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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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← all fields·9 papers on “wasserstein distance” in Statistical ML · 1 month

Scaling Limits of Constant-Stepsize SGD at Flat Minimacs.LG

SGD with constant stepsize converges to a non-Gaussian limit near flat minima.

problem Behavior of SGD near flat minima with convex objectives.

method Analyzes SGD with Markovian noise and contractive driving chain.

result Invariant law concentrates on scale

α^{1/m}

and converges weakly to a non-Gaussian stationary distribution.

SGD constant stepsize flat minima non-Gaussian limit Wasserstein distance

2026-07-17abs ↗pdf ↗

Linear Independent Component Analysis via Optimal Transportcs.LG

OT-ICA uses optimal transport to find independent components, outperforming traditional methods.

problem Finding independent components from linear mixtures of signals.

method OT-ICA uses the squared Wasserstein distance to maximize non-Gaussianity, optimizing projections via gradient descent.

result OT-ICA outperforms traditional proxy-based methods in various applications.

ICA Optimal Transport Wasserstein Distance Non-Gaussianity Gradient Descent

2026-07-15abs ↗pdf ↗

Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussianstat.ML

Study uses Wasserstein distance to identify causal orders and unmix sources.

problem Identifying causal relationships and separating sources in non-Gaussian data.

method Wasserstein distance for non-Gaussianity, linear ICA, causal inference.

result Exact identification of ICA unmixing matrix and causal orders.

Wasserstein distance ICA causal inference non-Gaussian data LiNGAM

2026-07-14abs ↗pdf ↗

Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Samplingstat.ML

New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.

problem Numerical stability issues in diffusion sampling despite small forward-marginal error.

method Constructing a smooth score field with arbitrarily small forward-marginal

L^2

error, showing nonexplosive behavior and moments of every order.

result Euler--Maruyama discretizations can converge in probability even when moments diverge, demonstrating failure of weak convergence.

numerical stability score matching diffusion sampling path-space total variation Wasserstein distance

2026-07-09abs ↗pdf ↗

Quantitative Gaussian-Process limits of Tensor Programscs.LG

Study Gaussian-process limits of neural networks using tensor programs.

problem Understanding the behavior of neural networks as they approach infinite width.

method Quantitative analysis through tensor programs and Wasserstein distance.

result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.

Gaussian-process neural networks tensor programs Wasserstein distance finite-width error bounds

2026-07-07abs ↗pdf ↗

Tightening the Score Matching Gap for Diffusion Modelsstat.ML

New bounds close the score matching gap for diffusion models.

problem The difference between sample quality and score matching loss in diffusion models.

method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.

result The quality of score approximation impacts closing the score matching gap for low noise scales.

diffusion models score matching KL divergence Wasserstein distance entropy flows

2026-07-05abs ↗pdf ↗

A Unified Framework for In-Context Learning with Causal and Masked Language Modelscs.LG

Unified framework for ICL in causal and masked models.

problem Understanding ICL in masked language models and comparing it to causal models.

method Developed a statistical learning framework representing context by empirical measure and predicting using context and query.

result Upper bounds for masked and autoregressive objectives under Wasserstein-type regularity conditions.

In-context learning Unified framework Causal language models Masked language models Excess-risk analysis

2026-07-05abs ↗pdf ↗

Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descentmath.PR

Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.

problem Understanding long-term behavior of finite-particle systems in relation to their mean-field limits.

method Developed uniform-in-time propagation-of-chaos results for continuous-time SVGD using cutoff strategies and finite-dimensional theories.

result Uniform-in-time propagation-of-chaos bounds in various metrics, including Langevin kernel Stein discrepancy, Wasserstein-1, and Wasserstein-2 distances.

Stein Variational Gradient Descent Propagation-of-Chaos Uniform-in-Time Langevin Kernel Wasserstein Distance

2026-06-30abs ↗pdf ↗

Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDSstat.ML

This paper improves MDS visualization by adjusting Wasserstein distances for heavy-tailed data.

problem Enhancing Multidimensional Scaling (MDS) for better pattern recognition with heavy-tailed distributions.

method Introduces Max-D-SW, a metric adjustment of Max-Sliced Wasserstein distance that aggregates over orthonormal bases.

result Max-D-SW provides a clear numerical advantage in MDS outcomes, especially for heavy-tailed distributions.

Multidimensional Scaling Wasserstein distance Max-D-SW Heavy-tailed distributions Pattern recognition

2026-06-29abs ↗pdf ↗