{"slug": "randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos", "title": "Randomly initialized autoencoders: fixed points and edge-of-chaos", "summary": "A new arXiv preprint (2608.14638v1) introduces local and global edge-of-chaos (EoC) definitions for randomly initialized autoencoders, using random matrix theory spectral techniques and the Sudakov-Fernique inequality to analyze fixed-point stability and perturbation responses. The authors show that initialization at the critical EoC regime offers stability advantages for autoencoders, extending prior mean-field EoC results to this network class.", "body_md": "arXiv:2608.14638v1 Announce Type: new\nAbstract: 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.\nEdge-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.\nThe 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.", "url": "https://wpnews.pro/news/randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos", "canonical_source": "https://arxiv.org/abs/2608.14638", "published_at": "2026-08-18 04:00:00+00:00", "updated_at": "2026-08-18 04:12:49.556047+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research"], "entities": ["arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos", "markdown": "https://wpnews.pro/news/randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos.md", "text": "https://wpnews.pro/news/randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos.txt", "jsonld": "https://wpnews.pro/news/randomly-initialized-autoencoders-fixed-points-and-edge-of-chaos.jsonld"}}