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.

[EX Q]: Understanding the optimization trajectory is critical to understand training of deep neural networks. We show how the hyperparameters of stochastic gradient descent influence the covariance of the gradients (K) and the Hessian of the training loss (H) along this trajectory. Based on a theoretical model, we predict that using a high learning rate or a small batch size in the early phase of training leads SGD to regions of the parameter space with (1) reduced spectral norm of K, and (2) improved conditioning of K and H. We show that the point on the trajectory after which these effects hold, which we refer to as the break-even point, is reached early during training. We demonstrate these effects empirically for a range of deep neural networks applied to multiple different tasks. Finally, we apply our analysis to networks with batch normalization (BN) layers and find that it is necessary to use a high learning rate to achieve loss smoothing effects attributed previously to BN alone.
[EX A]: In the early phase of training of deep neural networks there exists a "break-even point" which determines properties of the entire optimization trajectory.

[EX Q]: We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the model parameters with respect to a task-specific loss given an input sample. Our key innovation is the design of a linear model that incorporates both gradient features and the activation of the network. We show that our model provides a local linear approximation to a underlying deep model, and discuss important theoretical insight. Moreover, we present an efficient algorithm for the training and inference of our model without computing the actual gradients. Our method is evaluated across a number of representation learning tasks on several datasets and using different network architectures. We demonstrate strong results in all settings. And our results are well-aligned with our theoretical insight.
[EX A]: Given a pre-trained model, we explored the per-sample gradients of the model parameters relative to a task-specific loss, and constructed a linear model that combines gradients of model parameters and the activation of the model.

[EX Q]: We apply multi-task learning to image classification tasks on MNIST-like datasets. MNIST dataset has been referred to as the {\em drosophila} of machine learning and has been the testbed of many learning theories. The NotMNIST dataset and the FashionMNIST dataset have been created with the MNIST dataset as reference. In this work, we exploit these MNIST-like datasets for multi-task learning. The datasets are pooled together for learning the parameters of joint classification networks. Then the learned parameters are used as the initial parameters to retrain disjoint classification networks. The baseline recognition model are all-convolution neural networks. Without multi-task learning, the recognition accuracies for MNIST, NotMNIST and FashionMNIST are 99.56\%, 97.22\% and 94.32\% respectively. With multi-task learning to pre-train the networks, the recognition accuracies are respectively 99.70\%, 97.46\% and 95.25\%. The results re-affirm that multi-task learning framework, even with data with different genres, does lead to significant improvement.

[EX A]:
multi-task learning works