aiqbench analysis
This research advances theoretical learning theory by extending entropy flow methods to a broader class of Markov processes beyond specific noise structures like Langevin dynamics. By deriving exact entropy flow formulas for time-homogeneous Markov algorithms, the work establishes new connections between generalization error and the ergodic properties of these processes. The resulting framework provides more rigorous generalization bounds applicable to discrete-time settings and various concrete learning algorithms.
Generalization Bounds for Markov Algorithms through Entropy Flow Computations
arXiv:2502.07584v3 Announce Type: replace-cross Abstract: Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on information-theoretic tools and the so-called ``entropy flow'' method. This technique is compatible with a broad range of assumptions and leverages the convergence properties of learning dynamics to produce meaningful generalization bounds, which can also be informative or extend to discrete-time settings. Despite their success, existing entropy flow formulations are limited to specific noise and algorithm structures (\eg, Langevin dynamics). In this work, we exploit new technical tools to extend its applicability to all learning algorithms whose iterative dynamics is governed by a time-homogeneous Markov process. Our approach builds on a principled continuous-time approximation of Markov algorithms and introduces a new, exact entropy flow formula for such processes. Within this unified framework, we establish novel connections to a well-studied family of modified logarithmic Sobolev inequalities, which we use to connect the generalization error to the ergodic properties of Markov processes. Finally, we provide a detailed analysis of all the terms appearing in our theory and demonstrate its effectiveness by deriving new generalization bounds for several concrete algorithms.
Abstract:Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on information-theoretic tools and the so-called ``entropy flow'' method. This technique is compatible with a broad range of assumptions and leverages the convergence properties of learning dynamics to produce meaningful generalization bounds, which can also be informative or extend to discrete-time settings. Despite their success, existing entropy flow formulations are limited to specific noise and algorithm structures (\eg, Langevin dynamics). In this work, we exploit new technical tools to extend its applicability to all learning algorithms whose iterative dynamics is governed by a time-homogeneous Markov process. Our approach builds on a principled continuous-time approximation of Markov algorithms and introduces a new, exact entropy flow formula for such processes. Within this unified framework, we establish novel connections to a well-studied family of modified logarithmic Sobolev inequalities, which we use to connect the generalization error to the ergodic properties of Markov processes. Finally, we provide a detailed analysis of all the terms appearing in our theory and demonstrate its effectiveness by deriving new generalization bounds for several concrete algorithms.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2502.07584 [stat.ML]
(or arXiv:2502.07584v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2502.07584 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 293 words
Related coverage
Koopman Theory and Metaethics
LessWrong · Sep 19, 2026
Exploding variance of means of exponentials: least-squares to the rescue – Machine Learning Research Blog
francisbach.com · Sep 27, 2026
A brief history of quantum vs classical computational advantage
Quantum Journal · Sep 1, 2026
How can LLM RL Work Despite Information-Theoretic Inefficiency
LessWrong · Oct 16, 2026