Related papers: Constraint satisfaction problems and neural networ…
Neuroimaging has profoundly enhanced our understanding of the human brain by characterizing its structure, function, and connectivity through modalities like MRI, fMRI, EEG, and PET. These technologies have enabled major breakthroughs…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…
The use of machine learning methods helps to improve decision making in different fields. In particular, the idea of bridging predictions (machine learning models) and prescriptions (optimization problems) is gaining attention within the…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
A good feature representation is a determinant factor to achieve high performance for many machine learning algorithms in terms of classification. This is especially true for techniques that do not build complex internal representations of…
Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
Recurrent Neural Networks (RNNs) were recently successfully used to model the way neural activity drives task-related behavior in animals, operating under the implicit assumption that the obtained solutions are universal. Observations in…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…