arXiv research

The paper provides uniform length estimates for trajectories on flat cone surfaces.

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

Critical trajectories in a sphere are found for a specific bending functional.

Reasoning models generate differently based on problem difficulty, not just length.

Study of closed trajectories in hyperbolic plane with specific curvature constraints.

Representation learning of pedestrian trajectories transforms variable-length timestamp-coordinate tuples of a trajectory into a fixed-length vector representation that summarizes spatiotemporal characteristics. It is a crucial technique to connect feature-based data mining with trajectory data. Trajectory representati…

ATLAS adapts HMC step size and trajectory length for complex geometries.

A new method detects anomalies in trajectory data using normalizing flows.

We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length…

The paper proves a nonholonomic version of Maupertuis-Jacobi principle and shows that nonholonomic trajectories minimize length.

In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in ${\mathbb R}^{n}$. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiar…

Pattern ensembling fills in missing or inaccurate trajectory data.

Adaptive stopping in MCMC using classifier-based dynamics

Estimates MLDS using tensor decomposition, improving upon existing methods.

OSIRIS reduces variance in off-policy evaluation by omitting irrelevant states.

Study on estimating unstable open-loop matrices from state trajectories.

The paper improves lower bounds on deep neural network trajectories.

Cube edges curves minimize systole length.

The paper defines and analyzes conformal trajectories in 3D space forms.

A framework clusters vehicle motion trajectories efficiently.

Algorithm learns mixtures of Markov chains and MDPs from short trajectories.

Dynamic time warping (DTW) can be used to compute the similarity between two sequences of generally differing length. We propose a modification to DTW that performs individual and independent pairwise alignment of feature trajectories. The modified technique, termed feature trajectory dynamic time warping (FTDTW), is a…

TRAKNN detects rare atmospheric trajectories efficiently.

Neural network outperforms traditional methods in chaotic dynamics classification.

We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical con…

Which song will Smith listen to next? Which restaurant will Alice go to tomorrow? Which product will John click next? These applications have in common the prediction of user trajectories that are in a constant state of flux over a hidden network (e.g. website links, geographic location). What users are doing now may b…

New proof shows nonholonomic motions are geodesics, minimizing distance.

We describe our first-place solution to the Animal Behavior Challenge (ABC 2018) on predicting gender of bird from its GPS trajectory. The task consisted in predicting the gender of shearwater based on how they navigate themselves across a big ocean. The trajectories are collected from GPS loggers attached on shearwate…

We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface $M$ in a $d$-dimensional Finsler space with possibly irreversible Finsler metric. An example of such a system is a billiard in a sufficiently weak magnetic field. The $r$-periodic Fin…

Algorithm recovers graph from Glauber dynamics trajectory without mixing.

The paper improves model-based reinforcement learning by using multi-timestep objectives.

The paper investigates how neural network weights evolve to monitor training progress.

EBM life cycle project improves MCMC for image generation, defense, and density modeling.

Analyzes how quadratic differential trajectories change with variation, proving a wall-crossing formula.

Study learns dynamics of linear systems from multiple short trajectories.

Improved sampling efficiency for molecular systems using path gradients after Flow Matching.

Study of supervised learning from multiple non-independent sequences.

Paper proposes a new descriptor for early trajectory characterization in matrix iterations.

The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.

We use the criteria of Lalonde and McDuff to determine a new class of examples of length minimizing paths in the group $Ham(M)$. For a compact symplectic manifold $M$ of dimension two or four, we show that a path in $Ham(M)$, generated by an autonomous Hamiltonian and starting at the identity, which induces no non-cons…

Algorithm learns multiple LDS models from unlabeled short trajectories.

The number of closed billiard trajectories in a rational-angled polygon grows quadratically in the length. This paper gives an analogue on K3 surfaces, by considering special Lagrangian tori. The analogue of the angle of a billiard trajectory is a point on a twistor sphere, and the number of directions admitting a spec…

Identifies bilinear systems from a single trajectory with optimal sample complexity.

Recent developments in specialized computer hardware have greatly accelerated atomic level Molecular Dynamics (MD) simulations. A single GPU-attached cluster is capable of producing microsecond-length trajectories in reasonable amounts of time. Multiple protein states and a large number of microstates associated with f…

Recurrent auto-encoder model summarises sequential data through an encoder structure into a fixed-length vector and then reconstructs the original sequence through the decoder structure. The summarised vector can be used to represent time series features. In this paper, we propose relaxing the dimensionality of the dec…

A new algorithm for offline RL with trajectory-wise reward reduces bias and variance errors.

The study analyzes the performance of a nonparametric estimator for dynamical systems.

New insights on offline RL with state aggregation and trajectory data.