arXiv:2403. 10232v2 Announce Type: replace-cross Abstract: Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
arXiv:2510. 01175v2 Announce Type: replace Abstract: While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited.
arXiv:2505. 21423v3 Announce Type: replace Abstract: The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime.
arXiv:2606. 28662v1 Announce Type: cross Abstract: The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization.
arXiv:2504.16450v4 Announce Type: replace Abstract: We derive a differential equation that governs the evolution of the generalization gap when a model is trained by gradient descent-based methods. T...
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
arXiv:2605. 06938v2 Announce Type: replace-cross Abstract: Recently Brown et al.
The paper investigates how stochastic gradient descent (SGD) selects specific functional decompositions when training a deep linear residual network to learn the identity function. Although many weight configurations minimize the population loss, SGD consistently prefers particular solutions, especially under anisotropic label noise or different parametrizations. The authors explain this bias using an entropic loss term that penalizes the expected squared norm of the minibatch gradient, analytically characterizing its minimizers and showing that trained networks align with these predictions.
The paper introduces a unified matrix‑spectral framework that treats deep neural networks as data‑dependent products of linear operators, enabling the analysis of stability and interpretability through spectral quantities. It defines a Global Matrix Stability Index that aggregates spectral information from Jacobians, parameter gradients, Neural Tangent Kernel operators, and loss Hessians into a single stability scale, and shows that spectral entropy provides a more realistic measure of sensitivity than worst‑case bounds. Experiments on MNIST, CIFAR‑10, and CIFAR‑100 demonstrate that modest spectral regularization can significantly improve attribution stability without large changes to global spectral summaries.
arXiv:2607. 12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization.