arXiv Machine Learning June 30, 2026 By Chanju Park, Dario Bocchi, Francesco D'Amico, Biagio Lucini, Gert Aarts

Spectral phase transitions and trainability in neural network learning dynamics

Read the original on arXiv Machine Learning →

arXiv:2606. 28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

safety

arXiv Machine Learning

Jun 30

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

arXiv:2606. 29679v1 Announce Type: new Abstract: Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \times N$ distance matrix $M(t)$ on a held set of $N$ inputs.

By Igor Halperin

rag

arXiv Machine Learning

Jun 3

Neural Networks Provably Learn Spectral Representations for Group Composition

arXiv:2606. 02993v1 Announce Type: new Abstract: Understanding how structured internal structure emerges during neural network training is central to the study of deep learning.

By Jianliang He, Leda Wang, Fengzhuo Zhang, Siyu Chen, Zhuoran Yang

safety

arXiv Machine Learning

Jun 29

Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models

arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.

By Zhenyu Liao, Michael W. Mahoney

arXiv Machine Learning

Jun 30

Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization

arXiv:2606. 30226v1 Announce Type: new Abstract: Hessian spectral properties are a standard tool in analysing neural-network training, with eigenvalues linked to sharpness, generalization, and optimization dynamics.

By Marcelina Marjankowska, Valerio Modugno, Paolo Barucca

arXiv Machine Learning

Aug 10

Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks

arXiv:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.

By Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner

arXiv Machine Learning

Aug 4

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail

arXiv:2605. 31244v2 Announce Type: replace Abstract: Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance.

By Konstantin Nikolaou, Jonas Scheunemann, Sven Krippendorf, Samuel Tovey, Christian Holm

Related stories

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

Neural Networks Provably Learn Spectral Representations for Group Composition

Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models

Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization

Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail