├── README.md ├── digits.dat ├── img ├── nerual-net-nolabels.png ├── nerual-net-nolabels.psd ├── neuron-with-sigma.png ├── neuron.psd ├── simple-neuron.png ├── sine-approximation.png ├── square-letters.png ├── three-node-ex.png ├── threenodeex.png ├── unknown-error.psd ├── weighted-sum-error.psd └── weightedsumerror.png ├── neural-networks.tar.gz ├── neuralnetwork-tests.py ├── neuralnetwork.py ├── neuralnetwork.pyc ├── sine-neural-net.nb ├── sine.txt ├── sine2.txt ├── unittest.py └── unittest.pyc /README.md: -------------------------------------------------------------------------------- 1 | neural-networks 2 | =============== 3 | 4 | Python code and data sets used in the post ["Neural Networks and the Backpropagation Algorithm"](http://jeremykun.wordpress.com/2012/12/09/neural-networks-and-backpropagation/) 5 | -------------------------------------------------------------------------------- /img/nerual-net-nolabels.png: 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https://raw.githubusercontent.com/j2kun/neural-networks/89c0157b1d5c4af9d9ef6e7d066d6be5f548e74c/neural-networks.tar.gz -------------------------------------------------------------------------------- /neuralnetwork-tests.py: -------------------------------------------------------------------------------- 1 | from unittest import * 2 | from neuralnetwork import * 3 | 4 | def binaryNumbersTest(): 5 | network = Network() 6 | inputNodes = [InputNode(i) for i in range(3)] 7 | hiddenNodes = [Node() for i in range(3)] 8 | outputNode = Node() 9 | 10 | # weights are all randomized 11 | for inputNode in inputNodes: 12 | for node in hiddenNodes: 13 | Edge(inputNode, node) 14 | 15 | for node in hiddenNodes: 16 | Edge(node, outputNode) 17 | 18 | network.outputNode = outputNode 19 | network.inputNodes.extend(inputNodes) 20 | 21 | labeledExamples = [((0,0,0), 1), 22 | ((0,0,1), 0), 23 | ((0,1,0), 1), 24 | ((0,1,1), 0), 25 | ((1,0,0), 1), 26 | ((1,0,1), 0), 27 | ((1,1,0), 1), 28 | ((1,1,1), 0)] 29 | network.train(labeledExamples, maxIterations=5000) 30 | 31 | # test for consistency 32 | for number, isEven in labeledExamples: 33 | print "Error for %r is %0.4f. Output was:%0.4f" % (number, isEven - network.evaluate(number), network.evaluate(number)) 34 | 35 | 36 | def makeNetwork(numInputs, numHiddenLayers, numInEachLayer): 37 | network = Network() 38 | inputNodes = [InputNode(i) for i in range(numInputs)] 39 | outputNode = Node() 40 | network.outputNode = outputNode 41 | network.inputNodes.extend(inputNodes) 42 | 43 | layers = [[Node() for _ in range(numInEachLayer)] for _ in range(numHiddenLayers)] 44 | 45 | # weights are all randomized 46 | for inputNode in inputNodes: 47 | for node in layers[0]: 48 | Edge(inputNode, node) 49 | 50 | for layer1, layer2 in [(layers[i], layers[i+1]) for i in range(numHiddenLayers-1)]: 51 | for node1 in layer1: 52 | for node2 in layer2: 53 | Edge(node1, node2) 54 | 55 | for node in layers[-1]: 56 | Edge(node, outputNode) 57 | 58 | return network 59 | 60 | 61 | def sineTest(numLayers, numNodes): 62 | import math 63 | import random 64 | 65 | f = lambda x: 0.5 * (1.0 + math.sin(x)) 66 | domain = lambda: [random.random()*math.pi*4 for _ in range(100)] 67 | 68 | network = makeNetwork(1, numLayers, numNodes) 69 | labeledExamples = [((x,), f(x)) for x in domain()] 70 | network.train(labeledExamples, learningRate=0.25, maxIterations=100000) 71 | 72 | errors = [abs(f(x) - network.evaluate((x,))) for x in domain()] 73 | print "Avg error: %.4f" % (sum(errors) * 1.0 / len(errors)) 74 | 75 | with open('sine.txt', 'a') as theFile: 76 | vals = tuple((x,network.evaluate((x,))) for x in domain()) 77 | line = "{%s},\n" % (",".join(["{%s}" % ",".join([str(n) for n in x]) for x in vals]),) 78 | theFile.write(line) 79 | 80 | 81 | def digitsTest(): 82 | import random 83 | network = makeNetwork(256, 2, 15) 84 | 85 | digits = [] 86 | 87 | with open('digits.dat', 'r') as dataFile: 88 | for line in dataFile: 89 | (exampleStr, classStr) = line.split(',') 90 | digits.append(([int(x) for x in exampleStr.split()], float(classStr) / 9)) 91 | 92 | random.shuffle(digits) 93 | trainingData, testData = digits[:-500], digits[-500:] 94 | 95 | network.train(trainingData, learningRate=0.5, maxIterations=100000) 96 | errors = [abs(testPt[-1] - round(network.evaluate(testPt[0]))) for testPt in testData] 97 | print "Average error: %.4f" % (sum(errors)*1.0 / len(errors)) 98 | 99 | 100 | if __name__ == "__main__": 101 | #binaryNumbersTest() 102 | 103 | print "Sine" 104 | with open('sine.txt','w') as theFile: 105 | theFile.write("{") 106 | 107 | sineTest(1, 20) 108 | 109 | with open('sine.txt','a') as theFile: 110 | theFile.write("}\n") 111 | 112 | print "Digits" 113 | digitsTest() 114 | -------------------------------------------------------------------------------- /neuralnetwork.py: -------------------------------------------------------------------------------- 1 | import random 2 | import math 3 | 4 | def activationFunction(x): 5 | return 1.0 / (1.0 + math.exp(-x)) 6 | 7 | class Node: 8 | def __init__(self): 9 | self.lastOutput = None 10 | self.lastInput = None 11 | self.error = None 12 | self.outgoingEdges = [] 13 | self.incomingEdges = [] 14 | self.addBias() 15 | 16 | def addBias(self): 17 | self.incomingEdges.append(Edge(BiasNode(), self)) 18 | 19 | def evaluate(self, inputVector): 20 | if self.lastOutput is not None: 21 | return self.lastOutput 22 | 23 | self.lastInput = [] 24 | weightedSum = 0 25 | 26 | for e in self.incomingEdges: 27 | theInput = e.source.evaluate(inputVector) 28 | self.lastInput.append(theInput) 29 | weightedSum += e.weight * theInput 30 | 31 | self.lastOutput = activationFunction(weightedSum) 32 | self.evaluateCache = self.lastOutput 33 | return self.lastOutput 34 | 35 | def getError(self, label): 36 | ''' Get the error for a given node in the network. If the node is an 37 | output node, label will be used to compute the error. For an input node, we 38 | simply ignore the error. ''' 39 | 40 | if self.error is not None: 41 | return self.error 42 | 43 | assert self.lastOutput is not None 44 | 45 | if self.outgoingEdges == []: # this is an output node 46 | self.error = label - self.lastOutput 47 | else: 48 | self.error = sum([edge.weight * edge.target.getError(label) for edge in self.outgoingEdges]) 49 | 50 | return self.error 51 | 52 | def updateWeights(self, learningRate): 53 | ''' Update the weights of a node, and all of its successor nodes. 54 | Assume self is not an InputNode. If the error, lastOutput, and 55 | lastInput are None, then this node has already been updated. ''' 56 | 57 | if (self.error is not None and self.lastOutput is not None 58 | and self.lastInput is not None): 59 | 60 | for i, edge in enumerate(self.incomingEdges): 61 | edge.weight += (learningRate * self.lastOutput * (1 - self.lastOutput) * 62 | self.error * self.lastInput[i]) 63 | 64 | for edge in self.outgoingEdges: 65 | edge.target.updateWeights(learningRate) 66 | 67 | self.error = None 68 | self.lastInput = None 69 | self.lastOutput = None 70 | 71 | def clearEvaluateCache(self): 72 | if self.lastOutput is not None: 73 | self.lastOutput = None 74 | for edge in self.incomingEdges: 75 | edge.source.clearEvaluateCache() 76 | 77 | 78 | class InputNode(Node): 79 | ''' Input nodes simply evaluate to the value of the input for that index. 80 | As such, each input node must specify an index. We allow multiple copies 81 | of an input node with the same index (why not?). ''' 82 | 83 | def __init__(self, index): 84 | Node.__init__(self) 85 | self.index = index; 86 | 87 | def evaluate(self, inputVector): 88 | self.lastOutput = inputVector[self.index] 89 | return self.lastOutput 90 | 91 | def updateWeights(self, learningRate): 92 | for edge in self.outgoingEdges: 93 | edge.target.updateWeights(learningRate) 94 | 95 | def getError(self, label): 96 | for edge in self.outgoingEdges: 97 | edge.target.getError(label) 98 | 99 | def addBias(self): 100 | pass 101 | 102 | def clearEvaluateCache(self): 103 | self.lastOutput = None 104 | 105 | 106 | class BiasNode(InputNode): 107 | def __init__(self): 108 | Node.__init__(self) 109 | 110 | def evaluate(self, inputVector): 111 | return 1.0 112 | 113 | 114 | class Edge: 115 | def __init__(self, source, target): 116 | self.weight = random.uniform(0,1) 117 | self.source = source 118 | self.target = target 119 | 120 | # attach the edges to its nodes 121 | source.outgoingEdges.append(self) 122 | target.incomingEdges.append(self) 123 | 124 | 125 | class Network: 126 | def __init__(self): 127 | self.inputNodes = [] 128 | self.outputNode = None 129 | 130 | def evaluate(self, inputVector): 131 | assert max([v.index for v in self.inputNodes]) < len(inputVector) 132 | self.outputNode.clearEvaluateCache() 133 | 134 | output = self.outputNode.evaluate(inputVector) 135 | return output 136 | 137 | def propagateError(self, label): 138 | for node in self.inputNodes: 139 | node.getError(label) 140 | 141 | def updateWeights(self, learningRate): 142 | for node in self.inputNodes: 143 | node.updateWeights(learningRate) 144 | 145 | def train(self, labeledExamples, learningRate=0.9, maxIterations=10000): 146 | while maxIterations > 0: 147 | for example, label in labeledExamples: 148 | output = self.evaluate(example) 149 | self.propagateError(label) 150 | self.updateWeights(learningRate) 151 | 152 | maxIterations -= 1 153 | 154 | 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5 | } 6 | -------------------------------------------------------------------------------- /unittest.py: -------------------------------------------------------------------------------- 1 | def test(expected, actual): 2 | if expected != actual: 3 | import sys, traceback 4 | (filename, lineno, container, code) = traceback.extract_stack()[-2] 5 | print("Test: %r failed on line %d in file %r.\nExpected %r but got %r\n" % 6 | (code, lineno, filename, expected, actual)) 7 | 8 | -------------------------------------------------------------------------------- /unittest.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/j2kun/neural-networks/89c0157b1d5c4af9d9ef6e7d066d6be5f548e74c/unittest.pyc --------------------------------------------------------------------------------