arXiv research

Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.

The paper explores coalescent contractions in contractible spaces, providing criteria and examples.

We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Particle Gibbs Sampling method, which alternately samples coalescent times conditioned on coalescent tree structures, and tree…

We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate o…

New algorithms learn simple staged trees from data, improving model fit.

Paper connects Painlevé VI equation to irregular systems, solving monodromy data.

Extends ML fairness to handle minority groups over time.

Linear-cost unbiased estimates for complex models via couplings.

Bayesian Neural Networks detect gravitational wave events with high accuracy and real-time potential.

Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens when the charge difference is sufficiently small. However, Ristenpart et al disc…

We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural re…

Develops a variational method for ultrametric phylogenetic trees.

New definition of angular momentum avoids supertranslation ambiguity.

New RL approach builds short ancestral recombination graphs.

PipeDream-2BW accelerates large model training by 20x with minimal memory usage.

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize trajectory optimization by means of a denoising autoencoder that is trained on the …

Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction and optimization. Interestingly, most all prior work in imitation and reinforcemen…

The study analyzes optimization trajectories in neural networks to reveal redundancy and redundancy-reducing strategies.

The goal of this paper is to present a method for simultaneous trajectory and local stabilizing policy optimization to generate local policies for trajectory-centric model-based reinforcement learning (MBRL). This is motivated by the fact that global policy optimization for non-linear systems could be a very challengin…

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…

Paper characterizes optimal learning trajectories for high-dimensional nonlinear models.

Study on Heisenberg group's Lorentzian problems using Pontryagin's principle.

Optimizes trading trajectories for large portfolios quickly.

Bayesian method estimates dynamics from near-optimal trajectories.

GrateTile optimizes CNN feature map storage for efficient data access.

End-to-end framework optimizes constrained trajectories using data-driven methods.

Study models Indian stock market using hyperbolic geometry for market stability and volatility analysis.

We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the dist…

We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebra…

New method improves learning from multiple correlated data trajectories.

Paper finds optimal shapes for minimizing average lengths of billiard trajectories in specific polygons.

Develops a method to infer cell trajectories from RNA sequencing data.

Optimal execution of portfolio transactions is the essential part of algorithmic trading. In this paper we present in simple analytical form the optimal trajectory for risk-averse trader with the assumption of exponential market recovery and short-time investment horizon.

Adaptive optimization methods bias neural network trajectories towards regions of lower local geometry.

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energy-based model, where the observed expert trajectori…

Extends RL to random stopping times, improving optimization.

In distributed function computation, each node has an initial value and the goal is to compute a function of these values in a distributed manner. In this paper, we propose a novel token-based approach to compute a wide class of target functions to which we refer as "Token-based function Computation with Memory" (TCM) …

We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph clustering to regroup trajectories with similar profiles. Our experimental stud…

In this paper, we propose a reinforcement learning-based algorithm for trajectory optimization for constrained dynamical systems. This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Generating smooth, dynamically feasible trajectories could be difficult for such sy…

New algorithm infers trajectories from partial observations using optimal transport.

This work tackles uncertainty in multi-agent multi-modal trajectory forecasting.

A new method learns straight trajectories in one step for optimal flow matching.

Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory fr…

The paper develops a new theory to understand deep learning optimization.

Trajectory-level supervision allows efficient offline reinforcement learning.

A new reinforcement learning method reduces action complexity for robust control.

We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set o…

SOCRATES uses LLMs to automate simulation optimization of complex systems.