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.
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.
Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque. We address this objective-behavior gap by viewing representation learning as multimode magnetization and deriving, from concrete invariant-learning objectives, a Landau-type effective free energy whose low-order coefficients form objective signatures and induce distinct regularization phenotypes.
arXiv:2606. 17120v1 Announce Type: new Abstract: Deep neural networks (DNNs) exhibit first order phase transitions under variations of the L2 regularization strength, with each transition marking the onset of a new learnable feature.
arXiv:2607. 10285v1 Announce Type: new 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.
arXiv:2608. 01833v1 Announce Type: cross Abstract: Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization.
arXiv:2509. 24882v2 Announce Type: replace Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models.
arXiv:2606. 16013v1 Announce Type: cross Abstract: Interpreting machine-learning models has attracted increasing attention, particularly in the physical sciences, where one often seeks to understand the underlying mechanisms rather than merely make predictions.
arXiv:2604. 00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised.
arXiv:2606. 28242v1 Announce Type: cross Abstract: Understanding how performance scales jointly with model size and data is a central problem in modern machine learning.
arXiv:2607. 04135v1 Announce Type: cross Abstract: The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points.
arXiv:2606. 26128v1 Announce Type: new Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs).
The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points. This phenomenon is all the more surprising given that generalization error diverges when the number of model parameters approaches a critical value from below.