Proposes a dynamic matching algorithm for two-sided online markets.
problem Dynamic preferences in two-sided online matching platforms.
method Dynamic Matching Bandit Algorithm with statistical preference ranking estimation.
result Agent-optimal stable matching result with logarithmic regret bound.
Study dynamic matching in heterogeneous networks using ODE model.
problem Dynamic matching in heterogeneous networks with compatibility restrictions.
method Introduced an ODE model to evaluate matching algorithms.
result Demonstrated trade-off between quick matching and optimal matching.
Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebra…
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
problem Understanding the dynamics of Vlasov plasma and its kinetic moments.
method Hamiltonian (Lie-Poisson) analysis and matched pair decomposition.
result Observation of mutual interactions between subdynamics in Vlasov plasma.
The supplement proves the existence and properties of a dynamical system related to asset price bubbles.
problem Modeling asset price bubbles using liquidity and random matching.
method Proves the existence and properties of a dynamical system D.
result Existence and properties of the dynamical system D are proven.
The paper models market dynamics using a limit order book system to explain slippage and inefficiency.
problem Inefficiency in matching markets due to structural liquidity constraints and slippage.
method Introduces a market microstructure framework with a latent preference state matrix and a dynamic discrete choice execution model.
result Persistent slippage and regional invariance of preference orderings are explained by liquidity thresholds.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
Optimizes long-term social welfare in recommender systems by matching users to providers.
problem Realistic recommender systems dynamics affect all agents, not just users.
method Formulated as an optimal constrained matching problem, solved using dynamical system equilibrium selection.
result Ensures maximal social welfare with diverse viable providers, improving over myopic matching.
New analysis shows FM learns underlying dynamical structure, not just trajectory replay.
problem Understanding whether flow matching models learn transferable dynamical structure or merely replay trajectories.
method Derived velocity field implied by FM objective, characterized as a continuous-time dynamical system.
result FM models can be seen as parametric surrogates of nonparametric solutions, providing strong probabilistic forecasts.
New method learns flows between multiple distributions efficiently.
problem Learning dynamic transport maps between multiple empirical distributions.
method Combining flow matching and dynamic optimal transport with potential terms.
result OTP-FM achieves state-of-the-art performance on various datasets.
Generative models learn latent process to match target distributions.
problem Training flow-matching models with auxiliary stochastic dynamics.
method Introduces latent process generator matching, treating generative state as a deterministic image of a Markov process.
result Learn generator of a stochastic process with same marginal distributions.
New method trains reflected Schrödinger bridges without complex derivatives.
problem Training reflected Schrödinger bridges efficiently in high dimensions.
method Partially simulation-free framework with new sampling method.
result Generative performance maintained or slightly improved with reflected dynamics.
Paper introduces Decentralized Non-stationary Competing Bandits ( exttt{DNCB}) for dynamic matching markets.
problem Understanding dynamic two-sided matching markets with competing agents.
method Proposes a decentralized asynchronous learning algorithm ( exttt{DNCB}) for non-stationary environments.
result Obtains sub-linear (logarithmic) regret of exttt{DNCB} in dynamic settings.
3MSBM learns smooth trajectories from multiple snapshots.
problem Capturing long-range temporal dependencies in complex systems.
method Lifts dynamics to phase space, generalizes stochastic bridges to multi-marginal conditional problems, learns transport maps preserving intermediate marginals.
result Significantly improves convergence and scalability in capturing complex dynamics.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
Paper develops efficient recursive learning for multi-channel systems with heterogeneous dynamics.
problem Accurately learning system dynamics in complex, multi-channel systems with nonlinear and noisy data.
method Formulates system as Gaussian process state-space models (GPSSMs), introduces heterogeneous multi-output kernel, and develops recursive inference framework.
result Matches SOTA offline GPSSMs in accuracy with 1/100 runtime, and outperforms SOTA online GPSSMs by 70% in accuracy under noise with 1/20 runtime.
Score matching method improves image generation quality.
problem Score matching method underperforms GANs in metrics like Fréchet Inception Distance.
method DSM-ALS with denoising and improved sampling techniques.
result Score matching methods can match GANs in image generation quality.
It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic…
Proposes TSBP for matching topological signal distributions.
problem Matching signal distributions on topological domains.
method Topological Schrödinger Bridge (TSBP) with linear topology-aware stochastic dynamics.
result Derives closed-form topological SB (TSB) for Gaussian boundary distributions.
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
The design of personalized incentives or recommendations to improve user engagement is gaining prominence as digital platform providers continually emerge. We propose a multi-armed bandit framework for matching incentives to users, whose preferences are unknown a priori and evolving dynamically in time, in a resource c…
New method improves SBI efficiency and scalability.
problem Scalability issues in SBI methods for large datasets.
method Langevin dynamics with score matching, exploiting likelihood structure.
result Structured score network enhances statistical efficiency and scalability.
BM2 learns Schrödinger bridges using neural networks.
problem Learning dynamic transport maps between two distributions.
method Coupled Bridge Matching (BM2) with neural networks. result Preliminary theoretical analysis and numerical experiments show BM2's effectiveness. Score matching efficiency tied to distribution isoperimetric properties.
problem Understanding when score matching is as efficient as maximum likelihood.
method Connecting score matching efficiency to isoperimetric constants of distributions.
result Score matching is statistically efficient when the distribution has a small isoperimetric constant.
A new method improves flow matching by dynamically weighting density estimates.
problem High-dimensional integration inefficiency in flow matching.
method Density-weighted Dynamic Stein operators.
result Significant improvement in vector field smoothness and sampling efficiency.
Study asset price bubbles using random matching and stochastic factors.
problem Understanding and modeling asset price bubbles through investor contagion.
method Developed a stochastic model of liquidity-based asset price bubbles using random matching mechanism.
result Derived conditions for arbitrage-free financial market models.
SFM resolves small-scale physics challenges in weather data.
problem Challenges in super-resolving small-scale details in physical sciences like weather.
method Encoding inputs to a latent base distribution, flow matching for stochastic details, adaptive noise scaling.
result SFM framework significantly outperforms existing methods.
A scalable algorithm for sampling and fine-tuning models using Tilt Matching.
problem Efficient sampling and fine-tuning of generative models.
method Tilt Matching, arising from a dynamical equation, minimizes variance and inherits regularity from stochastic interpolants.
result Empirically verified to be efficient and highly scalable, providing state-of-the-art results.
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
problem Lack of reference atomistic forces makes force matching infeasible for MLCG force fields.
method Introduces noise-based kernels adapted to low-data regimes using normalizing flows.
result Flow-based kernels reduce local distortions while preserving global accuracy.
Improves sample efficiency in RL by matching model-based gradients.
problem Lack of sample efficiency in model-free RL.
method Gradient matching between model-based and model-free RL components.
result Improves sample efficiency without increasing asymptotic bias.
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical integration. However, for many real-world applications, only sparse observations are avail…
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.
Agent-based model simulates market dynamics with real-time order matching.
problem Realistic simulation of market dynamics with realistic price impact.
method Agent-based model with asynchronous, event-time order matching.
result Realistic price impact curves and stylized facts presented.
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching methods do not pass basic sanity checks: they fail when irrelevant variables are …
Improves generative models by using heavy-tailed noise in score matching.
problem High-dimensional limitations of Gaussian noise in generative models.
method Extended DSM to generalised normal distribution, relaxed key assumptions, developed iterative noise scaling algorithm.
result Heavy-tailed DSM leads to improved generative performance.
Enhances learning of structured distributions using nonlinear denoising score matching.
problem Learning structured distributions from noisy data.
method Latent Nonlinear Denoising Score Matching (LNDSM) integrating nonlinear dynamics with VAE-based latent score matching.
result LNDSM achieves superior sample quality and variability compared to structure-agnostic methods.
Model-based reinforcement learning approaches carry the promise of being data efficient. However, due to challenges in learning dynamics models that sufficiently match the real-world dynamics, they struggle to achieve the same asymptotic performance as model-free methods. We propose Model-Based Meta-Policy-Optimization…
Score matching errors are not sufficient for measuring diffusion model quality.
problem The L2 score matching error is not a reliable measure of diffusion model performance. method Decomposed score errors into gradient and solenoidal components and analyzed their geometric properties.
result Only the gradient component of the score error affects the marginal distributional quality.
A new method for estimating uncertainties in neural ODEs without numerical integration.
problem Accurate estimation of predictive uncertainties in neural ODEs.
method Distributional Gradient Matching (DGM) algorithm that jointly trains a smoother and a dynamics model.
result Significantly more accurate predictions compared to traditional methods.
CatFlow uses variational flow matching for efficient graph generation.
problem Graph generation tasks, especially for categorical data.
method Variational flow matching for categorical data, computationally efficient.
result CatFlow achieves strong results on graph generation tasks.
MFM improves generative model interpolations by learning approximate geodesics on data manifolds.
problem Straight interpolations fail to capture dynamics on data manifolds.
method Metric Flow Matching (MFM) learns approximate geodesics by minimizing kinetic energy of a data-induced Riemannian metric.
result MFM outperforms Euclidean baselines, achieving SOTA on single-cell trajectory prediction.
The paper uses moment matching method for pricing spread options under Lévy models.
problem Pricing spread options under Lévy models with mean-variance mixture.
method Moment matching method applied to Lévy models with mean-variance mixture.
result Obtains semi-closed form formulas for spread option prices.
TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.
problem Modeling irregularly sampled time series in medicine.
method Trajectory Flow Matching (TFM) using flow matching for generative modeling.
result TFM improves performance on clinical time series datasets.
BNEM improves Boltzmann sampler efficiency.
problem Generating IID samples from Boltzmann distributions efficiently.
method Bootstrapped Noised Energy Matching (NEM) combined with diffusion-based learning and bootstrapping.
result BNEM achieves state-of-the-art performance with improved robustness.
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.