As a heuristic for improving test accuracy in classification, the flooding method proposed by Ishida et al. (2020) sets a threshold for the average surrogate loss at training time; above the threshold, gradient descent is run as usual, but below the threshold, a switch to gradient is made. While setting the threshold is non-trivial and is usually done with validation data, this simple technique has proved remarkably effective in terms of accuracy. On the other hand, what if we are also interested in other metrics such as model complexity or average surrogate loss at test time? As an attempt to achieve better overall performance with less fine-tuning, we propose a softened, pointwise mechanism called SoftAD (soft ascent-descent) that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect of flooding, with no additional computational overhead. We contrast formal stationarity guarantees with those for flooding, and empirically demonstrate how SoftAD can realize classification accuracy competitive with flooding (and the more expensive alternative SAM) while enjoying a much smaller loss generalization gap and model norm.

While many such candidates are indeed essentially "optimal"

As a heuristic for improving test accuracy in classification, the "flooding" method proposed by Ishida et al. (2020) sets a threshold for the average surrogate loss at training time; above the threshold, gradient descent is run as usual, but below the threshold, a switch to gradient ascent is made. While setting the threshold is non-trivial and is usually done with validation data, this simple technique has proved remarkably effective in terms of accuracy. On the other hand, what if we are also interested in other metrics such as model complexity or average surrogate loss at test time? As an attempt to achieve better overall performance with less fine-tuning, we propose a softened, pointwise mechanism called SoftAD (soft ascent-descent) that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect of flooding, with no additional computational overhead. We contrast formal stationarity guarantees with those for flooding, and empirically demonstrate how SoftAD can realize classification accuracy competitive with flooding (and the more expensive alternative SAM) while enjoying a much smaller loss generalization gap and model norm.

As models grow larger and more complex, achieving better off-sample generalization with minimal trial-and-error is critical to the reliability and economy of machine learning workflows. As a proxy for the well-studied heuristic of seeking "flat" local minima, gradient regularization is a natural avenue, and first-order approximations such as Flooding and sharpness-aware minimization (SAM) have received significant attention, but their performance depends critically on hyperparameters (flood threshold and neighborhood radius, respectively) that are non-trivial to specify in advance. In order to develop a procedure which is more resilient to misspecified hyperparameters, with the hard-threshold "ascent-descent" switching device used in Flooding as motivation, we propose a softened, pointwise mechanism called SoftAD that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect. We contrast formal stationarity guarantees with those for Flooding, and empirically demonstrate how SoftAD can realize classification accuracy competitive with SAM and Flooding while maintaining a much smaller loss generalization gap and model norm. Our empirical tests range from simple binary classification on the plane to image classification using neural networks with millions of parameters; the key trends are observed across all datasets and models studied, and suggest a potential new approach to implicit regularization.