91cc\u7b14\u8005\u8bbe\u7f6e\u4e86\u8bad\u7ec31000\u6b65\uff0c\u6240\u4ee5\u7b14\u8005\u4e0d\u4f1a\u628a\u6240\u6709\u7684\u4ed8\u51fa\u90fd\u653e\u5728\u4e0b\u65b9\uff0c\u800c\u662f\u4f1a\u622a\u53d6\u5f00\u5934\u8ddf\u7ed3\u5c3e\u7684\u90e8\u5206\u8f93\u51fa\uff1a<\/p>\n\n\n\n
D:\\Data\\Anacondea\\envs\\lora\\python.exe D:\\Data\\Python\\Class_1\\main.py \nepoch 0 \u5f53\u524d\u635f\u5931\u503c\uff1a92.7359\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a-1.0240\uff0c\u76ee\u6807\uff1a2.0\nepoch 200 \u5f53\u524d\u635f\u5931\u503c\uff1a3.9360\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a0.9463\uff0c\u76ee\u6807\uff1a2.0\nepoch 400 \u5f53\u524d\u635f\u5931\u503c\uff1a2.1334\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a-0.2241\uff0c\u76ee\u6807\uff1a2.0\nepoch 600 \u5f53\u524d\u635f\u5931\u503c\uff1a1.5454\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a-0.3436\uff0c\u76ee\u6807\uff1a2.0\n...\n...\n...\nepoch 9000 \u5f53\u524d\u635f\u5931\u503c\uff1a0.0186\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a1.7727\uff0c\u76ee\u6807\uff1a2.0\nepoch 9200 \u5f53\u524d\u635f\u5931\u503c\uff1a0.0177\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a1.7738\uff0c\u76ee\u6807\uff1a2.0\nepoch 9400 \u5f53\u524d\u635f\u5931\u503c\uff1a0.0169\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a1.7748\uff0c\u76ee\u6807\uff1a2.0\nepoch 9600 \u5f53\u524d\u635f\u5931\u503c\uff1a0.0162\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a1.7760\uff0c\u76ee\u6807\uff1a2.0\nepoch 9800 \u5f53\u524d\u635f\u5931\u503c\uff1a0.0156\uff0c\u9a8c\u8bc1\u6837\u672c\u8f93\u51fa\uff1a1.7771\uff0c\u76ee\u6807\uff1a2.0<\/code><\/pre>\n\n\n\n
\u53ef\u4ee5\u60ca\u559c\u5730\u770b\u5230\uff0c\u635f\u5931\u503c\u6b63\u5728\u7a33\u6b65\u7684\u4e0b\u964d\uff0c\u5e76\u4e14\u9a8c\u8bc1\u6837\u672c\u7684\u8f93\u51fa\u4e5f\u8d8a\u6765\u8d8a\u903c\u8fd1\u76ee\u6807\u503c\u4e86\u3002\u90a3\u4e48\u6211\u4eec\u7684\u624b\u6413MLP\u5c31\u5b8c\u6210\u4e86\u3002<\/p>\n\n\n\n
\u7ed3\u8bed<\/h2><\/div>\n\n\n\n
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