The main success stories of deep learning, starting with ImageNet, depend on  convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines . Is there something special about deep convolutional networks that other learning machines do not possess ? Recent results in approximation theory have shown that there is an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure.  These mathematical results, however, do not say which tasks are expected to have input-output functions with hierarchical locality. Among all the possible hierarchically local tasks in vision, text and speech we explore a few of them experimentally by studying how they are affected by disrupting locality in the input images . We also discuss a taxonomy of tasks ranging from local, to hierarchically local, to global and make predictions about the type of networks required to perform efficiently on these different types of tasks .
The main success stories of deep learning, starting with ImageNet, depend on deep convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines , and also better than deep fully connected networks; but what is so special about deep convolutional networks ? Recent results in approximation theory proved an exponential advantage of deep convolutional networks with or without shared weights in approximating functions with hierarchical locality in their compositional structure. More recently, the hierarchical structure was proved to be hard to learn from data, suggesting that it is a powerful prior embedded in the architecture of the network. These mathematical results, however, do not say which real-life tasks correspond to input-output functions with hierarchical locality. To evaluate this, we consider a set of visual tasks where we disrupt the URLanization of images via "deterministic scrambling" to later perform a visual task on these images structurally-altered in the same way for training and testing. For object recognition we find, as expected, that scrambling does not affect the performance of shallow or deep fully connected networks contrary to the out-performance of convolutional networks. Not all tasks involving images are however affected. Texture perception and global color estimation are much less sensitive to deterministic scrambling showing that the underlying functions corresponding to these tasks are not hierarchically local; and also counter-intuitively showing that these tasks are better approximated by networks that are not deep (texture) nor convolutional (color). Altogether, these results shed light into the importance of matching a network architecture with its embedded prior of the task to be learned .
A
deep
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. Is there something
, and also better than deep fully connected networks; but what is so
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that other learning machines do not possess
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have shown that there is
proved
R
convolutional-like networks
convolutional networks with or without shared weights
A
More recently, the hierarchical structure was proved to be hard to learn from data, suggesting that it is a powerful prior embedded in the architecture of the network.
R
tasks are expected to have
real-life tasks correspond to
R
Among all the possible hierarchically local tasks in vision, text and speech we explore a few of them experimentally by studying how they are affected by disrupting locality in the input images . We also discuss a taxonomy of tasks ranging from local, to hierarchically local, to global and make predictions about the type of networks required to perform efficiently on these different types of tasks
To evaluate this, we consider a set of visual tasks where we disrupt the URLanization of images via "deterministic scrambling" to later perform a visual task on these images structurally-altered in the same way for training and testing. For object recognition we find, as expected, that scrambling does not affect the performance of shallow or deep fully connected networks contrary to the out-performance of convolutional networks. Not all tasks involving images are however affected. Texture perception and global color estimation are much less sensitive to deterministic scrambling showing that the underlying functions corresponding to these tasks are not hierarchically local; and also counter-intuitively showing that these tasks are better approximated by networks that are not deep (texture) nor convolutional (color). Altogether, these results shed light into the importance of matching a network architecture with its embedded prior of the task to be learned