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Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…

Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. A key development is the reformulation of the reverse sampling process as a deterministic probability flow…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…

Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…

Effective caching is crucial for the performance of modern-day computing systems. A key optimization problem arising in caching -- which item to evict to make room for a new item -- cannot be optimally solved without knowing the future.…

It is proved that one cannot approximate stably the first derivative of a smooth function given noisy values of this function and a bound on this function and its first derivative. Such an approximation is shown to be possible if an a…

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…

Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…

In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…

We propose a generic and interpretable learning framework for building robust text classification model that achieves accuracy comparable to full models under test-time budget constraints. Our approach learns a selector to identify words…

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…

This paper considers discrete-time linear systems with bounded additive disturbances, and studies the convergence properties of the backward reachable sets of robust controlled invariant sets (RCIS). Under a simple condition, we prove that…

We derive a new residual-type a posteriori estimator for a singularly perturbed reaction-diffusion problem with obstacle constraints. It generalizes robust residual estimators for unconstrained singularly perturbed equations. Upper and…

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…

Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…