Related papers: BN-invariant sharpness regularizes the training mo…

Curvature influences generalization, robustness, and how reliably neural networks respond to small input perturbations. Existing sharpness metrics are typically defined in parameter space (e.g., Hessian eigenvalues) and can be expensive,…

Explaining generalizations and preventing over-confident predictions are central goals of studies on the loss landscape of neural networks. Flatness, defined as loss invariability on perturbations of a pre-trained solution, is widely…

We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to…

Sharpness-aware minimization (SAM) improves generalization of various deep learning tasks. Motivated by popular architectures such as LoRA, we explore the implicit regularization of SAM for scale-invariant problems involving two groups of…

Inspired by two basic mechanisms in animal visual systems, we introduce a feature transform technique that imposes invariance properties in the training of deep neural networks. The resulting algorithm requires less parameter tuning, trains…

Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN…

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…

The largest eigenvalue of the Hessian, or sharpness, of neural networks is a key quantity to understand their optimization dynamics. In this paper, we study the sharpness of deep linear networks for univariate regression. Minimizers can…

How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

In this paper, we propose a generalization of the Batch Normalization (BN) algorithm, diminishing batch normalization (DBN), where we update the BN parameters in a diminishing moving average way. BN is very effective in accelerating the…

Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a…

Deep Neural Networks (DNNs) have begun to thrive in the field of automation systems, owing to the recent advancements in standardising various aspects such as architecture, optimization techniques, and regularization. In this paper, we take…

In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However,…

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…

Hessian based measures of flatness, such as the trace, Frobenius and spectral norms, have been argued, used and shown to relate to generalisation. In this paper we demonstrate that for feed forward neural networks under the cross entropy…

Batch Normalization (BN) has become an essential technique in contemporary neural network design, enhancing training stability. Specifically, BN employs centering and scaling operations to standardize features along the batch dimension and…

As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However,…

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) is a highly effective regularization technique for improving the generalization of deep neural networks for various settings. However, the underlying working of SAM remains elusive because of various…