Hessian Aware Low-Rank Weight Perturbation for Continual Learning

Continual learning aims to learn a series of tasks sequentially without forgetting the knowledge acquired from the previous ones. In this work, we propose the Hessian Aware Low-Rank Perturbation algorithm for continual learning. By modeling the parameter transitions along the sequential tasks with the weight matrix transformation, we propose to apply the low-rank approximation on the task-adaptive parameters in each layer of the neural networks. Specifically, we theoretically demonstrate the quantitative relationship between the Hessian and the proposed low-rank approximation. The approximation ranks are then globally determined according to the marginal increment of the empirical loss estimated by the layer-specific gradient and low-rank approximation error. Furthermore, we control the model capacity by pruning less important parameters to diminish the parameter growth. We conduct extensive experiments on various benchmarks, including a dataset with large-scale tasks, and compare our method against some recent state-of-the-art methods to demonstrate the effectiveness and scalability of our proposed method. Empirical results show that our method performs better on different benchmarks, especially in achieving task order robustness and handling the forgetting issue. A demo code can be found at https://github.com/lijiaqi/HALRP.

Ensemble Quantile Classifier

Both the median-based classifier and the quantile-based classifier are useful for discriminating high-dimensional data with heavy-tailed or skewed inputs. But these methods are restricted as they assign equal weight to each variable in an unregularized way. The ensemble quantile classifier is a more flexible regularized classifier that provides better performance with high-dimensional data, asymmetric data or when there are many irrelevant extraneous inputs. The improved performance is demonstrated by a simulation study as well as an application to text categorization. It is proven that the estimated parameters of the ensemble quantile classifier consistently estimate the minimal population loss under suitable general model assumptions. It is also shown that the ensemble quantile classifier is Bayes optimal under suitable assumptions with asymmetric Laplace distribution inputs.