{"id":58225,"date":"2025-08-16T06:59:49","date_gmt":"2025-08-15T22:59:49","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58225.html"},"modified":"2025-08-16T06:59:49","modified_gmt":"2025-08-15T22:59:49","slug":"kan%ef%bc%88kolmogorov-arnold-networks%ef%bc%89%e9%9d%a9%e5%91%bd%ef%bc%9a2025%e5%b9%b4%e6%9b%bf%e4%bb%a3mlp%e7%9a%84%e5%8f%af%e8%a1%8c%e6%80%a7%e9%aa%8c%e8%af%81","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58225.html","title":{"rendered":"KAN\uff08Kolmogorov-Arnold Networks\uff09\u9769\u547d\uff1a2025\u5e74\u66ff\u4ee3MLP\u7684\u53ef\u884c\u6027\u9a8c\u8bc1"},"content":{"rendered":"

1. \u5f15\u8a00<\/h4>\n

\u5728\u8fc7\u53bb\u5341\u4f59\u5e74\u4e2d\uff0c\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09\u4f5c\u4e3a\u6df1\u5ea6\u5b66\u4e60\u7684\u57fa\u7840\u7ed3\u6784\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u56fe\u50cf\u8bc6\u522b\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3001\u79d1\u5b66\u8ba1\u7b97\u7b49\u9886\u57df\u3002\u7136\u800c\uff0c\u968f\u7740\u4efb\u52a1\u590d\u6742\u5ea6\u548c\u6a21\u578b\u89c4\u6a21\u7684\u4e0d\u65ad\u589e\u957f\uff0cMLP \u5728\u53c2\u6570\u6548\u7387\u3001\u53ef\u89e3\u91ca\u6027\u3001\u6cdb\u5316\u80fd\u529b\u7b49\u65b9\u9762\u7684\u5c40\u9650\u9010\u6e10\u663e\u73b0\u3002\u4f20\u7edf MLP \u56fa\u5b9a\u5728\u8282\u70b9\u4e0a\u7684\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\uff08\u5982 ReLU\u3001Sigmoid\u3001Tanh\uff09\u5728\u8868\u8fbe\u80fd\u529b\u548c\u9002\u5e94\u6027\u4e0a\u5b58\u5728\u4e00\u5b9a\u74f6\u9888\uff0c\u5c24\u5176\u662f\u5728\u9700\u8981\u9ad8\u5ea6\u7ed3\u6784\u5316\u8868\u793a\u6216\u7b26\u53f7\u5316\u7406\u89e3\u7684\u4efb\u52a1\u4e2d\uff0c\u96be\u4ee5\u517c\u987e\u6027\u80fd\u4e0e\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n

2024 \u5e74\uff0c\u9ebb\u7701\u7406\u5de5\u5b66\u9662\uff08MIT\uff09\u56e2\u961f\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e Kolmogorov-Arnold \u8868\u793a\u5b9a\u7406\u7684\u65b0\u578b\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u2014\u2014Kolmogorov-Arnold Networks\uff08KAN\uff09\u3002\u8be5\u67b6\u6784\u5c06\u975e\u7ebf\u6027\u6620\u5c04\u4ece\u8282\u70b9\u79fb\u52a8\u5230\u8fb9\u4e0a\uff0c\u5e76\u901a\u8fc7\u53ef\u5b66\u4e60\u7684\u5355\u53d8\u91cf\u51fd\u6570\uff08\u5982\u6837\u6761\u51fd\u6570\uff09\u8fdb\u884c\u7ec4\u5408\uff0c\u4ece\u800c\u5728\u7406\u8bba\u4e0a\u4fdd\u8bc1\u4efb\u610f\u8fde\u7eed\u591a\u53d8\u91cf\u51fd\u6570\u7684\u7cbe\u786e\u8868\u793a\u3002KAN \u7684\u8bbe\u8ba1\u7406\u5ff5\u4e0d\u4ec5\u4fdd\u7559\u4e86\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u901a\u7528\u903c\u8fd1\u80fd\u529b\uff0c\u8fd8\u663e\u8457\u63d0\u5347\u4e86\u6a21\u578b\u5728\u4f4e\u6837\u672c\u3001\u7b26\u53f7\u5316\u5efa\u6a21\u4ee5\u53ca\u79d1\u5b66\u8ba1\u7b97\u573a\u666f\u4e2d\u7684\u8868\u73b0\u6f5c\u529b\u3002<\/p>\n

\u672c\u6587\u65e8\u5728\u5728\u6807\u51c6\u89c6\u89c9\u4efb\u52a1\u4e2d\u5bf9 KAN \u7684\u53ef\u884c\u6027\u8fdb\u884c\u9a8c\u8bc1\u3002\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u5c06\u590d\u73b0 MIT \u56e2\u961f\u5728\u8bba\u6587\u4e2d\u63d0\u51fa\u7684\u6838\u5fc3\u601d\u60f3\u4e0e\u5b9e\u73b0\u7ec6\u8282\uff0c\u5e76\u5728 MNIST \u4e0e CIFAR-10 \u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u5bf9\u6bd4\u5b9e\u9a8c\uff0c\u8bc4\u4f30\u5176\u5728\u51c6\u786e\u7387\u3001\u8bad\u7ec3\u6548\u7387\u3001\u53c2\u6570\u89c4\u6a21\u548c\u53ef\u89e3\u91ca\u6027\u65b9\u9762\u76f8\u5bf9\u4e8e MLP \u7684\u4f18\u52bf\u4e0e\u4e0d\u8db3\u3002\u901a\u8fc7\u8fd9\u4e00\u8fc7\u7a0b\uff0c\u6211\u4eec\u5e0c\u671b\u63a2\u8ba8 KAN \u5728 2025 \u5e74\u662f\u5426\u5177\u5907\u66ff\u4ee3 MLP \u7684\u73b0\u5b9e\u53ef\u80fd\u6027\u3002<\/p>\n

2. \u7406\u8bba\u57fa\u7840\u4e0e\u67b6\u6784\u673a\u5236<\/h4>\n

Kolmogorov-Arnold \u8868\u793a\u5b9a\u7406\u662f 20 \u4e16\u7eaa\u6570\u5b66\u5206\u6790\u7684\u91cd\u8981\u6210\u679c\u4e4b\u4e00\uff0c\u5176\u6838\u5fc3\u89c2\u70b9\u662f\uff1a\u4efb\u610f\u8fde\u7eed\u7684\u591a\u5143\u51fd\u6570\uff0c\u90fd\u53ef\u4ee5\u901a\u8fc7\u6709\u9650\u4e2a\u5355\u53d8\u91cf\u51fd\u6570\u7684\u52a0\u548c\u4e0e\u590d\u5408\u6765\u8868\u793a\u3002KAN\uff08Kolmogorov-Arnold Networks\uff09\u6b63\u662f\u57fa\u4e8e\u8fd9\u4e00\u601d\u60f3\uff0c\u5c06\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\u4e2d\u4f4d\u4e8e\u8282\u70b9\u4e0a\u7684\u56fa\u5b9a\u6fc0\u6d3b\u51fd\u6570\uff0c\u8fc1\u79fb\u81f3\u8fde\u63a5\u8fb9\u4e0a\uff0c\u5e76\u8ba9\u8fd9\u4e9b\u975e\u7ebf\u6027\u6620\u5c04\u53d8\u4e3a\u53ef\u5b66\u4e60\u7684\u5355\u53d8\u91cf\u51fd\u6570\u3002<\/p>\n

\u5728 KAN \u4e2d\uff0c\u6bcf\u4e00\u6761\u8fde\u63a5\u8fb9\u90fd\u4e0d\u518d\u662f\u5355\u4e00\u7684\u6743\u91cd\uff0c\u800c\u662f\u4e00\u4e2a\u53ef\u5b66\u4e60\u7684\u51fd\u6570\u6620\u5c04\uff08\u5e38\u7528\u6837\u6761\u51fd\u6570\u5b9e\u73b0\uff09\u3002\u8282\u70b9\u4e4b\u95f4\u7684\u8ba1\u7b97\u4e0d\u518d\u662f\u7b80\u5355\u7684\u7ebf\u6027\u52a0\u6743\uff0c\u800c\u662f\u591a\u4e2a\u5355\u53d8\u91cf\u51fd\u6570\u7684\u7ec4\u5408\u4e0e\u7d2f\u52a0\u3002\u8fd9\u79cd\u67b6\u6784\u7684\u76f4\u63a5\u597d\u5904\u662f\uff1a<\/p>\n

  • \n

    \u8868\u8fbe\u80fd\u529b\u63d0\u5347\uff1a\u8fb9\u4e0a\u53ef\u5b66\u4e60\u7684\u51fd\u6570\u80fd\u81ea\u9002\u5e94\u6570\u636e\u5206\u5e03\uff0c\u51cf\u5c11\u5bf9\u5927\u89c4\u6a21\u53c2\u6570\u7684\u4f9d\u8d56\u3002<\/p>\n<\/li>\n

  • \n

    \u53c2\u6570\u6548\u7387\u66f4\u9ad8\uff1a\u5728\u76f8\u540c\u7cbe\u5ea6\u4e0b\uff0c\u6240\u9700\u53c2\u6570\u91cf\u53ef\u6bd4 MLP \u5c11\u3002<\/p>\n<\/li>\n

  • \n

    \u53ef\u89e3\u91ca\u6027\u589e\u5f3a\uff1a\u6bcf\u6761\u8fb9\u7684\u51fd\u6570\u90fd\u53ef\u4ee5\u5355\u72ec\u5206\u6790\u3001\u53ef\u89c6\u5316\uff0c\u4fbf\u4e8e\u7406\u89e3\u6a21\u578b\u5982\u4f55\u6620\u5c04\u8f93\u5165\u5230\u8f93\u51fa\u3002<\/p>\n<\/li>\n

    \u5728\u5b9e\u73b0\u4e0a\uff0cKAN \u901a\u5e38\u4f1a\u4f7f\u7528\u6837\u6761\u63d2\u503c\uff08Spline\uff09\u6765\u8868\u793a\u53ef\u5b66\u4e60\u51fd\u6570\uff0c\u56e0\u4e3a\u6837\u6761\u5728\u6570\u503c\u7a33\u5b9a\u6027\u3001\u5149\u6ed1\u6027\u548c\u53ef\u5fae\u6027\u4e0a\u90fd\u8868\u73b0\u51fa\u8272\uff0c\u540c\u65f6\u68af\u5ea6\u8ba1\u7b97\u4e5f\u76f8\u5bf9\u5bb9\u6613\u3002MIT \u7684\u5f00\u6e90\u5b9e\u73b0\u63d0\u4f9b\u4e86 pykan \u5e93\uff0c\u53ef\u4ee5\u76f4\u63a5\u5728 PyTorch \u4e2d\u5b9a\u4e49\u548c\u8bad\u7ec3 KAN \u6a21\u578b\u3002<\/p>\n

    \u4e0b\u9762\u7ed9\u51fa\u4e00\u4e2a\u4f7f\u7528 pykan \u5e93\u5b9e\u73b0\u7b80\u5355 KAN \u67b6\u6784\u7684\u793a\u4f8b\u4ee3\u7801\uff08\u4ee5 MNIST \u8f93\u5165\u7ef4\u5ea6\u4e3a\u4f8b\uff09\uff1a<\/p>\n

    # \u5b89\u88c5 pykan \u5e93\uff08\u5982\u679c\u5c1a\u672a\u5b89\u88c5\uff09
    \n# pip install pykan torch torchvision<\/p>\n

    import torch
    \nimport torch.nn as nn
    \nimport torch.optim as optim
    \nfrom torchvision import datasets, transforms
    \nfrom pykan import KAN<\/p>\n

    # \u6570\u636e\u9884\u5904\u7406
    \ntransform = transforms.Compose([
    \n transforms.ToTensor(),
    \n transforms.Normalize((0.1307,), (0.3081,))
    \n])<\/p>\n

    train_dataset = datasets.MNIST(root=\\’.\/data\\’, train=True, download=True, transform=transform)
    \ntest_dataset = datasets.MNIST(root=\\’.\/data\\’, train=False, download=True, transform=transform)<\/p>\n

    train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=64, shuffle=True)
    \ntest_loader = torch.utils.data.DataLoader(test_dataset, batch_size=1000, shuffle=False)<\/p>\n

    # \u5b9a\u4e49 KAN \u6a21\u578b
    \n# \u8fd9\u91cc\u8f93\u5165\u4e3a 28*28 = 784 \u7ef4\uff0c\u8f93\u51fa\u4e3a 10 \u7c7b
    \n# hidden_sizes \u5b9a\u4e49\u6bcf\u5c42\u7684\u9690\u85cf\u5355\u5143\u6570
    \nmodel = KAN(
    \n layers_hidden=[784, 64, 32, 10], # \u7f51\u7edc\u5c42\u7ed3\u6784
    \n spline_order=3, # \u6837\u6761\u9636\u6570
    \n grid_size=16 # \u6837\u6761\u7f51\u683c\u5bc6\u5ea6
    \n)<\/p>\n

    # \u5b9a\u4e49\u635f\u5931\u51fd\u6570\u4e0e\u4f18\u5316\u5668
    \ncriterion = nn.CrossEntropyLoss()
    \noptimizer = optim.Adam(model.parameters(), lr=0.001)<\/p>\n

    # \u8bad\u7ec3\u51fd\u6570
    \ndef train(model, device, train_loader, optimizer, epoch):
    \n model.train()
    \n for batch_idx, (data, target) in enumerate(train_loader):
    \n data, target = data.view(data.size(0), -1).to(device), target.to(device)
    \n optimizer.zero_grad()
    \n output = model(data)
    \n loss = criterion(output, target)
    \n loss.backward()
    \n optimizer.step()
    \n if batch_idx % 100 == 0:
    \n print(f\\”Train Epoch: {epoch} [{batch_idx * len(data)}\/{len(train_loader.dataset)}] Loss: {loss.item():.6f}\\”)<\/p>\n

    # \u6d4b\u8bd5\u51fd\u6570
    \ndef test(model, device, test_loader):
    \n model.eval()
    \n test_loss = 0
    \n correct = 0
    \n with torch.no_grad():
    \n for data, target in test_loader:
    \n data, target = data.view(data.size(0), -1).to(device), target.to(device)
    \n output = model(data)
    \n test_loss += criterion(output, target).item()
    \n pred = output.argmax(dim=1)
    \n correct += pred.eq(target).sum().item()
    \n test_loss \/= len(test_loader.dataset)
    \n print(f\\”\\\\nTest set: Average loss: {test_loss:.4f}, Accuracy: {correct}\/{len(test_loader.dataset)} \\”
    \n f\\”({100. * correct \/ len(test_loader.dataset):.2f}%)\\\\n\\”)<\/p>\n

    # \u8bbe\u5907\u9009\u62e9
    \ndevice = torch.device(\\”cuda\\” if torch.cuda.is_available() else \\”cpu\\”)
    \nmodel.to(device)<\/p>\n

    # \u8bad\u7ec3\u4e0e\u6d4b\u8bd5\u5faa\u73af
    \nfor epoch in range(1, 6):
    \n train(model, device, train_loader, optimizer, epoch)
    \n test(model, device, test_loader)<\/p>\n

    \u8be5\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u5728 MNIST \u6570\u636e\u96c6\u4e0a\u5feb\u901f\u642d\u5efa\u5e76\u8bad\u7ec3\u4e00\u4e2a KAN \u6a21\u578b\u3002\u4e0e MLP \u4e0d\u540c\u7684\u662f\uff0c\u8fd9\u91cc\u7684\u6bcf\u4e00\u6761\u8fde\u63a5\u8fb9\u90fd\u4f7f\u7528\u4e86\u53ef\u5b66\u4e60\u7684\u6837\u6761\u51fd\u6570\u6765\u8fdb\u884c\u6620\u5c04\uff0c\u8fd9\u4f7f\u5f97\u7f51\u7edc\u5728\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u80fd\u591f\u7075\u6d3b\u5730\u9002\u5e94\u6570\u636e\u7684\u975e\u7ebf\u6027\u7279\u5f81\u3002<\/p>\n

    3. \u5b9e\u9a8c\u8bbe\u8ba1\u4e0e\u590d\u73b0\u65b9\u6848<\/h4>\n

    \u4e3a\u4e86\u7cfb\u7edf\u8bc4\u4f30 KAN \u5728\u6807\u51c6\u89c6\u89c9\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u5bf9\u6bd4\u5b9e\u9a8c\uff0c\u76ee\u6807\u662f\u9a8c\u8bc1\u5176\u5728\u51c6\u786e\u7387\u3001\u8bad\u7ec3\u6548\u7387\u3001\u53c2\u6570\u89c4\u6a21\u4e0e\u53ef\u89e3\u91ca\u6027\u65b9\u9762\u7684\u4f18\u52bf\u4e0e\u4e0d\u8db3\u3002\u672c\u5b9e\u9a8c\u91c7\u7528 MNIST \u548c CIFAR-10 \u4e24\u4e2a\u7ecf\u5178\u6570\u636e\u96c6\uff0c\u5e76\u4ee5 MLP \u4f5c\u4e3a\u57fa\u51c6\u6a21\u578b\u3002\u5b9e\u9a8c\u6d41\u7a0b\u5206\u4e3a\u6570\u636e\u51c6\u5907\u3001\u6a21\u578b\u5b9a\u4e49\u3001\u8bad\u7ec3\u6d41\u7a0b\u4e0e\u53ef\u89e3\u91ca\u6027\u53ef\u89c6\u5316\u56db\u4e2a\u90e8\u5206\u3002<\/p>\n

    \u5b9e\u9a8c\u76ee\u6807<\/p>\n

      \n
    • \n

      \u5728 MNIST \u4e0e CIFAR-10 \u6570\u636e\u96c6\u4e0a\u590d\u73b0 <\/p>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

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