arXiv Machine Learning

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

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

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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

arXiv Machine Learning

Jun 4

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

arXiv:2606. 04623v1 Announce Type: new Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds.

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

rag

arXiv Machine Learning

Jul 7

CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems

arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.

By Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

safety

arXiv Machine Learning

Sep 1

Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction

arXiv:2608.29867v1 Announce Type: new Abstract: Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear enc...

By Louen Pottier, Louis Lesueur, Anders Thorin

safety

arXiv Machine Learning

Aug 11

From Objectives to What Models Learn: A Landau Theory of Invariant Learning

arXiv:2608. 09396v1 Announce Type: new Abstract: Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque.

By Pinli Wang, Yue He, Peng Cui

arXiv Machine Learning

Jun 30

I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory

arXiv:2606. 29675v1 Announce Type: new Abstract: Bogomolny, Bohigas and Schmit (BBS) found that the spectrum of the pairwise distance matrix on N points sampled from a smooth d-dimensional manifold encodes a signature of the underlying geometry.

By Igor Halperin

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arXiv Machine Learning

Jul 8

Physics-Informed Neural Embeddings of PDE Solution Families

arXiv:2607. 06348v1 Announce Type: new Abstract: We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations.

By Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas, Leonid Sarieddine, David N. Spergel, Pedro Taranc\'on-\'Alvarez

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