我想知道为什么下面的代码无效..
from numpy import *
import theano.tensor as T
x = T.dmatrix("x")
mx = x[...,None,:]
a = T.ones((1,3))
T.grad(mx[...,0].dot(a).sum(), a).eval({x:ones((5,10)).astype(float32)})
出现以下错误：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/home/yu/anaconda3/lib/python3.5/site-packages/theano/compile/function_module.py in __call__(self, *args, **kwargs)
883 outputs =\
--> 884 self.fn() if output_subset is None else\
885 self.fn(output_subset=output_subset)
ValueError: Shape mismatch: A.shape[1] != x.shape[0]
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
<ipython-input-74-52410617594a> in <module>()
3 mx = x[...,None,:]
4 a = T.ones((1,3))
----> 5 T.grad(mx[...,0].dot(a).sum(), a).eval({x:ones((5,10)).astype(float32)})
/home/yu/anaconda3/lib/python3.5/site-packages/theano/gof/graph.py in eval(self, inputs_to_values)
517 args = [inputs_to_values[param] for param in inputs]
518
--> 519 rval = self._fn_cache[inputs](*args)
520
521 return rval
/home/yu/anaconda3/lib/python3.5/site-packages/theano/compile/function_module.py in __call__(self, *args, **kwargs)
896 node=self.fn.nodes[self.fn.position_of_error],
897 thunk=thunk,
--> 898 storage_map=getattr(self.fn, 'storage_map', None))
899 else:
900 # old-style linkers raise their own exceptions
/home/yu/anaconda3/lib/python3.5/site-packages/theano/gof/link.py in raise_with_op(node, thunk, exc_info, storage_map)
323 # extra long error message in that case.
324 pass
--> 325 reraise(exc_type, exc_value, exc_trace)
326
327
/home/yu/anaconda3/lib/python3.5/site-packages/six.py in reraise(tp, value, tb)
683 value = tp()
684 if value.__traceback__ is not tb:
--> 685 raise value.with_traceback(tb)
686 raise value
687
/home/yu/anaconda3/lib/python3.5/site-packages/theano/compile/function_module.py in __call__(self, *args, **kwargs)
882 try:
883 outputs =\
--> 884 self.fn() if output_subset is None else\
885 self.fn(output_subset=output_subset)
886 except Exception:
ValueError: Shape mismatch: A.shape[1] != x.shape[0]
Apply node that caused the error: CGemv{inplace}(AllocEmpty{dtype='float64'}.0, TensorConstant{1.0}, InplaceDimShuffle{1,0}.0, Rebroadcast{0}.0, TensorConstant{0.0})
Toposort index: 7
Inputs types: [TensorType(float64, vector), TensorType(float64, scalar), TensorType(float64, matrix), TensorType(float64, vector), TensorType(float64, scalar)]
Inputs shapes: [(3,), (), (3, 5), (1,), ()]
Inputs strides: [(8,), (), (8, 24), (80,), ()]
Inputs values: [array([ 0.00000000e+000, 4.94065646e-324, 9.88131292e-324]), array(1.0), 'not shown', array([ 1.]), array(0.0)]
Inputs type_num: [12, 12, 12, 12, 12]
Outputs clients: [[InplaceDimShuffle{x,0}(CGemv{inplace}.0)]]
Debugprint of the apply node:
CGemv{inplace} [id A] <TensorType(float64, vector)> ''
|AllocEmpty{dtype='float64'} [id B] <TensorType(float64, vector)> ''
| |TensorConstant{3} [id C] <TensorType(int64, scalar)>
|TensorConstant{1.0} [id D] <TensorType(float64, scalar)>
|InplaceDimShuffle{1,0} [id E] <TensorType(float64, matrix)> ''
| |Alloc [id F] <TensorType(float64, matrix)> ''
| |TensorConstant{(1, 1) of 1.0} [id G] <TensorType(float64, (True, True))>
| |Shape_i{0} [id H] <TensorType(int64, scalar)> ''
| | |x [id I] <TensorType(float64, matrix)>
| |TensorConstant{3} [id C] <TensorType(int64, scalar)>
|Rebroadcast{0} [id J] <TensorType(float64, vector)> ''
| |Subtensor{int8, ::, int64} [id K] <TensorType(float64, (True,))> ''
| |InplaceDimShuffle{0,x,1} [id L] <TensorType(float64, (False, True, False))> ''
| | |x [id I] <TensorType(float64, matrix)>
| |Constant{0} [id M] <int8>
| |Constant{0} [id N] <int64>
|TensorConstant{0.0} [id O] <TensorType(float64, scalar)>
Storage map footprint:
- x, Input, Shape: (5, 10), ElemSize: 8 Byte(s), TotalSize: 400 Byte(s)
- InplaceDimShuffle{0,x,1}.0, Shape: (5, 1, 10), ElemSize: 8 Byte(s), TotalSize: 400 Byte(s)
- Alloc.0, Shape: (5, 3), ElemSize: 8 Byte(s), TotalSize: 120 Byte(s)
- InplaceDimShuffle{1,0}.0, Shape: (3, 5), ElemSize: 8 Byte(s), TotalSize: 120 Byte(s)
- AllocEmpty{dtype='float64'}.0, Shape: (3,), ElemSize: 8 Byte(s), TotalSize: 24 Byte(s)
- Subtensor{int8, ::, int64}.0, Shape: (1,), ElemSize: 8 Byte(s), TotalSize: 8 Byte(s)
- Shape_i{0}.0, Shape: (), ElemSize: 8 Byte(s), TotalSize: 8.0 Byte(s)
- TensorConstant{1.0}, Shape: (), ElemSize: 8 Byte(s), TotalSize: 8.0 Byte(s)
- TensorConstant{0.0}, Shape: (), ElemSize: 8 Byte(s), TotalSize: 8.0 Byte(s)
- Constant{0}, Shape: (), ElemSize: 8 Byte(s), TotalSize: 8.0 Byte(s)
- Rebroadcast{0}.0, Shape: (1,), ElemSize: 8 Byte(s), TotalSize: 8 Byte(s)
- TensorConstant{3}, Shape: (), ElemSize: 8 Byte(s), TotalSize: 8.0 Byte(s)
- TensorConstant{(1, 1) of 1.0}, Shape: (1, 1), ElemSize: 8 Byte(s), TotalSize: 8 Byte(s)
- Constant{0}, Shape: (), ElemSize: 1 Byte(s), TotalSize: 1.0 Byte(s)
TotalSize: 593.0 Byte(s) 0.000 GB
TotalSize inputs: 441.0 Byte(s) 0.000 GB
HINT: Re-running with most Theano optimization disabled could give you a back-trace of when this node was created. This can be done with by setting the Theano flag 'optimizer=fast_compile'. If that does not work, Theano optimizations can be disabled with 'optimizer=None'.
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我认为上面的脚本包含广播操作错误， 所以在梯度操作之前没有使用广播如下，
x = T.tensor3("x")
mx = x
a = T.ones((1,3))
T.grad(mx[...,0].dot(a).sum(), a).eval({x:ones((5,1,10)).astype(float32)})
成功执行并抛弃了以下结果。
array([[ 5., 5., 5.]], dtype=float32)
但为什么前一种情况无效？ 广播的渐变在数学上是无效的吗？ 为什么形状会在梯度上发生错失？
你可以教我一些上述问题吗？