Related papers: A Scale Invariant Flatness Measure for Deep Networ…
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…
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…
Recent literature generalization in deep learning has examined the relationship between the curvature of the loss function at minima and generalization, mainly in the context of overparameterized neural networks. A key observation is that…
Toward achieving robust and defensive neural networks, the robustness against the weight parameters perturbations, i.e., sharpness, attracts attention in recent years (Sun et al., 2020). However, sharpness is known to remain a critical…
The performance of deep neural networks is often attributed to their automated, task-related feature construction. It remains an open question, though, why this leads to solutions with good generalization, even in cases where the number of…
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss…
It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a $\delta$ ball of parameters around…
It is well known that (stochastic) gradient descent has an implicit bias towards flat minima. In deep neural network training, this mechanism serves to screen out minima. However, the precise effect that this has on the trained network is…
The notion of flat minima has played a key role in the generalization studies of deep learning models. However, existing definitions of the flatness are known to be sensitive to the rescaling of parameters. The issue suggests that the…
The intuition that local flatness of the loss landscape is correlated with better generalization for deep neural networks (DNNs) has been explored for decades, spawning many different flatness measures. Recently, this link with…
Recent works on over-parameterized neural networks have shown that the stochasticity in optimizers has the implicit regularization effect of minimizing the sharpness of the loss function (in particular, the trace of its Hessian) over the…
Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of…
Flatness measures based on the spectrum or the trace of the Hessian of the loss are widely used as proxies for the generalization ability of deep networks. However, most existing definitions are either tailored to fully connected…
We analyze the training dynamics for deep linear networks using a new metric - layer imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data…
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…
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…
Recent works have highlighted scale invariance or symmetry present in the weight space of a typical deep network and the adverse effect it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show…
The concept of sharpness has been successfully applied to traditional architectures like MLPs and CNNs to predict their generalization. For transformers, however, recent work reported weak correlation between flatness and generalization. We…
The remarkable generalization ability of neural networks is usually attributed to the implicit bias of SGD, which often yields models with lower complexity using simpler (e.g. linear) and low-rank features. Recent works have provided…
Empirical evidence suggests that for a variety of overparameterized nonlinear models, most notably in neural network training, the growth of the loss around a minimizer strongly impacts its performance. Flat minima -- those around which the…