7 accepted papers
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical prob…
The principle of Maximal Coding Rate Reduction (MCR2) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However,…
The problem of projecting a matrix onto the space of
We provide a detailed analysis of the dynamics ofthe gradient flow in overparameterized two-layerlinear models. A particularly interesting featureof this model is that its nonlinear dynamics can beexactly solved as a consequence of a large num-ber of conservation laws that constrain the systemto fol…
Dropout and its extensions (e.g. DropBlock and DropConnect) are popular heuristics for training neural networks, which have been shown to improve generalization performance in practice. However, a theoretical understanding of their optimization and regularization properties remains elusive. Recent w…
Detecting, counting, and classifying various cell types in images of human blood is important in many biomedical applications. However, these tasks can be very difficult due to the wide range of biological variability and the resolution limitations of many imaging modalities. This paper proposes a…
The past few years have seen a dramatic increase in the performance of recognition systems thanks to the introduction of deep networks for representation learning. However, the mathematical reasons for this success remain elusive. A key issue is that the neural network training problem is nonconvex,…