New algorithm adapts to unknown demand smoothness for dynamic pricing.
problem Dynamic pricing with unknown Hölder smoothness of demand function.
method Self-similarity condition and adaptive algorithm.
result Adaptive algorithm achieves minimax optimal regret without prior knowledge of smoothness.
New metric improves latent dynamics inference from neural data.
problem Limitations of co-smoothing in predicting latent dynamics.
method Few-shot co-smoothing to assess latent dynamics.
result High co-smoothing models often have extraneous dynamics, which few-shot co-smoothing detects.
Efficient EP algorithm improves smoothing distribution inference in financial models.
problem Computational intractability of smoothing distribution in high dimensions.
method Adapted expectation propagation (EP) algorithms for the unified skew-normal family.
result Accuracy gains in financial illustrations over existing approximate algorithms.
New algorithms reduce dynamic regret for convex and smooth functions in non-stationary environments.
problem Online convex optimization in non-stationary environments.
method Proposed novel online algorithms exploiting smoothness to reduce dynamic regret.
result Dynamic regret improved to O(T) for convex and smooth functions. The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting…
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
Improved spectral clustering guarantees for dynamic stochastic block models.
problem Analyzing Spectral Clustering in dynamic stochastic block models.
method Extending guarantees to sparse and smooth DSBM, linking sparsity and smoothness.
result Improved error bounds for consistent recovery in dynamic DSBM.
Improved dynamic regret analysis for strongly convex and smooth functions.
problem Analyzing dynamic regret for online learning algorithms.
method Improved analysis of the Online Multiple Gradient Descent (OMGD) algorithm.
result Achieved a best-of-three-worlds guarantee for dynamic regret.
Study bounds topological entropy of toroidal attractors.
problem Bounding entropy of toroidal attractors.
method Analyzing topological properties of toroidal sets to bound entropy.
result Entropy of toroidal attractors is bounded from below.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, Hölder continuous) distributions. These distributions are of great significance for the behavior of the parent dynami…
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are effective at computing the expected value of a point at a future time given the …
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
Diffusion models improve creativity by smoothing the score function, leading to interpolated data.
problem Improving creativity in diffusion models.
method Analyzing the effect of score smoothing on diffusion model dynamics.
result Score smoothing causes diffusion models to generate data that interpolate the training set.
The paper develops techniques to study dynamical systems with Carnot metrics.
problem Understanding smooth dynamical systems in the presence of Carnot metrics.
method Employing techniques from Margulis-Mostow, Métivier, Mitchell, and Pansu on tangent cones, the paper establishes resonances between Lyapunov exponents.
result Local rigidity properties of higher hyperbolic rank metrics and uniform lattice actions on quaternionic and octonionic symmetric spaces.
New method approximates sampling from smooth potential distributions using a vanishing penalty.
problem Sampling from smooth potential distributions on high-dimensional spaces.
method Penalized Langevin dynamics (PLD) with vanishing penalty.
result Established upper bound on Wasserstein-2 distance for PLD approximation.
Develops theory for data-driven methods in dynamical systems.
problem Lack of analysis for data-driven methods in dynamical systems.
method Establishes existence of mapping and properties of operator learning architecture.
result Novel universal approximation theorems for smoothing and forecasting.
A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional manifolds.
Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.
problem Computing homology in discrete and smooth dynamical systems.
method Counting flow lines between orbits and critical points.
result Directly recovers Z2 homology from flow lines. Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the present paper is to provide a short overview of some results and open problems on s…
The paper improves competitive and dynamic regret bounds for smoothed online learning.
problem Smoothed online learning with hitting and switching costs.
method Optimization problems to minimize hitting cost, dynamic regret modification of existing algorithms.
result Improved competitive and dynamic regret bounds for various function classes.
Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
Proves rigidity of 3D partially hyperbolic systems via autonomous dynamics.
problem Rigidity of partially hyperbolic diffeomorphisms in 3D.
method Introducing autonomous dynamical systems to prove rigidity.
result Rigidity of partially hyperbolic diffeomorphisms on 3-manifolds.
A new dynamic learning-rate scheme for optimization.
problem Manual tuning of learning rates in optimization is time-consuming and error-prone.
method Locally optimal stepsize estimation for dynamic learning-rate scheduling.
result Our method achieves comparable performance with minimal tuning.
New model predicts energy prices volatility by smoothing time variation and persistence.
problem Separate study of volatility's time variation and persistence.
method Dynamic persistence model that allows shocks with heterogeneous persistence to vary smoothly over time.
result Significantly improves volatility forecasts over state-of-the-art models.
In unsupervised learning, there is no apparent straightforward cost function that can capture the significant factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static during the training process. The absence of concre…
In this paper we show that several dynamical systems with time delay can be described as vector fields associated to smooth functions via a bracket of Leibniz structure. Some examples illustrate the theoretical considerations.
Transformers handle infinite dimensional inputs effectively by feature extraction and dynamic feature selection.
problem Understanding the approximation and estimation ability of Transformers with infinite dimensional inputs.
method Anisotropic smoothness analysis and feature extraction properties of Transformers.
result Transformers avoid the curse of dimensionality and dynamically select important features.
Paper tackles dynamic behavior of variable topology mechanisms, presenting new transition conditions.
problem Dynamic behavior of mechanisms with changing kinematic topology.
method Presented new transition conditions for variable topology mechanisms using projected motion equations and Voronets equations.
result Results show the dynamic behavior of joint locking in 3R and 6DOF mechanisms.
Dynamic angles estimated from noisy measurements over time with smoothness constraints.
problem Recovering angles from noisy pairwise measurements over time.
method Three algorithms for joint estimation of angles under smoothness constraints.
result MSE converges to zero as T increases under milder conditions. A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
Paper defines dynamical coherence for flows and proves it under specific conditions.
problem Understanding the dynamics of partially hyperbolic flows.
method Introduces dynamical coherence and proves it for flows with a specific foliation.
result Dynamical coherence proved for flows with a particular foliation.
Study stabilizes second-order systems to first-order dynamics.
problem Stabilizing second-order systems to first-order dynamics.
method Feedback control of second-order systems on manifolds.
result Second-order systems can globally exponentially stabilize first-order dynamics for fully actuated systems.
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a conv…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, expon…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue,…
Estimates multiple linear systems on a graph with smoothness constraints.
problem Joint estimation of multiple linear systems under graph smoothness constraints.
method Proposes estimators for joint estimation of system matrices with error bounds.
result MSE converges to zero as m increases, typically polynomially fast w.r.t m. Smooth flows for physical systems with smooth energies and forces.
problem Smooth energies for physical simulations and force computation.
method Smooth mixture transformations on compact intervals and hypertori, using root-finding and the inverse function theorem.
result Smooth flows allow training by force matching and use as molecular dynamics potentials.
We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamic…
Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational Inference for Nonlinear Dynamics (VIND), a variational inference framework that is abl…
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 stability estimate for metric rigidity in hyperbolic dynamics.
problem Metric rigidity in hyperbolic dynamics.
method Radial source estimates in Hölder-Zygmund spaces for uniformly hyperbolic dynamics.
result Metrics with same marked length spectrum are isometric in C3+ε-close metrics in any dimension ≥2. State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…
Framework for continuous-time network data representation learning.
problem Learning reliable representations of dynamic network interactions.
method Three-stage process: intensity estimation, projection learning, evolving node representation construction.
result Trajectories satisfy structural and temporal coherence, providing robust inference.
Paper develops algorithms for PWA systems with polynomial regret.
problem Learning in piecewise affine systems due to discontinuities.
method Smoothed online learning framework applied to PWA systems.
result First algorithms with polynomial regret in PWA systems.