Autoencoder estimates parameters of noisy, multi-component damped signals.
problem Parameter estimation of damped sinusoidal signals under rapid decay and noise.
method Autoencoder-based approach using latent space for frequency, phase, decay, and amplitude estimation.
result High accuracy in parameter estimation, robustness to subdominant components and phase differences.
Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.
problem The Schur complement is used in both spatial modeling and portfolio allocation, but the parameters are different.
method The Schur complement is interpreted as reliability shrinkage of a conditional Gaussian.
result The Schur complement is the same in both applications.
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
problem Efficiently pricing multi-asset options in Lévy models.
method Optimized damping parameters and hierarchical adaptive quadrature.
result Significant speed-up in computational time for up to six dimensions.
Machine learning predicts nuclear physics parameters with high accuracy.
problem Predicting nuclear physics parameters for superheavy elements.
method Gradient boosted trees algorithm trained on nuclear data.
result Predictions have standard deviation from 0.00035 to 0.73.
Unified method for calculating financial option prices from characteristic functions.
problem Calculating financial option prices from characteristic functions in high dimensions.
method Damped Fourier-cosine expansion (COS) method.
result The method converges exponentially if the characteristic function decays exponentially.
New algorithm for computing Wasserstein barycenters with guarantees.
problem Computing Wasserstein barycenters with varying regularization strengths.
method Damped Sinkhorn iterations followed by exact maximization/minimization steps.
result First non-asymptotic convergence guarantees for approximating Wasserstein barycenters.
A new method uses higher-order Langevin dynamics with critical damping for better generative modeling.
problem Improving generative models using Langevin dynamics with auxiliary variables.
method Introducing higher-order Langevin dynamics with critical damping, providing closed-form solutions.
result Improved generative models with better performance as measured by FID metric.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
We discuss stochastic modeling of volatility persistence and anti-correlations in electricity spot prices, and for this purpose we present two mean-reverting versions of the multifractal random walk (MRW). In the first model the anti-correlations are modeled in the same way as in an Ornstein-Uhlenbeck process, i.e. via…
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We count the number of eigenvalues in a given horizontal strip deviating from this…
Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient β. Large β values can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typic…
Study shows how neural networks learn eigenfunctions of the NTK in underparameterized settings.
problem Understanding the dynamics of MSE optimization in underparameterized neural networks.
method Analysis of gradient flow dynamics, focusing on eigenfunctions of the NTK.
result Eigenfunctions of the NTK determine the learning dynamics in underparameterized networks.
DistillKac generates images quickly using damped wave equations.
problem Generating high-quality images efficiently.
method Uses damped wave equations and Kac dynamics for finite speed transport.
result Fast image generation with high quality and numerical stability.
Logarithmic-time schedules boost large-scale language model training efficiency.
problem Improving performance and efficiency in large-scale language model training.
method Designing time-varying hyperparameters (β1,β2,λ) for AdamW, specifically logarithmic-time scheduling with damping mechanisms. result ADANA optimizer achieves up to 40% compute efficiency compared to tuned AdamW, with gains persisting as model scale increases.
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…
The paper develops methods to infer modes of linear systems from noisy data.
problem Detecting oscillations in power flow in AC electrical networks.
method Develops methods to infer modes (real or complex) from observations of linear systems forced by Gaussian noise.
result Inference of damping rates, frequencies, and mode shapes for real and complex modes.
In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversio…
A new real-time method estimates system matrices and states using Kalman filter.
problem Real-time estimation of system matrices and states using Kalman filter.
method Estimation in an observation space, time-invariant interval, and online learning framework.
result Extraordinary performance in estimating matrices for damped oscillation model.
Develops geometric framework for dissipative field equations.
problem Dissipative field equations and their geometric analysis.
method Canonical k-contact manifolds, k-contactifications, splitting results, regularity conditions, criteria for PDEs. result Explicit Hamiltonian descriptions for various nonlinear PDEs.
The energy in a square membrane Ω subject to constant viscous damping on a subset ω⊂Ω decays exponentially in time as soon as ω satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch" condition. The rate τ(ω) of this decay satisfies τ(ω)=2min(−μ(ω),g(ω)) (see Lebeau [Math. Phys. Stud. …
Unified ODE model explains residual and non-residual networks.
problem Unclear relationship between residual and non-residual networks.
method Introducing a damping term in an ODE model to interpolate between ResNet and CNN architectures.
result Unified framework for understanding residual and non-residual networks.
PrecGD restores linear convergence in over-parameterized nonconvex matrix factorization.
problem Slow convergence of local search algorithms in over-parameterized nonconvex matrix factorization.
method Preconditioned Gradient Descent (PrecGD) with an inexpensive ℓ2 regularization. result PrecGD restores linear convergence rate even in the over-parameterized case.
Newton's method solves variational problems on manifolds.
problem Solving variational equations on manifolds.
method Newton's method with affine covariant damping strategy.
result Numerical results for variational problems demonstrated.
We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey and consumers as predators provides the required instability, but its natural d…
Improved sampling in generative models using CLDs with a hyperparameter.
problem Improving sampling performance in generative models.
method Extending Critically-damped Langevin Diffusions with a hyperparameter to control noise.
result Derivation of a novel upper bound on Wasserstein sampling error.
An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive stepsize of each individual parameter. The dynamic relaxation is adapted for stochast…
This paper proposes an alternative to the classical price-adjustment mechanism (called "tâtonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a proc…
Improved generative models using critically-damped Langevin diffusion.
problem Current score-based generative models (SGMs) use overly simplistic diffusion processes, leading to complex denoising tasks and suboptimal performance.
method Proposed a novel critically-damped Langevin diffusion (CLD) and derived a score matching objective and sampling scheme.
result CLD-based SGMs achieve superior performance in synthesis quality compared to previous methods.
Paper designs energy-based controllers and observers for complex systems.
problem Controlling and observing infinite-dimensional systems with in-domain actuation.
method Uses Stokes-Dirac structures and jet-bundle structures to derive controllers and observers.
result Control schemes derived in both frameworks are equivalent.
New method uses machine learning to optimize Fourier pricing methods.
problem Difficulty in tuning parameters for Fourier pricing methods.
method Learning tuning parameters of Fourier methods using machine learning.
result Very fast algorithms with full error control.
Stability of black holes proven in full subextremal range with positive cosmological constant.
problem Stability of Kerr-de Sitter black holes in the full subextremal range.
method Similar to previous proof in slowly rotating case, with implementation of constraint damping and verification of subprincipal symbol condition.
result Stability of Kerr-de Sitter black holes proven in the full subextremal range.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
In this paper we consider the composite self-concordant (CSC) minimization problem, which minimizes the sum of a self-concordant function f and a (possibly nonsmooth) proper closed convex function g. The CSC minimization is the cornerstone of the path-following interior point methods for solving a broad class of co…
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power…
A new FFT method for Heston model option pricing with explicit error bounds.
problem Efficiently pricing European options in the Heston model with high accuracy.
method Convolution-FFT method leveraging a continuously differentiable joint characteristic function.
result Explicit error bounds for FFT-based convolution method in Heston model.
The computation of Bayesian estimates of system parameters and functions of them on the basis of observed system performance data is a common problem within system identification. This is a previously studied issue where stochastic simulation approaches have been examined using the popular Metropolis--Hastings (MH) alg…
Improved numerical solution for BSDEs with reduced boundary errors.
problem Boundary errors in numerical solution of BSDEs.
method Modified damping and shifting schemes to transform target function into a bounded periodic function, applying Fourier transforms.
result Significant reduction in boundary errors with improved accuracy and convergence.
New method predicts quasar continuum near Lyman-α with high precision and accuracy.
problem Precise measurement of quasar red damping wing for epoch of reionization.
method Fully probabilistic approach using conditional neural spline flows.
result Achieved state-of-the-art precision and accuracy in predicting quasar continua.
APGD algorithm efficiently recovers over-parameterized matrices from noisy measurements.
problem Matrix sensing problem with over-parameterization and noisy measurements.
method Alternating preconditioned gradient descent (APGD) algorithm incorporating preconditioning terms.
result APGD converges to a near-optimal error at a linear rate.
New preconditioners speed up SGD on Lie groups.
problem Accelerating SGD convergence on Lie groups.
method Online updating of low-rank and matrix-free preconditioners.
result Preconditioners maintain symmetry and invariance.
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio α=p/N of the number p o…
New method identifies physical constants from video data alone.
problem Identifying physical constants from video data.
method Proves level-set slope-coverage condition ensures local affine mapping to true physical state, enabling exact parameter recovery.
result Underdamped systems identifiable from a single video clip, other regimes require three diverse trajectories.
Using a modified damped harmonic oscillator model equivalent to a model of market dynamics with price expectations, we analyze the reaction of financial markets to shocks. In order to do this, we gather data from indices of a variety of financial markets for the 1987 Black Monday, the Russian crisis of 1998, the crash …
Study on blow-up solutions for semilinear wave equations on specific manifolds.
problem Investigate blow-up and lifespan estimates for semilinear wave equations on asymptotically Euclidean manifolds.
method Use of exponential perturbation metric and construction of entire solutions for a related equation.
result Sharp upper bound estimates for the lifespan of solutions.
Introduces VSMD to improve generative diffusion processes without high costs.
problem High training costs and scalability issues in generative diffusion processes.
method Introduces variational Schrödinger momentum diffusion (VSMD) with adaptively transport-optimized variational scores and critical-damping transform.
result Efficiently generates anisotropic shapes while maintaining transport efficacy, outperforming alternatives.
Method leverages population data to deconvolve unknown noise and model parameters.
problem Deconvolution of unknown observational noise in distributional inversion problems.
method Large data sets from physical systems, modified gradient descent, active learning.
result Simultaneous deconvolution of noise and model parameters.
By using Hsu's multiplicative functional for the Neumann heat equation, a natural damped gradient operator is defined for the reflecting Brownian motion on compact manifolds with boundary. This operator is linked to quasi-invariant flows in terms of a integration by parts formula, which leads to the standard log-Sobole…