arXiv:2609. 15047v1 Announce Type: new Abstract: Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/\lambda$ in the weight decay.
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:2607. 23777v1 Announce Type: cross Abstract: The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data.
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2601. 19791v4 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting.
arXiv:2606. 04405v1 Announce Type: cross Abstract: Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes.
arXiv:2608. 07436v1 Announce Type: new Abstract: Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head.
The paper investigates fixed‑design random feature ridge regression beyond the mean‑kernel approximation, focusing on how the predictor’s nonlinear dependence on the empirical kernel affects training error, test error, and the conditional generalization gap. By deriving covariance‑level (one‑loop) corrections via a finite resolvent identity, the authors avoid an almost‑sure Neumann‑series assumption and provide explicit remainder bounds for training error. Numerical experiments demonstrate that including mixed train–test covariance tensors is essential for accurate test error predictions and reveal a width–regularization boundary where second‑order truncation becomes unreliable.
The study investigates the delayed transition from memorization to generalization—known as grokking—in two‑hidden‑layer MLPs trained on modular arithmetic. By exploring 384 hyperparameter configurations, the authors derive a power‑law scaling relation for the onset time of generalization, showing that data complexity dominates over model capacity. A clear phase boundary at weight decay around 1.0 separates grokking from non‑grokking regimes, and weight norm trajectories indicate implicit regularization during the transition.
The paper introduces a neighboring early‑stopping rule for adaptive regularization in kernel ridge regression with random features (KRR‑RF). By using a uniform grid in inverse regularization and comparing only adjacent estimators, the method reduces discrepancy checks and can be computed directly in the random‑feature space without forming the full kernel Gram matrix. Under standard source and capacity assumptions, the selected estimator achieves the oracle polynomial learning rate up to logarithmic factors, enabling regularization selection without prior knowledge of smoothness or capacity exponents.
arXiv:2607. 12735v1 Announce Type: new Abstract: Companion work showed the grokking delay is causally the time to form task-structured representations, injectable via a contrastive prior.
arXiv:2607. 06639v1 Announce Type: cross Abstract: On modular arithmetic, a network's embedding keeps compressing for tens of thousands of steps after it has already generalized.
The paper extends prior work on volume sampling by providing a Loewner envelope for the centered coefficient covariance in least‑squares regression with a fixed pool of features and responses. It characterizes when this envelope is tight, linking tightness to strict spectral properties of residuals, and introduces a residual‑augmented change of measure to derive a one‑sided slack bound. The results also offer geometric insights at the boundary and demonstrate non‑vacuous certificates through frozen‑feature examples, focusing on conditional centered, full‑Gram‑whitened covariance rather than population generalization.