Autoencoder Stability Explored Through Fixed Points and Edge-of-Chaos

Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo, Victor Slavin, Sasha Sodin· August 18, 2026 View original

Key takeaways

  • Autoencoder performance is linked to the existence and stability of their fixed points.
  • The "edge-of-chaos" concept is crucial for understanding network stability.
  • Local and global EoC are introduced for autoencoders to manage input perturbations.
  • Random Matrix Theory provides tools for analyzing autoencoder stability.

Who benefits

AI/ML DevelopmentSoftware EngineeringResearch & DevelopmentData Science

Summary

This paper investigates the performance of autoencoders by analyzing their fixed points and their relation to the "edge-of-chaos" concept, which describes the critical regime for stable signal propagation in neural networks. The study introduces local and global edge-of-chaos for autoencoders, using techniques from Random Matrix Theory.

This research delves into the fundamental properties of autoencoders, a specific class of deep neural networks, by examining their fixed points. The existence, stability, and basins of attraction of these fixed points are crucial for understanding autoencoder performance and are intrinsically linked to the concept of "edge-of-chaos." The "edge-of-chaos" (EoC) is a critical regime in neural network theory, separating ordered from chaotic signal propagation in randomly initialized networks. Operating near this regime offers benefits like network stability against input perturbations. This paper adapts the EoC notion specifically for autoencoders, introducing local and global EoC to control small and arbitrary input perturbations, respectively. The stability analysis of autoencoders is approached through the lens of nonlinear problems in Random Matrix Theory (RMT). Local EoC is studied using spectral RMT techniques, while global EoC is investigated via the Sudakov-Fernique inequality for Gaussian processes, providing a deeper theoretical understanding of autoencoder behavior.

Why it matters

Understanding the theoretical underpinnings of autoencoders, particularly their stability and initialization, can lead to more robust and efficient deep learning models, improving their reliability in various applications.

How to implement this in your domain

  1. 1Review initialization strategies for autoencoders in your deep learning projects.
  2. 2Consider the implications of "edge-of-chaos" for network stability when designing new architectures.
  3. 3Explore how theoretical insights from Random Matrix Theory can inform practical model development.
  4. 4Implement regularization techniques that promote stable fixed points in autoencoder training.

Original post by Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo, Victor Slavin, Sasha Sodin

"arXiv:2608.14638v1 Announce Type: new 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 attrac…"

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Originally posted by Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo, Victor Slavin, Sasha Sodin on X · view source

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