Randomly initialized autoencoders: fixed points and edge-of-chaos

[2608.14638] Randomly initialized autoencoders: fixed points and edge-of-chaos Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14638 (cs) [Submitted on 28 Jul 2026] Title: Randomly initialized autoencoders: fixed points and edge-of-chaos Authors: Leonid Berlyand , Roman Sarapin , Yitzchak Shmalo , Victor Slavin , Sasha Sodin View a PDF of the paper titled Randomly initialized autoencoders: fixed points and edge-of-chaos, by Leonid Berlyand and 4 other authors View PDF HTML (experimental) Abstract: In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points. This perspective naturally raises questions of existence, stability, and basins of attraction of these fixed points. These questions are addressed via the contractive properties of autoencoders, and are closely related to the notion of edge-of-chaos. Edge-of-chaos (EoC) is an important notion in the theory of DNNs. It describes the critical regime separating ordered and chaotic signal propagation through a randomly initialized network. Initialization at or near this critical regime offers several theoretical and practical advantages, including stability of the network w.r.t. perturbations of the input. EoC was previously introduced for broad classes of neural networks using mean-field averaging methods. In this paper we modify the notion of EoC for the study of autoencoders. Specifically, we introduce local and global EoC for autoencoders that control local (small) and global (arbitrary) perturbations of the input respectively. The study of stability of autoencoders falls within the scope of nonlinear problems in Random Matrix Theory (RMT). Our analysis of local EoC is based on spectral techniques of RMT, whereas global EoC is studied by employing Sudakov-Fernique inequality for Gaussian processes. Comments: 23 pages, 1 figure Subjects: Machine Learning (cs.LG) ; Probability (math.PR); Statistics Theory (math.ST) MSC classes: 60B20, 15B52 Cite as: arXiv:2608.14638 [cs.LG] (or arXiv:2608.14638v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14638 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Roman Sarapin [ view email ] [v1] Tue, 28 Jul 2026 13:58:14 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Randomly initialized autoencoders: fixed points and edge-of-chaos, by Leonid Berlyand and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs math math.PR math.ST stat stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators 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 . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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