I wonder why bellow code is invalid.. ```python 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)}) ``` bellow error is emerged. ``` --------------------------------------------------------------------------- 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) in () 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] '' |AllocEmpty{dtype='float64'} [id B] '' | |TensorConstant{3} [id C] |TensorConstant{1.0} [id D] |InplaceDimShuffle{1,0} [id E] '' | |Alloc [id F] '' | |TensorConstant{(1, 1) of 1.0} [id G] | |Shape_i{0} [id H] '' | | |x [id I] | |TensorConstant{3} [id C] |Rebroadcast{0} [id J] '' | |Subtensor{int8, ::, int64} [id K] '' | |InplaceDimShuffle{0,x,1} [id L] '' | | |x [id I] | |Constant{0} [id M] | |Constant{0} [id N] |TensorConstant{0.0} [id O] 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'. ``` I thought above script includes broadcasted operation was wrong, So no broadcasting used before gradient operation as follows, ```python 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)}) ``` successfully performed and dumped bellow result. ``` array([[ 5., 5., 5.]], dtype=float32) ``` But why did the former case invalid? Is the gradient with broadcasting mathmatically invalid? Why does shape miss much happen on gradient? Could you teach me about above question?

	@@ -1 +1 @@
1	- Why does this gradient is invalid?
1	+ Why does this gradient is invalid?(theano)

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