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1 import theano
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2 from theano import tensor, gof, scalar
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3 import numpy
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4
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5 class ScalarSigmoid(scalar.UnaryScalarOp):
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6 def impl(self, x):
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7 return 1.0 / (1 + numpy.exp(-x))
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8 def grad(self, (x,), (gz,)):
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9 return gz * scalar_sigmoid(x) * (1.0 - scalar_sigmoid(x)),
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10 def c_foreach(self, (x,), (z,)):
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11 return "%(z)s = 1.0 / (1 + exp(-%(x)s));" % locals()
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12 scalar_sigmoid = gof.op.constructor(ScalarSigmoid)
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13 Sigmoid, sigmoid, SigmoidInplace, sigmoid_inplace \
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14 = theano.tensor.broadcast(ScalarSigmoid, 'Sigmoid')
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15
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16
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17
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18 class CrossentropySoftmax1Hot(gof.op.Op):
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19 """A special compound Op for the output of neural-net classifiers.
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20
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21 This Op has two outputs:
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22 - KL(softmax(x), y)
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23 - softmax(x)
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24
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25 x[i] is assumed to be a dense vector
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26 softmax(x[i]) is the i'th distribution over len(x[i]) options
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27 y[i] is an integer index, encoding a 1-hot distribution
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28
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29 """
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30 nin=2
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31 nout=2
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32 def __init__(self, x, y_idx,**kwargs):
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33 x = tensor._as_tensor(x)
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34 y_idx = tensor._as_tensor(y_idx)
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35 # TODO: Is this correct? It used to be y, not y_idx
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36 nll = tensor.Tensor(x.dtype, y_idx.broadcastable)
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37 # nll = Tensor(x.dtype, y.broadcastable)
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38 sm = tensor.Tensor(x.dtype, x.broadcastable)
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39 self.inputs = [x, y_idx]
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40 self.outputs = [nll,sm]
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41 def perform(self):
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42 x, y_idx = [i.data for i in self.inputs]
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43 sm = numpy.zeros_like(x) # softmax
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44 nll = numpy.zeros(x.shape[0]) #nll(y | softmax(x))
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45 for i in xrange(sm.shape[0]):
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46 sm[i] = numpy.exp(x[i] - numpy.max(x[i])) #softmax
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47 sm[i] *= 1.0 / numpy.sum(sm[i]) #vector scale
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48 nll[i] = -numpy.log( sm[i, y_idx[i]]) #cross-entropy
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49 self.outputs[0].data = nll
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50 self.outputs[1].data = sm
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51 def grad(self, (x, y_idx), (g_nll, g_sm)):
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52 if g_sm is not None:
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53 raise NotImplementedError()
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54 nll, sm = cross_entropy_softmax_1hot(x, y_idx)
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55 dx = CrossentropySoftmax1Hot.Dx(g_nll, sm, y_idx).outputs[0]
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56 return dx, None
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57
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58 class Dx (gof.op.Op):
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59 nin=3
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60 nout=1
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61 """Gradient wrt x of the CrossentropySoftmax1Hot Op"""
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62 def __init__(self, dy, sm, y_idx,**kwargs):
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63 dy = tensor._as_tensor(dy)
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64 sm = tensor._as_tensor(sm)
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65 y_idx = tensor._as_tensor(y_idx)
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66 self.inputs = [dy, sm, y_idx]
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67 self.outputs = [tensor.Tensor(sm.dtype, sm.broadcastable)]
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68 def perform(self):
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69 dy,sm,y_idx = [i.data for i in self.inputs]
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70 dx = numpy.zeros_like(sm)
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71 for i in xrange(sm.shape[0]):
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72 dx[i] = dy[i] * sm[i] #vector scale
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73 dx[i, y_idx[i]] -= dy[i] #scalar decrement
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74 self.outputs[0].data = dx
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75 def grad(self, *args):
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76 raise NotImplementedError()
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77 cross_entropy_softmax_1hot = gof.op.constructor(CrossentropySoftmax1Hot)
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78
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79 #TODO: write a version of CrossentropySoftmax1Hot that accepts a bias for x, if
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80 # this op needs to be faster.
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81
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