arXiv Machine Learning September 15, 2026 By Gionni Marchetti

Learning the Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou Trajectories: A Nonlinear Approach using a Deep Autoencoder Model

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arXiv Machine Learning

Jul 22

On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers

arXiv:2607. 18584v1 Announce Type: new Abstract: We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems.

By Sixu Li, Thomas Jacob Maranzatto, Jan Peszek, Trevor Teolis, Semih Akkoc, Konstantin Riedl, Sennur Ulukus, Nicol\'as Garc\'ia Trillos

llms rag

arXiv Machine Learning

Sep 17

Symmetry without a manifold: intrinsic dimension on orbits

arXiv:2609. 17926v1 Announce Type: new Abstract: The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input.

By Chon-Fai Kam, Miloud Bessafi, Fr\'ed\'eric Cadet

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

Jul 3

On the Asymptotics of Self-Supervised Pre-training: Two-Stage M-Estimation and Representation Symmetry

arXiv:2603. 27631v2 Announce Type: replace Abstract: Self-supervised pre-training, where large corpora of unlabeled data are used to learn representations for downstream fine-tuning, has become a cornerstone of modern machine learning.

By Mohammad Tinati, Stephen Tu

fine-tuning

arXiv Machine Learning

Aug 18

Learning symplectic model reduction based on an approximation theorem of symplectic embeddings

arXiv:2606. 04623v2 Announce Type: replace Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds.

By Liyi Feng, Yifa Tang, Yulin Xie, Ruili Zhang, Aiqing Zhu

rag

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

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Related stories

On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers

Symmetry without a manifold: intrinsic dimension on orbits

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

On the Asymptotics of Self-Supervised Pre-training: Two-Stage M-Estimation and Representation Symmetry

Learning symplectic model reduction based on an approximation theorem of symplectic embeddings

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