python - Theano Scan Op 梯度中的断开输入

Question

我有许多不同大小的项目。对于每一组，一个(已知)项目是“正确”的。有一个函数可以为每个项目分配一个分数。这会产生项目分数的平面向量，以及告诉索引每个组从哪里开始以及有多大的向量。我希望对每组中的分数进行“softmax”操作来分配项目概率，然后取正确答案概率的对数之和。这是一个更简单的版本，我们只是返回正确答案的分数，而不使用 softmax 和对数。

import numpy                                                                                                                                                                                                                                                                          
import theano                                                                                                                                                                                                                                                                         
import theano.tensor as T                                                                                                                                                                                                                                                             
from theano.printing import Print                                                                                                                                                                                                                                                     

def scoreForCorrectAnswer(groupSize, offset, correctAnswer, preds):  
    # for each group, this will get called with the size of
    # the group, the offset of where the group begins in the 
    # predictions vector, and which item in that group is correct                                                                                                                                                                                                                                                                                                                                                                                                                                              
    relevantPredictions = preds[offset:offset+groupSize]                                                                                                                                                                                                                              
    ans = Print("CorrectAnswer")(correctAnswer)                                                                                                                                                                                                                                       
    return relevantPredictions[ans]       

groupSizes = T.ivector('groupSizes')                                                                                                                                                                                                                                                  
offsets = T.ivector('offsets')                                                                                                                                                                                                                                                        
x = T.fvector('x')                                                                                                                                                                                                                                                                    
W = T.vector('W')                                                                                                                                                                                                                                                                     
correctAnswers = T.ivector('correctAnswers')                                                                                                                                                                                                                                          

# for this simple example, we'll just score the items by
# element-wise product with a weight vector                                                                                                                                                                                                                                                                                  
predictions = x * W                                                                                                                                                                                                                                                                   

(values, updates) = theano.map(fn=scoreForCorrectAnswer,                                                                                                                                                                                                                                       
   sequences = [groupSizes, offsets, correctAnswers],                                                                                                                                                                                                                                
   non_sequences = [predictions] )                                                                                                                                                                                                                                                    

func = theano.function([groupSizes, offsets, correctAnswers,                                                                                                                                                                                                                          
        W, x], [values])                                                                                                                                                                                                                                                              

sampleInput = numpy.array([0.1,0.7,0.3,0.05,0.3,0.3,0.3], dtype='float32')                                                                                                                                                                                                            
sampleW = numpy.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], dtype='float32')                                                                                                                                                                                                           
sampleOffsets = numpy.array([0,4], dtype='int32')                                                                                                                                                                                                                                     
sampleGroupSizes = numpy.array([4,3], dtype='int32')                                                                                                                                                                                                                                  
sampleCorrectAnswers = numpy.array([1,2], dtype='int32')                                                                                                                                                                                                                              

data = func (sampleGroupSizes, sampleOffsets, sampleCorrectAnswers, sampleW, sampleInput)                                                                                                                                                                                             
print data                                                                                                                                                                                                                                                                            

#these all three raise the same exception (see below)                                                                                                                                                                                                                                             
gW1 = T.grad(cost=T.sum(values), wrt=W)                                                                                                                                                                                                                                               
gW2 = T.grad(cost=T.sum(values), wrt=W, disconnected_inputs='warn')                                                                                                                                                                                                                   
gW3 = T.grad(cost=T.sum(values), wrt=W, consider_constant=[groupSizes,offsets])   

这可以正确计算输出，但是当我尝试获取相对于参数 W 的梯度时，我得到(路径缩写):

Traceback (most recent call last):
  File "test_scan_for_stackoverflow.py", line 37, in <module>
    gW = T.grad(cost=T.sum(values), wrt=W)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 438, in grad
    outputs, wrt, consider_constant)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 698, in _populate_var_to_app_to_idx
    account_for(output)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 694, in account_for
    account_for(ipt)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 669, in account_for
    connection_pattern = _node_to_pattern(app)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 554, in _node_to_pattern
    connection_pattern = node.op.connection_pattern(node)
  File "Theano-0.6.0rc2-py2.7.egg/theano/scan_module/scan_op.py", line 1331, in connection_pattern
ils)
  File "Theano-0.6.0rc2-py2.7.egg/theano/scan_module/scan_op.py", line 1266, in compute_gradient
    known_grads={y: g_y}, wrt=x)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 511, in grad
    handle_disconnected(elem)
  File "Theano-0.6.0rc2-py2.7.egg/theano/gradient.py", line 497, in handle_disconnected
    raise DisconnectedInputError(message)
theano.gradient.DisconnectedInputError: grad method was asked to compute 
the gradient with respect to a variable that is not part of the 
computational graph of the cost, or is used only by a 
non-differentiable operator: groupSizes[t]

现在，groupSizes 是恒定的，因此没有理由需要对其进行任何渐变。通常，您可以通过抑制 DisconnectedInputError 或告诉 Theano 将 groupSizes 视为 T.grad 调用中的常量来处理此问题(请参阅示例脚本的最后几行)。但似乎没有任何方法可以将这些东西传递给 ScanOp 梯度计算中的内部 T.grad 调用。

我错过了什么吗？这是通过 ScanOp 进行梯度计算的方法吗？

Answer 1

截至 2 月中旬，这被证明是 Theano 的一个错误。 2013(0.6.0rc-2)。截至本文发布之日，该问题已在 github 上的开发版本中修复。