In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Q: First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the pro- hibitive computational cost in calculating the second-order information. In this paper, we propose a novel Gram-Gauss-Newton (GGN) algorithm to train deep neural networks for regression problems with square loss. Our method draws inspiration from the connection between neural network optimization and kernel regression of neural tangent kernel (NTK). Different from typical second-order methods that have heavy computational cost in each iteration, GGN only has minor overhead compared to first-order methods such as SGD. We also give theoretical results to show that for sufficiently wide neural networks, the convergence rate of GGN is quadratic. Furthermore, we provide convergence guarantee for mini-batch GGN algorithm, which is, to our knowledge, the first convergence result for the mini-batch version of a second-order method on overparameterized neural net- works. Preliminary experiments on regression tasks demonstrate that for training standard networks, our GGN algorithm converges much faster and achieves better performance than SGD.

A: A novel Gram-Gauss-Newton method to train neural networks, inspired by neural tangent kernel and Gauss-Newton method, with fast convergence speed both theoretically and experimentally.
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Q: Uncertainty estimation and ensembling methods go hand-in-hand. Uncertainty estimation is one of the main benchmarks for assessment of ensembling performance. At the same time, deep learning ensembles have provided state-of-the-art results in uncertainty estimation. In this work, we focus on in-domain uncertainty for image classification. We explore the standards for its quantification and point out pitfalls of existing metrics. Avoiding these pitfalls, we perform a broad study of different ensembling techniques. To provide more insight in the broad comparison, we introduce the deep ensemble equivalent (DEE) and show that many sophisticated ensembling techniques are equivalent to an ensemble of very few independently trained networks in terms of the test log-likelihood.

A: We highlight the problems with common metrics of in-domain uncertainty and perform a broad study of modern ensembling techniques.
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Q: In order to mimic the human ability of continual acquisition and transfer of knowledge across various tasks, a learning system needs the capability for life-long learning, effectively utilizing the previously acquired skills. As such, the key challenge is to transfer and generalize the knowledge learned from one task to other tasks, avoiding interference from previous knowledge and improving the overall performance. In this paper, within the continual learning paradigm, we introduce a method that effectively forgets the less useful data samples continuously across different tasks. The method uses statistical leverage score information to measure the importance of the data samples in every task and adopts frequent directions approach to enable a life-long learning property. This effectively maintains a constant training size across all tasks. We first provide some mathematical intuition for the method and then demonstrate its effectiveness with experiments on variants of MNIST and CIFAR100 datasets.

A:
A new method uses statistical leverage score information to measure the importance of the data samples in every task and adopts frequent directions approach to enable a life-long learning property.
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