Related papers: Sum-of-Squares Polynomial Flow
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…
For a given ground cost, approximating the Monge optimal transport map that pushes forward a given probability measure onto another has become a staple in several modern machine learning algorithms. The fourth-order Ma-Trudinger-Wang (MTW)…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting…
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless…
While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The…
We study a surprising phenomenon related to the representation of a cloud of data points using polynomials. We start with the previously unnoticed empirical observation that, given a collection (a cloud) of data points, the sublevel sets of…
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…
The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a…
Finding image correspondences remains a challenging problem in the presence of intra-class variations and large changes in scene layout.~Semantic flow methods are designed to handle images depicting different instances of the same object or…
Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…
In this paper, we develop machinery which makes it much easier to prove sum of squares lower bounds when the problem is symmetric under permutations of $[1,n]$ and the unsatisfiability of our problem comes from integrality arguments, i.e.…
Normalizing Flows are a powerful technique for learning and modeling probability distributions given samples from those distributions. The current state of the art results are built upon residual flows as these can model a larger hypothesis…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…
Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts,…
Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…
This paper reports on a dynamic semantic mapping framework that incorporates 3D scene flow measurements into a closed-form Bayesian inference model. Existence of dynamic objects in the environment can cause artifacts and traces in current…
3D situational awareness is critical for any autonomous system. However, when operating underwater, environmental conditions often dictate the use of acoustic sensors. These acoustic sensors are plagued by high noise and a lack of 3D…