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While deep learning is successful in a number of applications, it is not yet well understood theoretically. A theoretical characterization of deep learning should answer questions about their approximation power, the ...

In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) matrix A measures how much errors in the data b affect the solution x. Bounds of this type are important in many inverse ...

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. ...

A convolutional neural network strongly robust to adversarial perturbations at reasonable computational and performance cost has not yet been demonstrated. The primate visual ventral stream seems to be robust to small ...

Current machine learning algorithms are highly specialized to whatever it is they are meant to do –– e.g. playing chess, picking up objects, or object recognition. How can we extend this to a system that could solve a ...

Recent theoretical results show that gradient descent on deep neural networks under exponential loss functions locally maximizes classification margin, which is equivalent to minimizing the norm of the weight matrices under ...