6 accepted papers
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated probabilities are embedded in the posterior distribution. Howev…
Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to…
We study the type of solutions to which stochastic gradient descent converges when used to train a single hidden-layer multivariate ReLU network with the quadratic loss. Our results are based on a dynamical stability analysis. In the univariate case, it was shown that linearly stable minima correspo…
The loss terrains of over-parameterized neural networks have multiple global minima. However, it is well known that stochastic gradient descent (SGD) can stably converge only to minima that are sufficiently flat w.r.t. SGD's step size. In this paper we study the effect that this mechanism has on the…
It is well known that (stochastic) gradient descent has an implicit bias towards flat minima. In deep neural network training, this mechanism serves to screen out minima. However, the precise effect that this has on the trained network is not yet fully understood. In this paper, we characterize the…
In many areas of neuroscience and biological data analysis, it is desired to reveal common patterns among a group of subjects. Such analyses play important roles e.g., in detecting functional brain networks from fMRI scans and in identifying brain regions which show increased activity in response to…