Mercurial > pylearn
annotate nnet_ops.py @ 421:e01f17be270a
Kernel regression learning algorithm
author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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date | Sat, 19 Jul 2008 10:11:22 -0400 |
parents | 43d9aa93934e |
children | 18dbc1c11647 |
rev | line source |
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419
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1 ## This file contain ops that are not currently integrated in the core of threano. |
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2 ## Not all of those ops have been thoroughly tested. |
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3 |
24 | 4 import theano |
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5 from theano import tensor, scalar |
24 | 6 import numpy |
7 | |
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8 ############ |
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9 # |
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10 # SCALAR OPS |
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11 # |
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12 |
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13 class ScalarSigmoid(scalar.UnaryScalarOp): |
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14 @staticmethod |
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15 def st_impl(x): |
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16 if x < -30.0: |
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17 return 0.0 |
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18 if x > 30.0: |
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19 return 1.0 |
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20 return 1.0 / (1.0 + numpy.exp(-x)) |
24 | 21 def impl(self, x): |
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22 return ScalarSigmoid.st_impl(x) |
24 | 23 def grad(self, (x,), (gz,)): |
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24 y = scalar_sigmoid(x) |
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25 return [gz * y * (1.0 - y)] |
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26 def c_code(self, node, name, (x,), (z,), sub): |
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27 if node.inputs[0].type in [scalar.float32, scalar.float64]: |
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28 return """%(z)s = |
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29 %(x)s < -30.0 |
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30 ? 0.0 |
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31 : %(x)s > 30.0 |
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32 ? 1.0 |
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33 : 1.0 /(1.0+exp(-%(x)s));""" % locals() |
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34 raise NotImplementedError('only floatingpoint is implemented') |
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35 scalar_sigmoid = ScalarSigmoid(scalar.upgrade_to_float, name='scalar_sigmoid') |
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36 sigmoid = tensor.Elemwise(scalar_sigmoid, name='sigmoid') |
24 | 37 |
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38 class ScalarSoftplus(scalar.UnaryScalarOp): |
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39 @staticmethod |
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40 def static_impl(x): |
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41 if x < -30.0: |
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42 return 0.0 |
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43 if x > 30.0: |
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44 return x |
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45 return numpy.log1p(numpy.exp(x)) |
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46 def impl(self, x): |
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47 return ScalarSoftplus.static_impl(x) |
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48 def grad(self, (x,), (gz,)): |
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49 return [gz * scalar_sigmoid(x)] |
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50 def c_code(self, node, name, (x,), (z,), sub): |
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51 if node.inputs[0].type in [scalar.float32, scalar.float64]: |
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52 return """%(z)s = |
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53 %(x)s < -30.0 |
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54 ? 0.0 |
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55 : %(x)s > 30.0 |
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56 ? %(x)s |
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57 : log1p(exp(%(x)s));""" % locals() |
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58 raise NotImplementedError('only floating point x is implemented') |
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59 scalar_softplus = ScalarSoftplus(scalar.upgrade_to_float, name='scalar_softplus') |
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60 softplus = tensor.Elemwise(scalar_softplus, name='softplus') |
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61 |
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62 |
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63 ############ |
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64 # |
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65 # TENSOR OPS |
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66 # |
24 | 67 |
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68 class CrossentropySoftmax1HotWithBias(theano.Op): |
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69 """A special compound L{Op} for the output of neural-net classifiers. |
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70 |
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71 @type x: is a matrix of floats (32 or 64) |
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72 @type b: is a [row] vector of floats (32 or 64), length is number of cols in x |
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73 @type y_idx: a [column] vector of int (32 or 64), length is number of rows in x |
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74 |
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75 @precondition: every entry in y_idx is a valid (non-negative) column index into x |
24 | 76 |
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77 This L{Op} has two outputs: |
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78 - KL(softmax(x+b), y) |
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79 - softmax(x+b) |
24 | 80 |
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81 |
24 | 82 softmax(x[i]) is the i'th distribution over len(x[i]) options |
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83 |
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84 y_idx[i] is an integer index, encoding a 1-hot distribution. |
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85 |
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86 In practice, when we're trying to do classification, we have one row in x |
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87 and y_idx per example, and y[i] is the index of the (correct) class of the |
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88 i'th example. |
24 | 89 |
90 """ | |
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91 nin=3 |
24 | 92 nout=2 |
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93 def __init__(self, **kwargs): |
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94 theano.Op.__init__(self, **kwargs) |
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95 |
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96 def make_node(self, x, b, y_idx): |
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97 x = tensor.as_tensor(x) |
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98 b = tensor.as_tensor(b) |
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99 y_idx = tensor.as_tensor(y_idx) |
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100 if x.type.ndim != 2 \ |
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101 or x.type.dtype not in ['float32', 'float64']: |
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102 raise ValueError('x must be 2-d tensor of floats') |
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103 if b.type.ndim != 1 \ |
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104 or x.type.dtype not in ['float32', 'float64']: |
121 | 105 raise ValueError('b must be 1-d tensor of floats') |
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106 if y_idx.type.ndim != 1 \ |
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107 or y_idx.type.dtype not in ['int8', 'int16', 'int32', 'int64']: |
121 | 108 raise ValueError('y_idx must be 1-d tensor of ints') |
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109 |
24 | 110 # TODO: Is this correct? It used to be y, not y_idx |
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111 nll = tensor.Tensor(x.type.dtype, |
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112 y_idx.type.broadcastable).make_result() |
24 | 113 # nll = Tensor(x.dtype, y.broadcastable) |
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114 sm = x.type.make_result() |
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115 return theano.Apply(self, [x, b, y_idx], [nll, sm]) |
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116 def perform(self, node, input_storage, output_storage): |
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117 x, b, y_idx = input_storage |
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118 if b.shape[0] != x.shape[1]: |
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119 raise ValueError('b must have same number of columns as x') |
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120 if y_idx.shape[0] != x.shape[0]: |
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121 raise ValueError('y_idx must have same number of rows as x') |
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122 |
24 | 123 sm = numpy.zeros_like(x) # softmax |
124 nll = numpy.zeros(x.shape[0]) #nll(y | softmax(x)) | |
125 for i in xrange(sm.shape[0]): | |
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126 row = x[i] + b |
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127 sm[i] = numpy.exp(row - numpy.max(row)) #softmax |
24 | 128 sm[i] *= 1.0 / numpy.sum(sm[i]) #vector scale |
129 nll[i] = -numpy.log( sm[i, y_idx[i]]) #cross-entropy | |
117
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130 output_storage[0][0] = nll |
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131 output_storage[1][0] = sm |
30
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132 def grad(self, (x, b, y_idx), (g_nll, g_sm)): |
24 | 133 if g_sm is not None: |
134 raise NotImplementedError() | |
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135 nll, sm = crossentropy_softmax_1hot_with_bias(x, b, y_idx) |
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136 dx = CrossentropySoftmax1HotWithBiasDx()(g_nll, sm, y_idx) |
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137 db = tensor.sum(dx, axis = [0]) |
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138 return dx, db, None |
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139 |
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140 def c_headers(self): return ['<iostream>'] |
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141 def c_code(self, node, name, (x, b, y_idx), (nll, sm), sub): |
30
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142 # this implementation was lifted from |
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143 # /u/bergstrj/cvs/bergstrj/src/feb07/nn.cxx |
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144 |
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145 #TODO: put this into a templated function, in the support code |
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146 #TODO: declare the max of each row as an Op output |
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147 |
32 | 148 #TODO: set error messages for failures in this code |
149 | |
184
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150 #TODO: use this to accept float32 and int32: node.inputs[0].type.dtype_specs()[1] |
185
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151 y_idx_type = node.inputs[2].type.dtype_specs()[1] |
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152 |
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153 return """ |
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154 npy_intp* Nx = %(x)s->dimensions; |
34 | 155 |
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156 if (%(x)s->nd != 2) |
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157 { |
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158 PyErr_SetString(PyExc_ValueError, "a not 2d tensor"); |
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159 %(fail)s; |
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160 } |
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161 if (%(b)s->nd != 1) |
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162 { |
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163 PyErr_SetString(PyExc_ValueError, "b not 1d tensor"); |
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164 %(fail)s; |
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165 } |
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166 if (%(y_idx)s->nd != 1) |
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167 { |
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168 PyErr_SetString(PyExc_ValueError, "y_idx not 1d tensor"); |
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169 %(fail)s; |
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170 } |
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171 if (%(x)s->descr->type_num != PyArray_DOUBLE) |
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172 { |
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173 PyErr_SetString(PyExc_TypeError, "a not float64"); |
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174 %(fail)s; |
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175 } |
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176 if (%(b)s->descr->type_num != PyArray_DOUBLE) |
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177 { |
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178 PyErr_SetString(PyExc_TypeError, "b not float64"); |
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179 %(fail)s; |
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180 } |
185
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181 if ((%(y_idx)s->descr->type_num != PyArray_INT64) |
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182 && (%(y_idx)s->descr->type_num != PyArray_INT32) |
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183 && (%(y_idx)s->descr->type_num != PyArray_INT16) |
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184 && (%(y_idx)s->descr->type_num != PyArray_INT8)) |
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185 { |
185
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186 PyErr_SetString(PyExc_TypeError, "y_idx not int8, int16, int32, or int64"); |
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187 %(fail)s; |
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188 } |
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189 if ((%(x)s->dimensions[1] != %(b)s->dimensions[0]) |
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190 || (%(x)s->dimensions[0] != %(y_idx)s->dimensions[0])) |
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191 { |
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192 PyErr_SetString(PyExc_ValueError, "dimension mismatch in arguments"); |
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193 %(fail)s; |
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194 } |
34 | 195 |
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196 if ((NULL == %(nll)s) //initial condition |
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197 || (%(nll)s->dimensions[0] != %(y_idx)s->dimensions[0])) |
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198 { |
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199 if (NULL != %(nll)s) Py_XDECREF(%(nll)s); |
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200 %(nll)s = (PyArrayObject*)PyArray_SimpleNew(1, PyArray_DIMS(%(y_idx)s), type_num_%(x)s); |
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201 if(!%(nll)s) |
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202 { |
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203 PyErr_SetString(PyExc_MemoryError, "failed to alloc nll output"); |
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204 %(fail)s; |
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205 } |
34 | 206 } |
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207 if ((NULL == %(sm)s) |
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208 || (%(sm)s->dimensions[0] != %(x)s->dimensions[0]) |
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209 || (%(sm)s->dimensions[1] != %(x)s->dimensions[1])) |
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210 { |
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211 if (NULL != %(sm)s) Py_XDECREF(%(sm)s); |
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212 %(sm)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(x)s), type_num_%(x)s); |
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213 if(!%(sm)s) { |
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214 // The normal cleanup code will take care of %(nll)s |
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215 // Py_XDECREF(%(nll)s); %(nll)s=NULL; |
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216 PyErr_SetString(PyExc_MemoryError, "failed to alloc sm output"); |
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217 %(fail)s |
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218 } |
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219 } |
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220 |
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221 for (size_t i = 0; i < Nx[0]; ++i) |
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222 { |
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223 size_t j; |
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224 double sum = 0.0; |
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225 bool discount_max = false; |
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226 |
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227 const double* __restrict__ x_i = (double*)(%(x)s->data + %(x)s->strides[0] * i); |
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228 const double* __restrict__ b_i = (double*)(%(b)s->data); |
185
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229 const %(y_idx_type)s y_i = ((%(y_idx_type)s*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0]; |
30
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230 double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i); |
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231 double* __restrict__ nll_i = (double*)(%(nll)s->data + %(nll)s->strides[0] * i); |
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232 |
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233 npy_intp Sx = %(x)s->strides[1]/sizeof(double); |
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234 npy_intp Sb = %(b)s->strides[0]/sizeof(double); |
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235 npy_intp Ssm = %(sm)s->strides[1]/sizeof(double); |
24 | 236 |
30
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237 size_t row_max_j=0; |
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238 double row_max = x_i[0] + b_i[0]; |
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239 //try to compute sum and sm the easy way |
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240 for (j = 0; j < Nx[1]; ++j) |
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241 { |
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242 double row_ij = x_i[j * Sx] + b_i[j * Sb]; |
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243 row_max_j = (row_ij > row_max) ? j : row_max_j; |
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244 row_max = (row_ij > row_max) ? row_ij : row_max; |
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245 |
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246 double sm_ij = exp(row_ij); |
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247 sum += sm_ij; |
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248 sm_i[j * Ssm] = sm_ij; |
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249 } |
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250 if ((0.0 == sum) || (isinf(sum))) |
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251 { |
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252 //our cheap trick didn't work... try again and do it better. |
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253 discount_max = true; |
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254 sum = 0.0; //reset sum and recompute.... |
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255 for (j = 0; j < Nx[1]; ++j) |
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256 { |
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257 double row_ij = x_i[j * Sx] + b_i[j * Sb]; |
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258 |
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259 double sm_ij = exp(row_ij - row_max); |
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260 sum += sm_ij; |
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261 sm_i[j * Ssm] = sm_ij; |
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262 } |
32 | 263 if ( (0.0 == sum) || (isinf(sum))) |
264 { | |
265 //that was our best... | |
266 %(fail)s; | |
267 } | |
30
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268 //if we still can't sum it up, we're screwed. |
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269 //So far, this assertion has never failed... |
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270 } |
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271 |
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272 //cblas_dscal(x.N, 1.0 / sum, &mat_at(s,i,0), s.n); |
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273 double sum_inv = 1.0 / sum; |
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274 for (j = 0; j < Nx[1]; ++j) |
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275 { |
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276 sm_i[j * Ssm] *= sum_inv; |
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277 } |
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278 |
32 | 279 if (y_i >= Nx[1]) |
280 { | |
281 %(fail)s; | |
282 } | |
30
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283 |
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284 nll_i[0] = - x_i[y_i*Sx] |
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285 - b_i[y_i*Sb] |
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286 + (discount_max ? row_max : 0.0) |
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287 + log(sum); |
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288 //mat_at(y,i,0) = -log( mat_at(s,i,t[i])); //less accurate? |
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289 //mat_at(y,i,0) = - mat_at(x,i,t[i]) - mat_at(b,0,t[i]) + (discount_max ? maxi : 0.0) + log(sum); |
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290 } |
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291 """ % dict(locals(), **sub) |
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292 crossentropy_softmax_1hot_with_bias = CrossentropySoftmax1HotWithBias() |
30
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293 |
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294 class CrossentropySoftmax1HotWithBiasDx (theano.Op): |
30
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295 nin=3 |
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296 nout=1 |
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297 """Gradient wrt x of the CrossentropySoftmax1Hot Op""" |
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298 def __init__(self, **kwargs): |
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299 theano.Op.__init__(self,**kwargs) |
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300 def make_node(self, dy, sm, y_idx,**kwargs): |
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301 dy = tensor.as_tensor(dy) |
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302 sm = tensor.as_tensor(sm) |
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303 y_idx = tensor.as_tensor(y_idx) |
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304 return theano.Apply(self, [dy, sm, y_idx],[sm.type.make_result()]) |
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305 def perform(self, node, input_storage, output_storage): |
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306 dy,sm,y_idx = input_storage |
30
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307 dx = numpy.zeros_like(sm) |
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308 for i in xrange(sm.shape[0]): |
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309 dx[i] = dy[i] * sm[i] #vector scale |
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310 dx[i, y_idx[i]] -= dy[i] #scalar decrement |
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311 output_storage[0][0] = dx |
30
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312 def grad(self, *args): |
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313 raise NotImplementedError() |
181
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314 def c_code(self, node, name, (dnll, sm, y_idx), (dx,), sub): |
185
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315 y_idx_type = node.inputs[2].type.dtype_specs()[1] |
32 | 316 return """ |
317 | |
67
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318 if ((%(dnll)s->descr->type_num != PyArray_DOUBLE) |
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319 || (%(sm)s->descr->type_num != PyArray_DOUBLE) |
185
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320 ) |
67
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321 { |
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322 PyErr_SetString(PyExc_TypeError, "types should be float64, float64, int64"); |
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323 %(fail)s; |
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324 } |
185
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325 if ((%(y_idx)s->descr->type_num != PyArray_INT64) |
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326 && (%(y_idx)s->descr->type_num != PyArray_INT32) |
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327 && (%(y_idx)s->descr->type_num != PyArray_INT16) |
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328 && (%(y_idx)s->descr->type_num != PyArray_INT8)) |
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329 { |
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330 PyErr_SetString(PyExc_TypeError, "y_idx not int8, int16, int32, or int64"); |
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331 %(fail)s; |
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332 } |
67
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333 if ((%(dnll)s->nd != 1) |
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334 || (%(sm)s->nd != 2) |
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335 || (%(y_idx)s->nd != 1)) |
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336 { |
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337 PyErr_SetString(PyExc_ValueError, "rank error"); |
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338 %(fail)s; |
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339 } |
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340 if ((%(dnll)s->dimensions[0] != %(sm)s->dimensions[0]) |
68 | 341 || (%(dnll)s->dimensions[0] != %(y_idx)s->dimensions[0])) |
67
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342 { |
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343 PyErr_SetString(PyExc_ValueError, "dimension mismatch"); |
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344 %(fail)s; |
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345 } |
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346 if ((NULL == %(dx)s) |
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347 || (%(dx)s->dimensions[0] != %(sm)s->dimensions[0]) |
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348 || (%(dx)s->dimensions[1] != %(sm)s->dimensions[1])) |
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349 { |
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350 if (NULL != %(dx)s) Py_XDECREF(%(dx)s); |
68 | 351 %(dx)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(sm)s), type_num_%(sm)s); |
67
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352 if(!%(dx)s) { |
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353 PyErr_SetString(PyExc_MemoryError, "failed to alloc dx output"); |
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354 %(fail)s |
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355 } |
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356 } |
24 | 357 |
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358 for (size_t i = 0; i < %(dx)s->dimensions[0]; ++i) |
32 | 359 { |
360 const double dnll_i = ((double*)(%(dnll)s->data + %(dnll)s->strides[0] * i))[0]; | |
361 | |
185
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362 const %(y_idx_type)s y_i = ((%(y_idx_type)s*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0]; |
32 | 363 |
364 const double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i); | |
365 npy_intp Ssm = %(sm)s->strides[1]/sizeof(double); | |
366 | |
367 double* __restrict__ dx_i = (double*)(%(dx)s->data + %(dx)s->strides[0] * i); | |
368 npy_intp Sdx = %(dx)s->strides[1]/sizeof(double); | |
369 | |
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370 for (size_t j = 0; j < %(dx)s->dimensions[1]; ++j) |
32 | 371 { |
372 dx_i[j * Sdx] = dnll_i * sm_i[j * Ssm]; | |
373 } | |
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374 if (y_i >= %(dx)s->dimensions[1]) |
32 | 375 { |
376 %(fail)s; | |
377 } | |
378 dx_i[y_i * Sdx] -= dnll_i; | |
379 } | |
380 """ % dict(locals(), **sub) | |
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381 |
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382 def crossentropy_softmax_1hot(x, y_idx, **kwargs): |
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383 b = tensor.zeros_like(x[0,:]) |
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384 return crossentropy_softmax_1hot_with_bias(x, b, y_idx, **kwargs) |
382
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385 |
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386 def binary_crossentropy(output, target): |
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387 """ |
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388 Compute the crossentropy of binary output wrt binary target. |
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389 @note: We do not sum, crossentropy is computed by component. |
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390 @todo: Rewrite as a scalar, and then broadcast to tensor. |
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391 """ |
383 | 392 return -(target * tensor.log(output) + (1 - target) * tensor.log(1 - output)) |
419
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393 |
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394 |
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395 |
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396 class Prepend_scalar_constant_to_each_row(theano.Op): |
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397 def __init__(self, val = 0): |
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398 if isinstance(val, float): |
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399 val = scalar.constant(val) |
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400 self.val = val |
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401 |
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402 def make_node(self, mat): |
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403 #check type of input |
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404 if not isinstance(mat,theano.Result) or not mat.type==tensor.matrix().type: |
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405 raise TypeError("Expected a matrix as input") |
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406 x = tensor.as_tensor(mat) |
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407 y = tensor.as_tensor(self.val) |
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408 if x.type.dtype != y.type.dtype: |
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409 TypeError("the value to prepend don't have the same type as the matrix") |
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410 |
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411 node = theano.Apply(op=self, inputs=[mat], outputs=[tensor.matrix()]) |
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412 return node |
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413 |
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414 def perform(self, node, (mat, ), (output, )): |
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415 new_shape=(mat.shape[0],mat.shape[1]+1) |
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416 if output[0] == None: |
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417 output[0]=numpy.empty(new_shape,dtype=mat.dtype) |
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418 out=output[0] |
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419 else: |
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420 if output[0].shape!=new_shape: |
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421 try: |
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422 output[0].resize(new_shape) |
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423 except: |
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424 output[0]=numpy.empty(new_shape, dtype=mat.dtype) |
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425 out=output[0] |
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426 |
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427 out[:,0].fill(self.val.data) |
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428 out[:,1:]=mat |
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429 |
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430 def grad(self, (mat,), (goutput,)): |
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431 return goutput[:,1:] |
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432 |
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433 class Prepend_scalar_to_each_row(theano.Op): |
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434 def make_node(self, val, mat): |
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435 #check type of input |
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436 if isinstance(val, float): |
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437 val = scalar.constant(val) |
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438 if not isinstance(mat,theano.Result) or not mat.type==tensor.matrix().type: |
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439 raise TypeError("Expected a matrix as input") |
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440 x = tensor.as_tensor(mat) |
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441 y = tensor.as_tensor(val) |
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442 if x.type.dtype != y.type.dtype: |
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443 TypeError("the value to prepend don't have the same type as the matrix") |
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444 |
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445 node = theano.Apply(op=self, inputs=[val,mat], outputs=[tensor.matrix()]) |
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446 return node |
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447 |
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448 def perform(self, node, (val,mat), (output, )): |
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449 new_shape=(mat.shape[0],mat.shape[1]+1) |
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450 if output[0] == None: |
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451 output[0]=numpy.empty(new_shape,dtype=mat.dtype) |
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452 out=output[0] |
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453 else: |
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454 if output[0].shape!=new_shape: |
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455 try: |
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456 output[0].resize(new_shape) |
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457 except: |
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458 output[0]=numpy.empty(new_shape, dtype=mat.dtype) |
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459 out=output[0] |
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460 out[:,0].fill(val) |
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461 out[:,1:]=mat |
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462 |
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463 def grad(self, (val, mat), (goutput,)): |
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464 return goutput[:,0], goutput[:,1:] |
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465 |
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466 prepend_scalar_to_each_row = Prepend_scalar_to_each_row() |
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467 prepend_0_to_each_row = Prepend_scalar_constant_to_each_row(0.) |
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468 prepend_1_to_each_row = Prepend_scalar_constant_to_each_row(1.) |
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469 |
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470 class solve(theano.Op): |
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471 """ |
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472 Find the solution to the linear equation Ax=b, |
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473 where A is a 2d matrix and b is a 1d or 2d matrix. |
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474 It use numpy.solve to find the solution. |
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475 """ |
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476 |
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477 def make_node(self, A, b): |
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478 if not isinstance(A, theano.Result) or not A.type==tensor.matrix().type: |
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479 raise TypeError("We expected that A had a matrix type") |
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480 if not isinstance(B, theano.Result) or not B.type==tensor.matrix().type: |
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481 raise TypeError("We expected that B had a matrix type") |
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482 |
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483 node = theano.Apply(op=self, inputs=[A, B], outputs=[tensor.matrix()]) |
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484 return node |
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485 |
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486 def perform(self, node, (A, B), (output, )): |
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487 ret=numpy.solve(A,B) |
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488 output[0]=ret |
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489 |
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490 def grad(self, (theta, A, B), (gtheta,)): |
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491 raise NotImplementedError() |
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492 |
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493 |