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:2607. 27000v1 Announce Type: cross Abstract: Optimization in non-convex neural network models is strongly influenced by the geometry of the solution space: sparse, isolated, point-like clusters are typically algorithmically inaccessible, whereas wide and flat regions can be found efficiently despite being relatively rare.
arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.
arXiv:2609.08873v1 Announce Type: cross Abstract: Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over th...
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:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.
arXiv:2607. 15702v1 Announce Type: cross Abstract: We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations.
arXiv:2607. 19390v1 Announce Type: new Abstract: A recent report finds that orthogonalizing the mLSTM memory matrix at read time (five Newton-Schulz iterations, trained through) substantially improves noisy associative recall.
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: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.
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.