Generalization Bounds for Markov Algorithms through Entropy Flow Computations
Benjamin DupuisMaxime HaddoucheGeorge DeligiannidisUmut Simsekli
Sep 2026
Machine LearningData Science
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.
Agile - denoting "the quality of being agile, readiness for motion, nimbleness, activity, dexterity in motion" - software development methods are attempting to offer an answer to the eager business community asking for lighter weight along with faster and nimbler software development processes. This is especially the case with the rapidly growing and volatile Internet software industry as well as for the emerging mobile application environment. The new agile methods have evoked substantial amount of literature and debates. However, academic research on the subject is still scarce, as most of existing publications are written by practitioners or consultants. The aim of this publication is to begin filling this gap by systematically reviewing the existing literature on agile software development methodologies. This publication has three purposes. First, it proposes a definition and a classification of agile software development approaches. Second, it analyses ten software development methods that can be characterized as being "agile" against the defined criterion. Third, it compares these methods and highlights their similarities and differences. Based on this analysis, future research needs are identified and discussed.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 728 citations· ⚡54
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
