arXiv research

Develops Hamiltonian Score Matching and Generative Flows for machine learning.

Improved efficiency in HMC samplers reduces dissipative behavior.

New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the comput…

SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.

HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.

Generative models on spheres improve discrete sequence sampling.

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geo…

New couplings improve understanding of molecular dynamics convergence.

In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate induct…

RHMC accelerates sampling from log-concave distributions.

In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dim…

Formulates mechanics for probability distributions on statistical manifold.

The paper develops methods to reduce deployment risk under dynamic covariate shifts.

The paper studies time-optimal problems on specific Lie groups, describing orbits and integrals.

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates…

We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual $E^\ast$ to a vector bundle $E$. If this almost Dirac structure is integrable (Dir…

UWM-JEPA predicts future scenarios in belief space, improving accuracy in partially observed environments.

Proposes bivariate DeepKriging for efficient wind field prediction.

HMC with leapfrog integrator mixes faster than MALA under certain smoothness conditions.

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike F…

DSNE visualizes data velocity in lower dimensions.

RFM improves CNFs by adding a boundary constraint term and matching velocity fields.

Log-ergodic model improves velocity of money prediction.

The paper concerns a simple model of bicycle kinematics: a bicycle is represented by an oriented segment of constant length in n-dimensional space that can move in such a way that the velocity of its rear end is aligned with the segment (the rear wheel is fixed on the bicycle frame). Starting with a closed trajectory o…

Optimal self-distillation improves generative models' velocity risk and mode recovery.

New method estimates velocity fields for minimizing $f$-divergences without overfitting.

We prove that, in a space-time of dimension n>3 with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is zero. The other way, if the covariant divergence of the Weyl tensor is zero, then…

New connections share geodesics with superintegrable systems.

Proves strong solutions for graphical Brakke flows with $L^2$ normal velocity.

CCVFM uses coreset to improve generative models by refining residual flows.

SAGE generates subsurface velocity models from sparse well logs and seismic images.

New method distinguishes cause from effect using causal velocity.

CAVI speeds up Bayesian MIDAS regression by 107x-1,772x with similar accuracy.

LFIS uses a time-dependent velocity field to sample from complex distributions.

NN-Turb generates turbulent velocity statistics using neural networks.

Bitcoin's monetary velocity is constrained by network friction, leading to significant utility contraction during shocks.

The determinants of the velocity of money have been examined based on life-cycle hypothesis. The velocity of money can be expressed by reciprocal of the average value of holding time which is defined as interval between participating exchanges for one unit of money. This expression indicates that the velocity is govern…

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.

Neural solver computes Wasserstein geodesics and velocity fields efficiently.

Develops scalable model for learning velocity fields in complex traffic scenarios.

Generative sampler learns velocity fields for efficient posterior inference.

Improved generative models using critically-damped Langevin diffusion.

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

An $(r,n)$-velocity is an $r$-jet with source at $0 \in \R^n$, and target in a manifold $Y$. An $(r,n)$-velocity is said to be regular, if it has a representative which is an immersion at $0 \in \R^{n}$. The manifold $T^{r}_{n}Y$ of $(r,n)$-velocities as well as its open, $L^{r}_{n}$-invariant, dense submanifold $\Imm …

Study uses neural networks to predict wall quantities in turbulent flows.

In this study, the concept of dual Lorentzian homotetic exponential motions in is discussed and their velocities, accelerations obtained. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained. Finally, the theorems related to acceleration and acceleration cen…

The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-f…