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annotate nnet_ops.py @ 69:8c2607f387e6

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added softplus, elaborated sigmoid
author James Bergstra <bergstrj@iro.umontreal.ca>
date Mon, 21 Apr 2008 15:23:49 -0400
parents 315eb36ff954
children 76e5c0f37165
rev   line source
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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
69
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5 ############
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6 #
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7 # SCALAR OPS
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8 #
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9
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10 class ScalarSigmoid(scalar.FloatUnaryScalarOp):
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11 @staticmethod
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12 def st_impl(x):
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13 if x < -30.0:
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14 return 0.0
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15 if x > 30.0:
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16 return 1.0
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17 return 1.0 / (1.0 + numpy.exp(-x))
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18 def impl(self, x):
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19 return ScalarSigmoid.st_impl(x)
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20 def grad(self, (x,), (gz,)):
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21 y = scalar_sigmoid(x)
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22 return [gz * y * (1.0 - y)]
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23 def c_foreach(self, (x,), (z,), sub):
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24 if 'float' in self.inputs[0].dtype:
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25 return """%(z)s =
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26 %(x)s < -30.0
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27 ? 0.0
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28 : %(x)s > 30.0
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29 ? 1.0
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30 : 1.0 /(1.0+exp(-%(x)s));""" % locals()
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31 raise NotImplementedError('only floatingpoint is implemented')
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32 scalar_sigmoid = gof.op.constructor(ScalarSigmoid)
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33 Sigmoid, sigmoid, SigmoidInplace, sigmoid_inplace =\
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34 tensor.broadcast(ScalarSigmoid, 'Sigmoid')
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36 class ScalarSoftplus(scalar.FloatUnaryScalarOp):
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37 @staticmethod
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38 def static_impl(x):
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39 if x < -30.0:
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40 return 0.0
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41 if x > 30.0:
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42 return x
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43 return numpy.log1p(numpy.exp(x))
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44 def impl(self, x):
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45 return ScalarSoftplus.static_impl(x)
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46 def grad(self, (x,), (gz,)):
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47 return [gz * scalar_sigmoid(x)]
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48 def c_foreach(self, (x,), (z,), sub):
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49 if 'float' in self.inputs[0].dtype:
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50 return """%(z)s =
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51 %(x)s < -30.0
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52 ? 0.0
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53 : %(x)s > 30.0
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54 ? %(x)s
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55 : log1p(exp(%(x)s));""" % locals()
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56 raise NotImplementedError('only floating point x is implemented')
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57 scalar_softplus = gof.op.constructor(ScalarSoftplus)
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58 Softplus, softplus, SoftplusInplace, softplus_inplace =\
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59 tensor.broadcast(ScalarSoftplus, 'Softplus')
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60
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61
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62 ############
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63 #
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64 # TENSOR OPS
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65 #
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66
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67
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68 class CrossentropySoftmax1Hot(gof.op.Op):
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69 """A special compound Op for the output of neural-net classifiers.
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70
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71 This Op has two outputs:
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72 - KL(softmax(x), y)
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73 - softmax(x)
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74
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75 x[i] is assumed to be a dense vector
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76 softmax(x[i]) is the i'th distribution over len(x[i]) options
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77 y[i] is an integer index, encoding a 1-hot distribution
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78
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79 """
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80 nin=2
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81 nout=2
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82 def __init__(self, x, b, y_idx, **kwargs):
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83 x = tensor._as_tensor(x)
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84 b = tensor._as_tensor(b)
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85 y_idx = tensor._as_tensor(y_idx)
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86 if len(x.broadcastable) != 2 \
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87 or x.dtype not in ['float32', 'float64']:
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88 raise ValueError('x must be 2-d tensor of floats')
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89 if len(b.broadcastable) != 1 \
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90 or x.dtype not in ['float32', 'float64']:
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91 raise ValueError('x must be 1-d tensor of floats')
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92 if len(y_idx.broadcastable) != 1 \
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93 or y_idx.dtype not in ['int32', 'int64']:
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94 raise ValueError('x must be 1-d tensor of ints')
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95
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96 # TODO: Is this correct? It used to be y, not y_idx
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97 nll = tensor.Tensor(x.dtype, y_idx.broadcastable)
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98 # nll = Tensor(x.dtype, y.broadcastable)
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99 sm = tensor.Tensor(x.dtype, x.broadcastable)
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100 self.inputs = [x, b, y_idx]
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101 self.outputs = [nll, sm]
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102 def perform(self):
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103 x, b, y_idx = [i.data for i in self.inputs]
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104 if b.shape[0] != x.shape[1]:
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105 raise ValueError('b must have same shape as x[0]')
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106
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107 sm = numpy.zeros_like(x) # softmax
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108 nll = numpy.zeros(x.shape[0]) #nll(y | softmax(x))
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109 for i in xrange(sm.shape[0]):
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110 row = x[i] + b
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111 sm[i] = numpy.exp(row - numpy.max(row)) #softmax
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112 sm[i] *= 1.0 / numpy.sum(sm[i]) #vector scale
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113 nll[i] = -numpy.log( sm[i, y_idx[i]]) #cross-entropy
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114 self.outputs[0].data = nll
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115 self.outputs[1].data = sm
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116 def grad(self, (x, b, y_idx), (g_nll, g_sm)):
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117 if g_sm is not None:
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118 raise NotImplementedError()
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119 nll, sm = crossentropy_softmax_1hot(x, b, y_idx)
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120 dx = CrossentropySoftmax1HotDx(g_nll, sm, y_idx).outputs[0]
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121 db = tensor.Sum(dx, axis = [0]).outputs[0]
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122 return dx, db, None
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123
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124 def c_headers(self): return ['<iostream>']
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125 def c_code(self, (x, b, y_idx), (nll, sm), sub):
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126 # this implementation was lifted from
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127 # /u/bergstrj/cvs/bergstrj/src/feb07/nn.cxx
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128
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129 #TODO: put this into a templated function, in the support code
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130 #TODO: declare the max of each row as an Op output
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131
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132 #TODO: set error messages for failures in this code
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133
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134 return """
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135 npy_intp* Nx = %(x)s->dimensions;
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136
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137 if (%(x)s->nd != 2)
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138 {
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139 PyErr_SetString(PyExc_ValueError, "a not 2d tensor");
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140 %(fail)s;
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141 }
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142 if (%(b)s->nd != 1)
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143 {
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144 PyErr_SetString(PyExc_ValueError, "b not 1d tensor");
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145 %(fail)s;
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146 }
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147 if (%(y_idx)s->nd != 1)
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148 {
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149 PyErr_SetString(PyExc_ValueError, "y_idx not 1d tensor");
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150 %(fail)s;
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151 }
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152 if (%(x)s->descr->type_num != PyArray_DOUBLE)
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153 {
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154 PyErr_SetString(PyExc_TypeError, "a not float64");
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155 %(fail)s;
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156 }
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157 if (%(b)s->descr->type_num != PyArray_DOUBLE)
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158 {
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159 PyErr_SetString(PyExc_TypeError, "b not float64");
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160 %(fail)s;
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161 }
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162 if (%(y_idx)s->descr->type_num != PyArray_INT64)
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163 {
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164 PyErr_SetString(PyExc_TypeError, "y_idx not int64");
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165 %(fail)s;
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166 }
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167 if ((%(x)s->dimensions[1] != %(b)s->dimensions[0])
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168 || (%(x)s->dimensions[0] != %(y_idx)s->dimensions[0]))
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169 {
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170 PyErr_SetString(PyExc_ValueError, "dimension mismatch in arguments");
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171 %(fail)s;
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172 }
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173
67
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174 if ((NULL == %(nll)s) //initial condition
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175 || (%(nll)s->dimensions[0] != %(y_idx)s->dimensions[0]))
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176 {
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177 if (NULL != %(nll)s) Py_XDECREF(%(nll)s);
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178 %(nll)s = (PyArrayObject*)PyArray_SimpleNew(1, PyArray_DIMS(%(y_idx)s), type_num_%(x)s);
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179 if(!%(nll)s)
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180 {
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181 PyErr_SetString(PyExc_MemoryError, "failed to alloc nll output");
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182 %(fail)s;
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183 }
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184 }
67
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185 if ((NULL == %(sm)s)
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186 || (%(sm)s->dimensions[0] != %(x)s->dimensions[0])
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187 || (%(sm)s->dimensions[1] != %(x)s->dimensions[1]))
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188 {
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189 if (NULL != %(sm)s) Py_XDECREF(%(sm)s);
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190 %(sm)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(x)s), type_num_%(x)s);
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191 if(!%(sm)s) {
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192 // The normal cleanup code will take care of %(nll)s
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193 // Py_XDECREF(%(nll)s); %(nll)s=NULL;
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194 PyErr_SetString(PyExc_MemoryError, "failed to alloc sm output");
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195 %(fail)s
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196 }
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197 }
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198
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199 for (size_t i = 0; i < Nx[0]; ++i)
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200 {
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201 size_t j;
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202 double sum = 0.0;
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203 bool discount_max = false;
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204
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205 const double* __restrict__ x_i = (double*)(%(x)s->data + %(x)s->strides[0] * i);
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206 const double* __restrict__ b_i = (double*)(%(b)s->data);
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207 const long int y_i = ((long int*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0];
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208 double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i);
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209 double* __restrict__ nll_i = (double*)(%(nll)s->data + %(nll)s->strides[0] * i);
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210
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211 npy_intp Sx = %(x)s->strides[1]/sizeof(double);
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212 npy_intp Sb = %(b)s->strides[0]/sizeof(double);
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213 npy_intp Ssm = %(sm)s->strides[1]/sizeof(double);
24
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214
30
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215 size_t row_max_j=0;
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216 double row_max = x_i[0] + b_i[0];
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217 //try to compute sum and sm the easy way
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218 for (j = 0; j < Nx[1]; ++j)
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219 {
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220 double row_ij = x_i[j * Sx] + b_i[j * Sb];
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221 row_max_j = (row_ij > row_max) ? j : row_max_j;
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222 row_max = (row_ij > row_max) ? row_ij : row_max;
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223
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224 double sm_ij = exp(row_ij);
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225 sum += sm_ij;
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226 sm_i[j * Ssm] = sm_ij;
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227 }
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228 if ((0.0 == sum) || (isinf(sum)))
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229 {
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230 //our cheap trick didn't work... try again and do it better.
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231 discount_max = true;
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232 sum = 0.0; //reset sum and recompute....
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233 for (j = 0; j < Nx[1]; ++j)
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234 {
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diff changeset
235 double row_ij = x_i[j * Sx] + b_i[j * Sb];
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236
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237 double sm_ij = exp(row_ij - row_max);
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238 sum += sm_ij;
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239 sm_i[j * Ssm] = sm_ij;
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240 }
32
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241 if ( (0.0 == sum) || (isinf(sum)))
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242 {
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diff changeset
243 //that was our best...
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diff changeset
244 %(fail)s;
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245 }
30
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diff changeset
246 //if we still can't sum it up, we're screwed.
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diff changeset
247 //So far, this assertion has never failed...
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248 }
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249
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diff changeset
250 //cblas_dscal(x.N, 1.0 / sum, &mat_at(s,i,0), s.n);
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diff changeset
251 double sum_inv = 1.0 / sum;
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diff changeset
252 for (j = 0; j < Nx[1]; ++j)
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253 {
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254 sm_i[j * Ssm] *= sum_inv;
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255 }
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diff changeset
256
32
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diff changeset
257 if (y_i >= Nx[1])
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258 {
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diff changeset
259 %(fail)s;
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diff changeset
260 }
30
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261
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262 nll_i[0] = - x_i[y_i*Sx]
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263 - b_i[y_i*Sb]
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264 + (discount_max ? row_max : 0.0)
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265 + log(sum);
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266 //mat_at(y,i,0) = -log( mat_at(s,i,t[i])); //less accurate?
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267 //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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268 }
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269 """ % dict(locals(), **sub)
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270
25
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diff changeset
271 crossentropy_softmax_1hot = gof.op.constructor(CrossentropySoftmax1Hot)
24
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272
30
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273 class CrossentropySoftmax1HotDx (gof.op.Op):
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274 nin=3
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275 nout=1
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diff changeset
276 """Gradient wrt x of the CrossentropySoftmax1Hot Op"""
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277 def __init__(self, dy, sm, y_idx,**kwargs):
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278 dy = tensor._as_tensor(dy)
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279 sm = tensor._as_tensor(sm)
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280 y_idx = tensor._as_tensor(y_idx)
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281 self.inputs = [dy, sm, y_idx]
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282 self.outputs = [tensor.Tensor(sm.dtype, sm.broadcastable)]
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283 def perform(self):
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284 dy,sm,y_idx = [i.data for i in self.inputs]
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285 dx = numpy.zeros_like(sm)
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286 for i in xrange(sm.shape[0]):
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287 dx[i] = dy[i] * sm[i] #vector scale
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288 dx[i, y_idx[i]] -= dy[i] #scalar decrement
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289 self.outputs[0].data = dx
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290 def grad(self, *args):
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291 raise NotImplementedError()
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292 def c_code(self, (dnll, sm, y_idx), (dx,), sub):
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293 return """
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294
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295 if ((%(dnll)s->descr->type_num != PyArray_DOUBLE)
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296 || (%(sm)s->descr->type_num != PyArray_DOUBLE)
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297 || (%(y_idx)s->descr->type_num != PyArray_INT64))
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298 {
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299 PyErr_SetString(PyExc_TypeError, "types should be float64, float64, int64");
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300 %(fail)s;
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301 }
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302 if ((%(dnll)s->nd != 1)
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303 || (%(sm)s->nd != 2)
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304 || (%(y_idx)s->nd != 1))
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305 {
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306 PyErr_SetString(PyExc_ValueError, "rank error");
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307 %(fail)s;
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308 }
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309 if ((%(dnll)s->dimensions[0] != %(sm)s->dimensions[0])
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310 || (%(dnll)s->dimensions[0] != %(y_idx)s->dimensions[0]))
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311 {
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312 PyErr_SetString(PyExc_ValueError, "dimension mismatch");
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313 %(fail)s;
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314 }
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315 if ((NULL == %(dx)s)
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316 || (%(dx)s->dimensions[0] != %(sm)s->dimensions[0])
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317 || (%(dx)s->dimensions[1] != %(sm)s->dimensions[1]))
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318 {
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319 if (NULL != %(dx)s) Py_XDECREF(%(dx)s);
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320 %(dx)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(sm)s), type_num_%(sm)s);
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321 if(!%(dx)s) {
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322 PyErr_SetString(PyExc_MemoryError, "failed to alloc dx output");
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323 %(fail)s
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324 }
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325 }
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326
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327 for (size_t i = 0; i < %(dx)s->dimensions[0]; ++i)
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328 {
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329 const double dnll_i = ((double*)(%(dnll)s->data + %(dnll)s->strides[0] * i))[0];
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330
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331 const long int y_i = ((long int*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0];
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332
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333 const double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i);
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334 npy_intp Ssm = %(sm)s->strides[1]/sizeof(double);
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335
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336 double* __restrict__ dx_i = (double*)(%(dx)s->data + %(dx)s->strides[0] * i);
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337 npy_intp Sdx = %(dx)s->strides[1]/sizeof(double);
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338
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339 for (size_t j = 0; j < %(dx)s->dimensions[1]; ++j)
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340 {
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341 dx_i[j * Sdx] = dnll_i * sm_i[j * Ssm];
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342 }
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343 if (y_i >= %(dx)s->dimensions[1])
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344 {
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345 %(fail)s;
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346 }
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347 dx_i[y_i * Sdx] -= dnll_i;
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348 }
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349 """ % dict(locals(), **sub)
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James Bergstra <bergstrj@iro.umontreal.ca>
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350