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Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Improved Baselines with Representation Autoencoders Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent Calibeating for general proper losses: A Bregman divergence approach Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space Sample-efficient inductive matrix completion with noise and inexact side-information Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Reasoning Models Don't Just Think Longer, They Move Differently TabPFN-3: Technical Report Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models Towards a holistic understanding of Selection Bias for Causal Effect Identification Adaptive Kernel Density Estimation with Pre-training Coreset-Induced Conditional Velocity Flow Matching RISED: A Pre-Deployment Evaluation Framework for High-Stakes AI Decision-Support Systems, with Application to Healthcare ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage Model-based Bootstrap of Controlled Markov Chains Online Learning-to-Defer with Varying Experts Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification Keeping Score: Efficiency Improvements in Neural Likelihood Surrogate Training via Score-Augmented Loss Functions One-Step Generative Modeling via Wasserstein Gradient Flows Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty A Composite Activation Function for Learning Stable Binary Representations Adaptive Calibration in Non-Stationary Environments Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimation Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage On Variance Reduction in Learning Mean Flows When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? 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Complete version Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer Spatio-temporal probabilistic forecast using MMAF-guided learning Conformal Policy Control The Implicit Curriculum: Learning Dynamics in RL with Verifiable Rewards Probabilistic NDVI Forecasting from Sparse Satellite Time Series and Weather Covariates Constrained Policy Optimization with Cantelli-Bounded Value-at-Risk Factorizable joint shift revisited Feature Learning Dynamics in Infinite-Depth Neural Networks Statistically-Guided Meta-Learning for Cross-Deployment Activity Recognition in Distributed Fiber-Optic Sensing DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions Neural ARFIMA model for forecasting BRIC exchange rates with long memory Neural Stochastic Differential Equations on Compact State Spaces: Theory, Methods, and Application to Suicide Risk Modeling BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization Random Walk Learning and the Pac-Man Attack Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models Post-Training Augmentation Invariance Optimizing LLM Inference: Fluid-Guided Online Scheduling with Memory Constraints Dataset-Driven Channel Masks in Transformers for Multivariate Time Series
Matrix concentration inequalities for time-inhomogeneous Markov chains
Luca Zanetti · 2026-05-23 · via stat updates on arXiv.org

We establish Chernoff-type bounds for the largest eigenvalue of sums of Hermitian random matrices generated by a time-inhomogeneous Markov chain. Our primary regime assumes a compact state space and contractivity of each Markov kernel in Wasserstein distance, i.e., positive Ollivier-Ricci curvature. This assumption is convenient to verify in inhomogeneous settings and is satisfied by several chains of practical interest, such as stochastic gradient descent on strongly convex smooth objectives. We also develop analogous bounds for noncompact state spaces under a notion of spectral gap for inhomogeneous chains introduced by Saloff-Coste and Zuniga. Finally, we illustrate the utility of our results through an analysis of the Elo rating system, a popular method for ranking players in sports analytics, under a dynamic version of the Bradley-Terry-Luce model.