Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model

arXiv:2607.10285v2 Announce Type: replace Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process. We quantify learning across multiple spatial (coarse-graining) scales and reveal two distinct dynamical regimes that appear sequentially, controlled by the main hyperparameters (model depth, width, and learning rate): one in which magnetization and another in which energy is learned across scales. The first exhibits error fluctuations ordered to scale and learns global averages only; The second gradually resolves smaller scales relevant for the energy representation. Deep models trained at moderate and fast rates become arrested before reaching these regimes. We connect reconstruction errors with the latent representations using a novel analysis of self-recursive trajectories. These intrinsic dynamics are induced by prediction errors, exposing how training drives representation changes for macroscopic concepts. We utilize the intuition that learning operates as a process driven far from equilibrium by fluctuations from the training data to provide an interpretive basis grounded in both the physical world and the machine models that represent it.

Abstract:We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process. We quantify learning across multiple spatial (coarse-graining) scales and reveal two distinct dynamical regimes that appear sequentially, controlled by the main hyperparameters (model depth, width, and learning rate): one in which magnetization and another in which energy is learned across scales. The first exhibits error fluctuations ordered to scale and learns global averages only; The second gradually resolves smaller scales relevant for the energy representation. Deep models trained at moderate and fast rates become arrested before reaching these regimes. We connect reconstruction errors with the latent representations using a novel analysis of self-recursive trajectories. These intrinsic dynamics are induced by prediction errors, exposing how training drives representation changes for macroscopic concepts. We utilize the intuition that learning operates as a process driven far from equilibrium by fluctuations from the training data to provide an interpretive basis grounded in both the physical world and the machine models that represent it.

Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2607.10285 [cs.LG]

(or arXiv:2607.10285v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.10285 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.

aiqbench analysis

Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model

Related coverage