{"id":719,"date":"2026-02-10T01:37:47","date_gmt":"2026-02-09T17:37:47","guid":{"rendered":"https:\/\/qubitledge.com\/?p=719"},"modified":"2026-02-10T01:40:24","modified_gmt":"2026-02-09T17:40:24","slug":"%e8%ae%a9%e5%b7%b4%e6%99%ae%e6%b4%9b%e5%a4%ab%e7%9a%84%e7%8b%97%e9%9d%9e%e7%9b%91%e7%9d%a3%e5%bc%8f%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/qubitledge.com\/index.php\/2026\/02\/10\/%e8%ae%a9%e5%b7%b4%e6%99%ae%e6%b4%9b%e5%a4%ab%e7%9a%84%e7%8b%97%e9%9d%9e%e7%9b%91%e7%9d%a3%e5%bc%8f%e5%ad%a6%e4%b9%a0\/","title":{"rendered":"\u8ba9\u5df4\u666e\u6d1b\u592b\u7684\u72d7\u975e\u76d1\u7763\u5f0f\u5b66\u4e60"},"content":{"rendered":"\n

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

\u5df4\u666e\u6d1b\u592b\u7684\u72d7<\/h2>\n\n\n\n

\u4eca\u5929\u8c46\u74e3\u63a8\u9001\u7684\u4e00\u7bc7\u5173\u4e8e\u517b\u72d7\u7684\u6587\u7ae0\u8ba9\u6211\u60f3\u8d77\u4e86\u4e2d\u5b66\u8bfe\u672c\u8bfb\u5b66\u8fc7\u4e00\u4e2a\u5173\u4e8e\u6761\u4ef6\u53cd\u5c04\u7684\u7ecf\u5178\u5b9e\u9a8c\uff1a\u5df4\u666e\u6d1b\u592b\u7684\u72d7\u3002\u4fc4\u56fd\u751f\u7406\u5b66\u5bb6\u5df4\u666e\u6d1b\u592b\u5728\u7814\u7a76\u7684\u72d7\u7684\u6d88\u5316\u65f6\u53d1\u73b0\u72d7\u770b\u5230\u8089\u4f1a\u81ea\u52a8\u6d41\u53e3\u6c34\uff0c\u5982\u679c\u6447\u94c3\uff0c\u4f46\u662f\u4e0d\u7ed9\u8089\uff0c\u72d7\u662f\u4e0d\u4f1a\u6d41\u53e3\u6c34\u7684\u3002\u4e8e\u662f\u5df4\u666e\u6d1b\u592b\u6bcf\u6b21\u7ed9\u8089\u524d\u5148\u6447\u94c3\uff0c\u518d\u7ed9\u8089\uff0c\u91cd\u590d\u591a\u6b21\u3002\u540e\u6765\u53ea\u6447\u94c3\u3001\u4e0d\u7ed9\u8089\uff0c\u53d1\u73b0\u72d7\u7167\u6837\u4f1a\u6d41\u53e3\u6c34\uff0c\u94c3\u58f0\u53d8\u6210\u4e86\u6761\u4ef6\u523a\u6fc0\uff0c\u6d41\u53e3\u6c34\u53d8\u6210\u4e86\u6761\u4ef6\u53cd\u5c04\u3002\u4e8e\u662f\u4ed6\u63a8\u8bba\u51fa\uff0c\u539f\u672c\u65e0\u5173\u7684\u523a\u6fc0\uff0c\u901a\u8fc7\u548c\u80fd\u81ea\u7136\u5f15\u53d1\u53cd\u5e94\u7684\u523a\u6fc0\u53cd\u590d\u914d\u5bf9\uff0c\u4e5f\u80fd\u5355\u72ec\u5f15\u53d1\u540c\u6837\u53cd\u5e94\u3002<\/p>\n\n\n\n

\u200b\"image-20260209155550336\"\u200b<\/p>\n\n\n\n

\u56de\u60f3\u521a\u5f00\u59cb\u4f7f\u7528QQ\u7684\u5e74\u4ee3\uff0c\u4e0a\u7ebf\u5c31\u662f\u5f69\u8272\u5934\u50cf\uff0c\u4e0b\u7ebf\u5c31\u662f\u7070\u8272\u5934\u50cf\u3001\u6211\u4eec\u4e0d\u4f1a\u4e0b\u610f\u8bc6\u7684\u53cd\u590d\u767b\u5f55QQ\u6536\u770b\u662f\u5426\u6709\u4eba\u4f1a\u7ed9\u4e8e\u81ea\u5df1\u4fe1\u606f\u7559\u8a00\u6216\u56de\u590d\u3002\u56e0\u4e3a\u4f60\u4f1a\u6e05\u695a\u7684\u77e5\u9053\u7070\u8272\u5934\u50cf\u7684\u5bf9\u65b9\u65e0\u6cd5\u7acb\u523b\u56de\u590d\u4f60\u7684\u4fe1\u606f\uff0c\u6216\u8005\u5bf9\u65b9\u9690\u8eab\u60c5\u51b5\u5373\u4ee3\u8868\u4e86\u5bf9\u65b9\u65e0\u793e\u4ea4\u9700\u6c42\u7684\u72b6\u6001\u3002\u73b0\u4ee3\u5fae\u4fe1\u5f53\u9053\uff0cQQ\u9010\u6e10\u6ca1\u843d\uff0c\u8fd9\u79cd\u73b0\u8c61\u5728\u91d1\u878d\u91cc\u79f0\u4e3acannibalization\uff08\u4ea7\u54c1\u8695\u98df\uff09\u3002\u5f53\u8fd9\u6b3e\u4ea7\u54c1\u73b0\u5728\u5927\u5bb6\u4e0d\u5f97\u4e0d\u634f\u7740\u9f3b\u5b50\u7528\u7684\u65f6\u5019\u3002\u6574\u4e2a\u4e92\u8054\u7f51\u7684\u903b\u8f91\u5df2\u53d1\u751f\u7ffb\u5929\u8986\u5730\u7684\u53d8\u5316\u3002<\/p>\n\n\n\n

\u4f60\u6709\u6ca1\u6709\u53d1\u73b0\uff0c\u73b0\u5728\u51e0\u4e4e\u6240\u6709\u4ea7\u54c1\uff0c\u90fd\u5728\u8bad\u7ec3\u4f60\u5bf9\u4fe1\u53f7\u505a\u51fa\u53cd\u5e94\uff1f\u4e0a\u5230\u5fae\u4fe1\u3001\u98de\u4e66\u7b49\u5373\u65f6\u901a\u8baf\uff0c\u4e0b\u5230\u5404\u7c7b\u624b\u6e38\u3001\u77ed\u89c6\u9891\uff0c\u90fd\u9010\u6e10\u53d8\u6210\u4e86\u76d1\u7763\u5f0f\u7684\u4efb\u52a1\u5236\u6a21\u5f0f\u3002\u5f53\u6211\u4eec\u542c\u5230\u624b\u673a\u7684\u6d88\u606f\u63d0\u793a\u97f3\u4f1a\u4e0b\u610f\u8bc6\u7684\u770b\u624b\u673a\uff0c\u5f53\u540e\u53f0\u7684\u6e38\u620f\u8d44\u6e90\u5806\u79ef\u6ee1\u4e86\u540e\u4f1a\u9700\u8981\u6253\u5361\uff0c\u79ef\u5206\u3001\u62bd\u5956\uff0c\u66fe\u51e0\u4f55\u65f6\uff0c\u6211\u4eec\u5df2\u9010\u6e10\u53d8\u4e3a\u5bf9\u4fe1\u53f7\u4ea7\u751f\u672c\u80fd\u53cd\u5e94\u3002\u73b0\u4ee3\u4ea7\u54c1\u4e0d\u662f\u5728\u670d\u52a1\u4f60\uff0c\u800c\u662f\u5728\u7ed9\u4f60\u505a\u6761\u4ef6\u53cd\u5c04\u8bad\u7ec3\u3002<\/p>\n\n\n\n

\u4e3a\u4e86\u514b\u670d\u8fd9\u79cd\u88ab\u52a8\u7684\u8bad\u7ec3\u3002\u4e3a\u4f55\u6211\u4eec\u4e0d\u628a\u8fd9\u4e2a\u8fc7\u7a0b\u6539\u4e3a\u975e\u76d1\u7763\u5f0f\u5b66\u4e60\uff08Unsupervised Learning\uff09\u5462\uff1f<\/p>\n\n\n\n

\u200b\"image.png\"
Image by JackieLou DL<\/a> from Pixabay<\/a><\/p>\n\n\n\n

\u4f5c\u4e3a\u673a\u5668\u5b66\u4e60\u7684\u4e00\u4e2a\u7c7b\u522b\u3002\u975e\u76d1\u7763\u5f0f\u5b66\u4e60\uff08Unsupervised Learning\uff09\u7b80\u5355\u8bf4\uff0c\u5c31\u662f\u4e0d\u7ed9\u7b54\u6848\uff0c\u8ba9\u6a21\u578b\u81ea\u5df1\u201c\u770b\u6570\u636e\u3001\u627e\u95e8\u9053\u201d\u3002\u975e\u76d1\u7763\u5f0f\u5b66\u4e60\u8ba9\u6a21\u578b\u5728\u4e00\u79cd\u5728\u6ca1\u6709\u5df2\u77e5\u6807\u7b7e\u7684\u6570\u636e\u4e2d\uff0c\u8ba9\u5176\u81ea\u52a8\u53d1\u73b0\u6570\u636e\u7ed3\u6784\u548c\u89c4\u5f8b\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\uff0c\u5e38\u7528\u4e8e\u805a\u7c7b\u3001\u964d\u7ef4\u548c\u5f02\u5e38\u68c0\u6d4b\u3002\u90a3\u5230\u5e95\u5982\u4f55\u5c06\u5df4\u666e\u6d1b\u592b\u7684\u72d7\u5b9e\u9a8c\u6539\u9020\u4e3a\u975e\u76d1\u7763\u5f0f\u5b66\u4e60\u5462\uff1f\u72d7\u72d7\u4ece\u5173\u5fc3\u6709\u6ca1\u6709\u5403\u7684\u53d8\u4e3a\u5173\u5fc3\uff1a\u94c3\u94db\u548c\u8089\u603b\u662f\u540c\u65f6\u51fa\u73b0\uff0c\u90a3\u4e3b\u4eba\u5582\u6211\u548c\u6447\u94c3\u94db\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u4e8b\u60c5\u5462\uff1f<\/p>\n\n\n\n

\u9996\u5148\u8ba9\u6211\u4eec\u5047\u8bbe\u641e\u5230\u4e86\u9a6c\u65af\u514b\u7684\u8111\u673a\u63a5\u53e3\u62ff\u7ed9\u72d7\u72d7\u7528\u4e00\u5929\u3002\u8d6b\u5e03\uff08Donald Hebb\uff09\u5219\u4e3a\u6211\u4eec\u7684\u5b9e\u9a8c\u63d0\u4f9b\u4e86\u5047\u8bbe\u6a21\u578b\u8d6b\u5e03\u5b66\u4e60\u7406\u8bba (Hebbian Learning)\u3002\u6211\u4eec\u53ea\u9700\u8981\u5c06\u94c3\u58f0+\u6c14\u5473\u5171\u73b0\u540e\uff0c\u4e0d\u7acb\u523b\u7ed9\u98df\u7269\uff0c\u771f\u6b63\u5582\u98df\u53d1\u751f\u5728\u4e0e\u94c3\u58f0\u65e0\u5173\u7684\u968f\u673a\u65f6\u95f4\uff0c\u5e76\u89c2\u5bdf\u72d7\u72d7\u7684\u8111\u673a\u6570\u636e\u7ed3\u679c\u3002<\/p>\n\n\n\n

\u6ce8\uff1a\u4e0d\u770b\u4e0b\u5217\u516c\u5f0f\u4e0d\u5f71\u54cd\u7406\u89e3\u7ed3\u8bba<\/p>\n\n\n\n

\u5047\u8bbe\u94c3\u58f0\u4e3a\u795e\u7ecf\u5143A\uff08x_i\uff09\u3001\u8089\u4e3a\u795e\u7ecf\u5143B\uff08x_j\uff09\uff0c\u90a3\u7a81\u89e6\u6743\u91cd w_{ij} \u7684\u53d8\u5316\u6b63\u6bd4\u4e8e\u795e\u7ecf\u5143 i \u548c j \u7684\u6fc0\u6d3b\u4e58\u79ef<\/p>\n\n\n\n

\u0394<\/mi><\/mrow>w<\/mi>i<\/mi>j<\/mi><\/mrow><\/msub>=<\/mo>\u03b7<\/mi>\u22c5<\/mo>x<\/mi>i<\/mi><\/msub>\u22c5<\/mo>x<\/mi>j<\/mi><\/msub><\/mrow>\\Delta w_{ij} = \\eta \\cdot x_i \\cdot x_j<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u5b9e\u9645\u4e0a\uff0c\u6ca1\u6709\u4eba\u544a\u8bc9\u72d7\u72d7\u201c\u4f60\u5e94\u8be5\u5b66\u4f1a\u4ec0\u4e48\u201d\uff0c\u4f46\u662f\u5404\u79cd\u4fe1\u53f7\u7684\u540c\u65f6\u51fa\u73b0\uff08\u94c3\u58f0\u3001\u8089\u5473\u3001\u6d41\u53e3\u6c34\uff09\uff0c\u8ba9\u72d7\u72d7\u4e0d\u77e5\u4e0d\u89c9\u7684\u628a\u5b83\u4eec\u81ea\u52a8\u7ed1\u5b9a\u5728\u4e00\u8d77\u3002\u5982\u679c\u8111\u673a\u80fd\u591f\u6355\u6349\u5230\u72d7\u72d7\u7684\u795e\u7ecf\u5143\u6ce2\u52a8\u4fe1\u53f7\uff0c\u90a3\u4e5f\u8bb8\u8bc1\u660e\u4e86\u72d7\u72d7\u4ece\u6d41\u53e3\u6c34\u8fd9\u6837\u7684\u7ed3\u679c\u671f\u5f85\uff0c\u53d8\u6210\u4e86\u5b66\u4f1a\u5bf9\u73af\u5883\u89c4\u5f8b\u603b\u7ed3\uff0c\u5f62\u6210\u81ea\u6211\u7684\u8ba4\u77e5\u5730\u56fe\u3002\u751a\u81f3\uff0c\u72d7\u72d7\u53ef\u80fd\u4e0d\u4f1a\u6d41\u53e3\u6c34\uff0c\u4f46\u662f\u72d7\u72d7\u4f1a\u53d8\u4e3a\u5f02\u5e38\u654f\u9510\u3002\u4e00\u65e6\u94c3\u58f0\u54cd\u8d77\u800c\u8089\u6ca1\u51fa\u73b0\uff0c\u5b83\u4f1a\u611f\u5230\u975e\u5e38\u5f3a\u70c8\u7684\u5f02\u5e38\u68c0\u6d4b\u4fe1\u53f7\u3002\u94c3\u58f0\u4e0d\u518d\u7b49\u4e8e\u8089\uff0c\u800c\u662f\u94c3\u58f0\u548c\u8089\u5728\u672c\u72d7\u7684\u4e16\u754c\u89c2\u91cc\u662f\u4e00\u4ef6\u4e8b\u3002<\/p>\n\n\n\n

\u3010\u975e\u6280\u672f\u8bfb\u8005\u53ef\u8df3\u8fc7\u4ee5\u4e0b\u5c0f\u8282\u3011\u4e3a\u4e86\u8bc1\u660e\uff1a\u4e16\u754c\u91cc\uff0c\u94c3\u58f0\u548c\u8089\u603b\u662f\u4e00\u8d77\u51fa\u73b0\uff0c\u6a21\u578b\uff08\u72d7\u72d7\uff09\u88ab\u8feb\u7528\u4e00\u4e2a\u201c\u6982\u5ff5\u201d\u53bb\u7406\u89e3\u5b83\u4eec\uff0c\u53ea\u8981\u7ed9\u94c3\u58f0\uff0c\u5b83\u5c31\u4f1a\u8111\u8865\u51fa\u8089\u3002<\/p>\n\n\n\n

\u4e8e\u662f\u6211\u4eec\u7528\u81ea\u7f16\u7801\u5668\u5b9e\u73b0\u8fd9\u4e2a\u975e\u76d1\u7763\u7684\u6761\u4ef6\u53cd\u5c04\u6a21\u62df\u3002\u6211\u4eec\u5728PyTorch\u4e2d\u6a21\u62df\u8fd9\u4e2a\u5b9e\u9a8c\uff1a<\/p>\n\n\n\n

import torch\nimport torch.nn as nn\nimport torch.optim as optim\n\n# 1. \u6a21\u62df\u73af\u5883\u6570\u636e\uff1a\u94c3\u58f0\u548c\u8089\u603b\u662f\u9ad8\u5ea6\u540c\u6b65\n# \u751f\u6210 1000 \u6761\u6570\u636e\uff0c\u6a21\u62df\u94c3\u58f0\u548c\u8089\u603b\u662f\u540c\u65f6\u51fa\u73b0\uff08\u5e26\u4e00\u70b9\u566a\u58f0\uff09\ndata = torch.cat([\n    torch.ones(500, 2) + torch.randn(500, 2) * 0.1, # \u90fd\u6709\n    torch.zeros(500, 2) + torch.randn(500, 2) * 0.1 # \u90fd\u6ca1\u6709\n], dim=0)\n\n# 2. \u5b9a\u4e49\u81ea\u7f16\u7801\u5668\nclass PavlovAE(nn.Module):\n    def __init__(self):\n        super(PavlovAE, self).__init__()\n        # \u7f16\u7801\u5668\uff1a2\u7ef4 -> 1\u7ef4 (\u6f5c\u7a7a\u95f4)\n        self.encoder = nn.Linear(2, 1)\n        # \u89e3\u7801\u5668\uff1a1\u7ef4 -> 2\u7ef4 (\u91cd\u6784)\n        self.decoder = nn.Linear(1, 2)\n\n    def forward(self, x):\n        latent = torch.sigmoid(self.encoder(x)) # \u538b\u7f29\n        reconstructed = self.decoder(latent)     # \u8fd8\u539f\n        return reconstructed, latent\n\n# 3. \u8bad\u7ec3\u8fc7\u7a0b\ndevice = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\nmodel = PavlovAE().to(device)\ncriterion = nn.MSELoss()\noptimizer = optim.Adam(model.parameters(), lr=0.01)\n\ndata = data.to(device)\nfor epoch in range(200):\n    output, _ = model(data)\n    loss = criterion(output, data)\n    \n    optimizer.zero_grad()\n    loss.backward()\n    optimizer.step()\n    \n    if (epoch + 1) % 50 == 0:\n        print(f\"Epoch [{epoch+1}\/200], Loss: {loss.item():.4f}\")\n\n# 4. \u5b9e\u9a8c\u6d4b\u8bd5\nprint(\"\\n--- \u5b9e\u9a8c\u7ed3\u679c ---\")\nwith torch.no_grad():\n    # \u6d4b\u8bd5 A\uff1a\u53ea\u7ed9\u94c3\u58f0 [1, 0]\n    test_bell = torch.tensor([[1.0, 0.0]]).to(device)\n    prediction, latent = model(test_bell)\n    \n    print(f\"\u8f93\u5165\u4fe1\u53f7 (\u53ea\u6709\u94c3\u58f0): {test_bell.cpu().numpy()}\")\n    print(f\"\u6f5c\u7a7a\u95f4\u7279\u5f81 (\u7406\u89e3\u4e3a'\u665a\u9910'\u7684\u6982\u5ff5): {latent.item():.4f}\")\n    print(f\"\u6a21\u578b\u91cd\u6784\u7ed3\u679c (\u8111\u8865\u51fa\u7684\u753b\u9762): {prediction.cpu().numpy()}\")\n<\/code><\/pre>\n\n\n\n
\u5bfc\u5165Pycharm\u8fd0\u884c\u540e\u7ed3\u679c\u5982\u4e0b\uff1a
\u200b\"image.png\"\u200b<\/p>\n\n\n\n
Loss\u7ed3\u679c\u9010\u6e10\u4e0b\u964d\uff0c\u72d7\u72d7\u9010\u6e10\u7406\u89e3\u4e86\u5403\u996d\u65f6\u523b\u3002\u6f5c\u5728\u7a7a\u95f4\u7279\u5f81\u7684\u51fa\u73b0\u7ed9\u4e86\u72d7\u72d7\u4e00\u79cd\u4e0d\u662f\u771f\u5403\u996d\uff0c\u4f46\u662f\u6709\u70b9\u50cf\u5403\u996d\u7684\u4fe1\u53f7\uff0c\u8fd9\u662f\u5b83\u5df2\u7ecf\u5f00\u59cb\u5fc3\u7406\u4e0a\u51c6\u5907\u5403\u996d\u4e86\u3002\u6b63\u597d\u8bf4\u660e\u975e\u76d1\u7763\u7248\u5df4\u666e\u6d1b\u592b\u5b9e\u9a8c\u771f\u7684\u8dd1\u901a\u4e86\u3002<\/p>\n\n\n\n
\u8ff7\u832b\u5b9a\u4ef7<\/h2>\n\n\n\n
\u200b\"image.png\"
Image by Raniere<\/a> from Pixabay<\/a><\/p>\n\n\n\n
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\u200b\"image.png\"
mage by Moritz Strohm<\/a> from Pixabay<\/a><\/p>\n\n\n\n
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\u200b\"image.png\"
Image by Albrecht Fietz<\/a> from Pixabay<\/a><\/p>\n\n\n\n
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