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
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.
By Ibrahim Talha Ersoy, Karoline Wiesner
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.
By Max Weinmann, Miriam Klopotek
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.
By Lai Shun Chan, Xiaotian Zhang, Yue Shang, Ge Zhang, Entao Yang
The paper presents a spectral theory explaining the phenomenon of grokking, where an initial fit to training data is followed by a delayed improvement in generalization. It shows that for homogeneous networks trained with squared loss and L₂ weight decay, residuals after memorization influence the neural tangent kernel (NTK) dynamics, leading to a transition from lazy to rich learning. The theory predicts that grokking timescales depend on the product of learning rate and weight decay, and that stronger decay can halt fitting, with empirical validation on modular addition tasks using MLPs and Transformers.
By Lenz Pracher, Pascal de Jong, Oskar Lieshaus, Alan Jeffares, Steffen Rulands