Sensitivity of DNN-based classifiers to centering and orientation of object in images Is DNN classification senstitive to centering and orientation of object in images?
for instance:
Let us assume that a DNN is trained with letters always appearing in the same given orientation (e.g. tilted by 10°) and the same given location (e.g. always in the top left corner).
Without further training:


*

*Would the system be able to correctly classify letters appearing in a different position (e.g. the bottom right corner)?

*Would the system be able to correctly classify letters appearing in a different orientation (e.g. tilted by 90°)?
Maybe the answer differs depending on the specific kind of DNN used (e.g. convolutional ones) or even ad-hoc ones where this problem had to be specifically taken into account. If it is the case, please specify which are sentitives and which are not.
 A: Convolutional neural networks have a built in translation invariance so they can detect different types of features all over the image. Also using pooling layers allows the CNN to detect more robust spatial activation patterns. For instance, the pooling layer allows the CNN to learn more spatially robust activation patterns.
It's discussed in Gradient-Based Learning Applied to Document Recognition refer to Section II.A on Convolutional Neural Networks. I quote:

Once a feature has been detected its exact location becomes less important. Only its approximate location relative to other features is relevant. For example, once we know that the input image contains the endpoint of a roughly horizontal segment in the upper left area, a corner in the upper right area, and the endpoint of a roughly vertical segment in the lower portion of the image, we can tell the input image is a 7. Not only is the precise position of each of those features irrelevant for identifying the pattern, it is potentially harmful because positions are likely to vary for different instances of the character. A simple way to reduce the precision with which the position of distinctive features is encoded is to reduce the spatial resolution of the feature map. This can be achieved with so-called subsampling layers...

And on it goes. 
I believe as long as your data has enough of these translated rotated images, the convolutional neural network can learn these corresponding features. However, I believe if your data does not have a lot of rotated examples, it can be hard for relatively shallow conv nets to learn the rotations. I make a difference between translation symmetry and rotational symmetry because as I mentioned before, the conv net builds in translation invariance but the same is not true for rotations. 
This article Deep Networks Resemble Human Feed-forward Vision in Invariant Object Recognition shows that deeper conv nets can learn more rotational invariances. They are using datasets with pose variations. 
