我刚尝试了PyBrain，希望它能学习简单的线性函数 f(x) = 4x+1：
# Build the networkfrom pybrain.tools.shortcuts import buildNetworknet = buildNetwork(1, 2, 1, bias=True)# Add samplesfrom pybrain.datasets import SupervisedDataSetds = SupervisedDataSet(1, 1)for x in range(1000): ds.addSample((x, ), (4*x+1,))# Train with samplesfrom pybrain.supervised.trainers import BackpropTrainertrainer = BackpropTrainer(net, ds)for i in range(100): error = trainer.train() print("Error: %0.2f" % error)# See if it remembers print("Test function f(x)=4x+1")for i in range(10): print("f(%i) = %i" % (i, net.activate((i, ))))但当我执行这段代码时，得到的结果非常错误：
f(0) = 1962f(1) = 1962f(2) = 1962f(3) = 1962f(4) = 1962f(5) = 1962f(6) = 1962f(7) = 1962f(8) = 1962f(9) = 1962为什么这不起作用呢？
尝试2
代码：
# Build the networkfrom pybrain.tools.shortcuts import buildNetworknet = buildNetwork(1, 2, 1, bias=True)# Add samplesfrom pybrain.datasets import SupervisedDataSetds = SupervisedDataSet(1, 1)for x in range(1000): ds.addSample((x, ), (4*x+1,)) ds.addSample((x, ), (4*x+1,))# Train with samplesfrom pybrain.supervised.trainers import BackpropTrainertrainer = BackpropTrainer(net, ds, learningrate=0.001, momentum=0.99)print("Start training")a = trainer.trainUntilConvergence(dataset=ds, maxEpochs=100, verbose=True, continueEpochs=10, validationProportion=0.1)print(a)print("Finished training")# See if it remembersprint("Test function f(x)=4x+1")for i in range(10): print("f(%i) = %i" % (i, net.activate((i, ))))输出：
Start trainingtrain-errors: [ 827395.411895 755443.286202 722073.904381 748336.584579 [...]695939.638106 726953.086185 736527.150008 739789.458146 736074.235677 731222.936020 675937.725009]valid-errors: [ 2479217.507148 915115.526570 703748.266402 605613.979311 592809.132542 686959.683977 612248.174146 [...]655606.225724 637762.864477 643013.094767 620825.083765 609063.451602 607935.458244 716839.447374]([827395.41189463751, 755443.28620243724, 722073.90438077366, 748336.58457926242, 739568.58919456392, 725496.58682491502, [...]637762.86447708646, 643013.09476733557, 620825.08376532339, 609063.45160197129, 607935.45824447344, 716839.44737418776])Finished trainingTest function f(x)=4x+1f(0) = 1955f(1) = 1955f(2) = 1955f(3) = 1955f(4) = 1955f(5) = 1955f(6) = 1955f(7) = 1955f(8) = 1955f(9) = 1955回答：
神经网络通常用于训练函数 
。这意味着你不能直接使用线性函数的 (x, f(x)) 对来进行训练。（然而，这可以通过线性回归来实现）。
相反，网络需要用变量的聚类来训练，例如类似于以下内容：
#!/usr/bin/env pythonfrom random import normalvariate# Build the networkfrom pybrain.tools.shortcuts import buildNetworknet = buildNetwork(2, 1, 1, bias=True)# Add samplesfrom pybrain.datasets import SupervisedDataSetds = SupervisedDataSet(2, 1)for i in range(100): x = normalvariate(3, 0.6) y = normalvariate(2, 1) ds.addSample((x, y), (0,))for i in range(100): x = normalvariate(7, 0.5) y = normalvariate(1, 0.1) ds.addSample((x, y), (1,))# Train with samplesfrom pybrain.supervised.trainers import BackpropTrainertrainer = BackpropTrainer(net, ds, learningrate=0.1, momentum=0.99)print("Start training")print(trainer.train())a = trainer.trainUntilConvergence(dataset=ds, maxEpochs=1000, verbose=True, continueEpochs=10, validationProportion=0.1, outlayer=softmax)print("Finished training")print(trainer.train())# See if it remembersprint("Test function f(x)=4x+1")for x in range(-10,10): for y in range(-10,10): print("f(%i, %i) = %i" % (x, y, net.activate((x, y))))print("f(%i, %i) = %i" % (3, 2, net.activate((3, 2))))print("f(%i, %i) = %i" % (7, 1, net.activate((7, 1))))可以在我的博客上找到一个带有可视化的工作示例。
