arXiv:2601. 10962v2 Announce Type: replace Abstract: Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear.
arXiv:2608.24568v1 Announce Type: cross Abstract: Deep neural networks generalize well despite their highly nonconvex, overparameterized loss landscapes, a phenomenon often associated with the geomet...
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
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:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv:2606. 30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory.
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.
The paper investigates how the local landscape geometry of language model pre‑training evolves, identifying two distinct phases. In Phase I, the landscape starts sharp, causing instability and loss plateaus at high learning rates, which explains the need for learning‑rate warmup and suggests longer warmups for larger peak rates. In Phase II, the geometry is governed by gradient noise scale, revealing a depth‑flatness trade‑off that motivates a dynamic batch‑size scheduler that starts small and grows later in training.
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
arXiv:2606. 18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate.
arXiv:2606. 31282v1 Announce Type: new Abstract: Modern deep neural networks often contain far more parameters than needed to fit their training data, yet they achieve impressive generalization.
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: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.