Related papers: On the Maximum Hessian Eigenvalue and Generalizati…
Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more…
Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…
When several models have similar training scores, classical model selection heuristics follow Occam's razor and advise choosing the ones with least capacity. Yet, modern practice with large neural networks has often led to situations where…
Batch normalization is currently the most widely used variant of internal normalization for deep neural networks. Additional work has shown that the normalization of weights and additional conditioning as well as the normalization of…
Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have…
Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization…
Classical analyses of gradient descent (GD) define a stability threshold based on the largest eigenvalue of the loss Hessian, often termed sharpness. When the learning rate lies below this threshold, training is stable and the loss…
Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization…
Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of…
Sharpness-Aware Minimization (SAM) aims to improve generalization by minimizing a worst-case perturbed loss over a small neighborhood of model parameters. However, during training, its optimization behavior does not always align with…
Neural networks that land in flat regions of the loss landscape tend to generalise better than those in sharp regions. Sharpness-Aware Minimisation exploits this to improve generalisation. But function-preserving reparameterisation can…
Can modifying the training data distribution guide optimizers toward solutions with improved generalization when training large language models (LLMs)? In this work, we theoretically analyze an in-context linear regression model with…
Recent findings by Cohen et al., 2021, demonstrate that when training neural networks using full-batch gradient descent with a step size of $\eta$, the largest eigenvalue $\lambda_{\max}$ of the full-batch Hessian consistently stabilizes…
We conjecture that the inherent difference in generalisation between adaptive and non-adaptive gradient methods in deep learning stems from the increased estimation noise in the flattest directions of the true loss surface. We demonstrate…
Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM's…
We propose \emph{MaxUp}, an embarrassingly simple, highly effective technique for improving the generalization performance of machine learning models, especially deep neural networks. The idea is to generate a set of augmented data with…
Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss within a fixed parameter-space radius neighborhood. SAM and its variants mainly rely on a first-order linearized surrogate, while flat minima are…
The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…
Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions…
A key component of most neural network architectures is the use of normalization layers, such as Batch Normalization. Despite its common use and large utility in optimizing deep architectures, it has been challenging both to generically…