An Introduction to Lévy and Feller Processes. Advanced Courses in Mathematics - CRM Barcelona 2014

Visibility in the Boolean Model on Harmonic Manifolds

Global estimates on the Brenier map

Geodesics and Wandering Exponents in Brochette First-Passage Percolation

State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits

Randomly twisted transfer operators and singular values statistics

Generalized Bessel-Dunkl diffusions

An almost sure invariance principle for the Takagi-van der Waerden class functions

Central limit theorems for high dimensional lattice polytopes: cosmological polytopes

Convergence rate estimates for semigroups and heat kernels associated with resistance forms

Second-order Poincaré inequalities and localization on the Poisson space

Maximum Probability of Independence in Transitive Matroids

On global solutions to the semidiscrete stochastic heat equation

The Poisson Tail Conjecture for Primes in Short Intervals

A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage

Holographic functions and neural networks

From Betting to Empirical Bernstein LIL

Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise

Pointwise Generalization in Deep Neural Networks

Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors

Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process

A note on connections between the Föllmer process and the denoising diffusion probabilistic model

Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures

Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations

A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights

Propagation of Chaos in Contextual Flow Maps

Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures

$α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors

Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model

On the Limits of Latent Reuse in Diffusion Models

State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives

A Unified Framework for Critical Scaling of Inverse Temperature in Self-Attention

Expected Batch Optimal Transport Plans and Consequences for Flow Matching

Partial Model Sharing Improves Byzantine Resilience in Federated Conformal Prediction

GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms

Uniform Scaling Limits in AdamW-Trained Transformers

Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation

Scaling Limits of Long-Context Transformers

Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once

Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit

Convergent Stochastic Training of Attention and Understanding LoRA

Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models

Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective

Time-Inhomogeneous Preconditioned Langevin Dynamics

Matrix-Decoupled Concentration for Autoregressive Sequences: Dimension-Free Guarantees for Sparse Long-Context Rewards

Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature

Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows

Grokability in five inequalities

Almost-Orthogonality in Lp Spaces: A Case Study with Grok

On Computing Total Variation Distance Between Mixtures of Product Distributions

Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

Soft-to-Hard Routing in Sparse Mixture-of-Experts Models

Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach

Decentralized Proximal Stochastic Gradient Langevin Dynamics

A Review of the Receiver Operating Characteristic Curve and a Proof About the Area Beneath It

Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models

Well-Conditioned Oblivious Perturbations in Linear Space

Mathematical Foundations for Peer-to-Peer Lattice Computation

Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model

Phase Transitions in the Fluctuations of Functionals of Random Neural Networks

Ultrametric OGP - parametric RDT \emph{symmetric} binary perceptron connection

Geometric regularization of autoencoders via observed stochastic dynamics

A Wasserstein Geometric Framework for Hebbian Plasticity

Neural Continuous-Time Markov Chain: Discrete Diffusion via Decoupled Jump Timing and Direction

One-Shot Generative Flows: Existence and Obstructions

Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization

node2vec or triangle-biased random walks: stationarity, regularity & recurrence

Some Theoretical Limitations of t-SNE

Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version

Tail-Aware Information-Theoretic Generalization for RLHF and SGLD

Diffusion Processes on Implicit Manifolds

Degrees, Levels, and Profiles of Contextuality

High-accuracy log-concave sampling with stochastic queries

Variational Optimality of Föllmer Processes in Generative Diffusions

Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold

Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics

A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios

Feature Learning Dynamics in Infinite-Depth Neural Networks

On The Hidden Biases of Flow Matching Samplers

Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm

Normalizing Flows on Quotient Manifolds via Boundary Quotients

Differentiable Filtering for Learning Hidden Markov Models

Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

Posterior Bayesian Neural Networks with Dependent Weights

Exponentially Fading Memory Signature

A decision-theoretic approach to dealing with uncertainty in quantum mechanics

On Statistical Estimation of Edge-Reinforced Random Walks

Efficiency of Parallel and Restart Exploration Strategies in Model Free Stochastic Simulations

The feasibility of multi-graph alignment: a Bayesian approach

Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent

Mean-field limit from general mixtures of experts to quantum neural networks

On an $L^2$ norm for stationary ARMA processes

Mirror Descent-Ascent for mean-field min-max problems

Universal approximation property of Banach space-valued random feature models including random neural networks

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense

Conditional stochastic differential equations driven by fractional Brownian motion

Large deviations for the mean-field limit of Hawkes processes

Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection

Change of measure through the Legendre transform

On quantitative Laplace-type convergence results for some exponential probability measures, with two applications

Convergence rates for gradient descent in the training of overparameterized artificial neural networks with piecewise affine activation

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