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.

The machine learning and computer vision community is witnessing an unprecedented rate of new tasks being proposed and addressed, thanks to the power of deep convolutional networks to find complex mappings from X to Y. The advent of each task often accompanies the release of a large-scale human-labeled dataset, for supervised training of the deep network. However, it is expensive and time-consuming to manually label sufficient amount of training data. Therefore, it is important to develop algorithms that can leverage off-the-shelf labeled dataset to learn useful knowledge for the target task. While previous works mostly focus on transfer learning from a single source, we study multi-source transfer across domains and tasks (MS-DTT), in a semi-supervised setting. We propose GradMix, a model-agnostic method applicable to any model trained with gradient-based learning rule. GradMix transfers knowledge via gradient descent, by weighting and mixing the gradients from all sources during training. Our method follows a meta-learning objective, by assigning layer-wise weights to the source gradients, such that the combined gradient follows the direction that can minimize the loss for a small set of samples from the target dataset. In addition, we propose to adaptively adjust the learning rate for each mini-batch based on its importance to the target task, and a pseudo-labeling method to leverage the unlabeled samples in the target domain. We perform experiments on two MS-DTT tasks: digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method against multiple baselines.
We propose a gradient-based method to transfer knowledge from multiple sources across different domains and tasks.

We extend the recent results of (Arora et al., 2019) by a spectral analysis of representations corresponding to kernel and neural embeddings. They showed that in a simple single layer network, the alignment of the labels to the eigenvectors of the corresponding Gram matrix determines both the convergence of the optimization during training as well as the generalization properties. We generalize their result to kernel and neural representations and show that these extensions improve both optimization and generalization of the basic setup studied in (Arora et al., 2019).
Spectral analysis for understanding how different representations can improve optimization and generalization.

In this paper, we propose a novel technique for improving the stochastic gradient descent (SGD) method to train deep networks, which we term \emph{PowerSGD}. The proposed PowerSGD method simply raises the stochastic gradient to a certain power $\gamma\in[0,1]$ during iterations and introduces only one additional parameter, namely, the power exponent $\gamma$ (when $\gamma=1$, PowerSGD reduces to SGD). We further propose PowerSGD with momentum, which we term \emph{PowerSGDM}, and provide convergence rate analysis on both PowerSGD and PowerSGDM methods. Experiments are conducted on popular deep learning models and benchmark datasets. Empirical results show that the proposed PowerSGD and PowerSGDM obtain faster initial training speed than adaptive gradient methods,  comparable generalization ability with SGD, and improved robustness to hyper-parameter selection and vanishing gradients. PowerSGD is essentially a gradient modifier via a nonlinear transformation. As such, it is orthogonal and complementary to other techniques for accelerating gradient-based optimization.

We propose a new class of optimizers for accelerated non-convex optimization via a nonlinear gradient transformation.