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コードの下に無効である理由かしら...エラー以下は、なぜ、この勾配が無効である（theano）
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)})
登場：？
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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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私は、スクリプトの上に放送され、操作を含んで考え、 間違っていましたしたがって、以下のようにグラディエント操作の前に使用される放送はありません。
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)})
succeうまく実行し、結果を捨てた。
array([[ 5., 5., 5.]], dtype=float32)
なぜ前者は無効ですか？ ブロードキャストのグラデーションは数学的に無効ですか？
グラデーションでシェイプミスが多く発生するのはなぜですか？
上記の質問について教えてください。