arXiv research

Polynomial-time reachability for LTI systems with TLL NN controllers is achieved.

Guaranteed reachable set for unknown nonlinear systems on manifolds.

We quantify content availability and user discovery opportunities in recommender systems.

Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs, computes the lower and upper bound on the function values. Because the network and the …

Procedure verifies if machine learning models assign fixed predictions that preclude access.

Study analyzes and enhances robustness of neural networks for classification and regression.

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

Improves data-driven reachability estimation for complex systems.

Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.

This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.

GraphReach improves GNN performance by incorporating node positions.

Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.

Influence maximization (IM) is the problem of finding for a given $s\geq 1$ a set $S$ of $|S|=s$ nodes in a network with maximum influence. With stochastic diffusion models, the influence of a set $S$ of seed nodes is defined as the expectation of its reachability over simulations, where each simulation specifies a det…

Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.

CIfly simplifies causal inference tasks with linear-time reachability primitives.

Deep learning method proves convergence for solving HJI equations.

In finance industry portfolio construction deals with how to divide the investors' wealth across an asset-classes' menu in order to maximize the investors' gain. Main approaches in use at the present are based on variations of the classical Markowitz model. However, recent evolutions of the world market showed limitati…

Improved exploration algorithm for unknown MDPs with reduced sample complexity.

We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain e…

Safe imitation learning with a safety layer for flexible training.

How can we design safe reinforcement learning agents that avoid unnecessary disruptions to their environment? We show that current approaches to penalizing side effects can introduce bad incentives, e.g. to prevent any irreversible changes in the environment, including the actions of other agents. To isolate the source…

Compact reachability embeddings for hierarchical data

GoTube verifies neural networks over time, scaling to large horizons.

We consider examples of the $\mathbb H$-type groups with the natural horizontal distribution generated by the commutation relations of the group. In the contrast with the previous studies we furnish the horizontal distribution with the Lorentzian metric, which is nondegenerate metric of index 1 instead of a positive de…

CAST improves spectral clustering for multi-scale data by integrating reachability similarity.

DARLING tackles non-stationary RL with guarantees, improving dynamic regret.

The paper certifies neural network-based control barrier functions efficiently.

We address the problem of verifying neural-based perception systems implemented by convolutional neural networks. We define a notion of local robustness based on affine and photometric transformations. We show the notion cannot be captured by previously employed notions of robustness. The method proposed is based on re…

Active sampling selects few points for accurate model reduction of high-fidelity systems.

CUDC collects diverse data for offline RL by predicting future states.

Improves RL from historical data by stitching trajectories.

C-Learning estimates reachability over time to solve multi-goal tasks.

Recommender systems often rely on models which are trained to maximize accuracy in predicting user preferences. When the systems are deployed, these models determine the availability of content and information to different users. The gap between these objectives gives rise to a potential for unintended consequences, co…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output propertie…

New distances for causal graphs improve evaluation of learned structures.

We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every move of the sequence. This conditional setting leads to a possibility of irreve…

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-se…

A new clustering algorithm considers data smoothness for better performance.

In this article, we consider the rolling (or development) of two Riemannian connected manifolds $(M,g)$ and $(\hat{M},\hat{g})$ of dimensions $2$ and $3$ respectively, with the constraints of no-spinning and no-slipping. The present work is a continuation of \cite{MortadaKokkonenChitour}, which modelled the general set…

In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. In this paper, we address the problem of safely exploring fin…

In this paper, we consider two cases of rolling of one smooth connected complete Riemannian manifold $(M,g)$ onto another one $(\hM,\hg)$ of equal dimension $n\geq 2$. The rolling problem $(NS)$ corresponds to the situation where there is no relative spin (or twist) of one manifold with respect to the other one. As for…

Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.

We perform a geometric study of the equilibrium locus of the flow that models the diffusion process over a circular network of cells. We prove that when considering the set of all possible values of the parameters, the equilibrium locus is a smooth manifold with corners, while for a given value of the parameters, it is…

We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both $\SU(1,1)$ and $\CSU(1,1)$, connecting two fixed points. In particular, we prove that …

Efficient adjustment sets found for cost-minimized causal estimations.

Estimates convex hulls of smooth function images with error bounds.

Study improves understanding of why agentic theorem provers succeed.

We prove a lower bound for feature dimension in linear MDPs and propose a novel dynamics aggregation framework.