A common heuristic used to explain the generalization of first-order gradient methods on non-convex neural networks is that "flat interpolators generalize well" (Hochreiter and Schmidhuber, 1994; Keskar et al. , 2017), where flatness can be measured by the trace of the Hessian of the empirical loss.
arXiv:2606. 04429v1 Announce Type: cross Abstract: A common heuristic used to explain the generalization of first-order gradient methods on non-convex neural networks is that "flat interpolators generalize well" (Hochreiter and Schmidhuber, 1994; Keskar et al.
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
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:2609.07755v1 Announce Type: new Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
arXiv:2607. 13631v1 Announce Type: new Abstract: 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.
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.
Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness.
arXiv:2608. 03197v1 Announce Type: new Abstract: Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear.
The paper investigates how the geometry of teacher neural networks affects the learnability of student networks in teacher‑student setups. By formalizing learnability as the success rate of reaching the global minimum, the authors identify two teacher distributions—one maximizing node dissimilarity (easy) and one minimizing it (hard)—that lead to markedly different success rates across various settings and activation functions. They analyze the loss landscape of small networks, revealing two types of suboptimal local minima (out‑of‑bounds and interior) whose attraction regions depend on teacher structure, and demonstrate that adjusting learning rates for the readout layer and inner biases can improve success rates. whyItMatters:"The study highlights that teacher geometry, often overlooked, plays a crucial role in determining how effectively a student network can learn, offering guidance for designing more realistic teacher‑student experiments."
arXiv:2510. 07758v3 Announce Type: replace Abstract: Sharpness (of the loss minima) is widely believed to be a good indicator of generalization of neural networks.
arXiv:2605. 05209v2 Announce Type: replace-cross Abstract: Flat minima are an account of why deep networks generalise.