Related papers: OT-Transformer: A Continuous-time Transformer Arch…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…
This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles;…
Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
In this paper, we formulate optimization problems to perform optimal transmission switching (OTS) in order to operate power transmission grids most efficiently. In any given electrical network, several of the transmission lines are…
The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…
We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…
Understanding trajectory diversity is a fundamental aspect of addressing practical traffic tasks. However, capturing the diversity of trajectories presents challenges, particularly with traditional machine learning and recurrent neural…
Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applications that require out-of-sample estimates. To this end, we…
Transformers have transformed modern machine learning, driving breakthroughs in computer vision, natural language processing, and robotics. At the core of their success lies the attention mechanism, which enables the modeling of global…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
Continuous motorization and urbanization around the globe leads to an expansion of population in major cities. Therefore, ever-growing pressure imposed on the existing mass transit systems calls for a better technology, Intelligent…
This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
Accurate trajectory prediction is a cornerstone for the safe operation of autonomous driving systems, where understanding the dynamic behavior of surrounding agents is crucial. Transformer-based architectures have demonstrated significant…
Transformer training is notoriously difficult, requiring a careful design of optimizers and use of various heuristics. We make progress towards understanding the subtleties of training Transformers by carefully studying a simple yet…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
Modular robots have the potential to revolutionize automation, as one can optimize their composition for any given task. However, finding optimal compositions is non-trivial. In addition, different compositions require different base…
Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture…