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 Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc. Prior works have focused on empirical results or pursued a theoretical treatment under overly simplified settings.
arXiv:2605. 29547v2 Announce Type: replace-cross Abstract: Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators.
By Ruoran Xu, Borong She, Xiaobo Jin, Qiufeng Wang
arXiv:2606. 04327v1 Announce Type: cross Abstract: We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions.
By Tian Ding, Dawei Li, Ruoyu Sun
arXiv:2606. 05326v1 Announce Type: cross Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the loss and the sharpness.
By Antonin Chodron de Courcel
AYLA is a loss reparameterization framework that applies a sigmoid‑controlled power‑law transformation to the empirical loss, dynamically adjusting gradient magnitudes without changing stationary points or optimal solutions. By reshaping optimization trajectories, AYLA accelerates descent in flat or saddle‑dominated regions and stabilizes late‑stage training, leading to improved feature recovery in two‑layer tanh networks on synthetic Gaussian data. Experiments show enhanced weight alignment, neuron similarity, activation correlation, and richer internal representations, while mitigating rank collapse and promoting a transition from lazy to active feature‑learning regimes.
By Behnam Gheshlaghi, Shahin Atakishiyev