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:2605. 05209v2 Announce Type: replace-cross Abstract: Flat minima are an account of why deep networks generalise.
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:2608. 03386v1 Announce Type: new Abstract: Contemporary deep learning methods generalize well even when they fit their training data perfectly, a phenomenon known as benign interpolation.
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. 01521v1 Announce Type: new Abstract: A central problem in machine learning is that models can achieve near-perfect training performance while generalizing substantially less well to unseen examples.
arXiv:2202. 08832v3 Announce Type: replace-cross Abstract: We study a general class of optimization problems with decision variable $\boldsymbol{\Theta} \in \mathbb{R}^{p \times k}$ and cost function which is the sum of $n$ terms, each dependent on $\boldsymbol{\Theta}$ through the $k$-dimensional projection $\boldsymbol{\Theta}^\top \boldsymbol{x}_i$, where $\boldsymbol{x}_i$, $i \leq n$ are i.
arXiv:2501. 18530v3 Announce Type: replace-cross Abstract: We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, raising questions about practical identifiability.
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.