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: Supervised deep learning requires a large amount of training samples with annotations (e.g. label class for classification task, pixel- or voxel-wised label map for segmentation tasks), which are expensive and time-consuming to obtain. During the training of a deep neural network, the annotated samples are fed into the network in a mini-batch way, where they are often regarded of equal importance. However, some of the samples may become less informative during training, as the magnitude of the gradient start to vanish for these samples. In the meantime, other samples of higher utility or hardness may be more demanded for the training process to proceed and require more exploitation. To address the challenges of expensive annotations and loss of sample informativeness, here we propose a novel training framework which adaptively selects informative samples that are fed to the training process. The adaptive selection or sampling is performed based on a hardness-aware strategy in the latent space constructed by a generative model. To evaluate the proposed training framework, we perform experiments on three different datasets, including MNIST and CIFAR-10 for image classification task and a medical image dataset IVUS for biophysical simulation task. On all three datasets, the proposed framework outperforms a random sampling method, which demonstrates the effectiveness of our framework.

A: This paper introduces a framework for data-efficient representation learning by adaptive sampling in latent space.
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Q: Training methods for deep networks are primarily variants on stochastic gradient descent.   Techniques that use (approximate) second-order information are rarely used because of the computational cost and noise associated with those approaches in deep learning contexts.   However, in this paper, we show how feedforward deep networks exhibit a low-rank derivative structure.   This low-rank structure makes it possible to use second-order information without needing approximations and without incurring a significantly greater computational cost than gradient descent.   To demonstrate this capability, we implement Cubic Regularization (CR) on a feedforward deep network with stochastic gradient descent and two of its variants.   There, we use CR to calculate learning rates on a per-iteration basis while training on the MNIST and CIFAR-10 datasets.   CR proved particularly successful in escaping plateau regions of the objective function.   We also found that this approach requires less problem-specific information (e.g. an optimal initial learning rate) than other first-order methods in order to perform well.

A: We show that deep learning network derivatives have a low-rank structure, and this structure allows us to use second-order derivative information to calculate learning rates adaptively and in a computationally feasible manner.
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Q: The backpropagation algorithm is the de-facto standard for credit assignment in artificial neural networks due to its empirical results. Since its conception, variants of the backpropagation algorithm have emerged. More specifically, variants that leverage function changes in the backpropagation equations to satisfy their specific requirements. Feedback Alignment is one such example, which replaces the weight transpose matrix in the backpropagation equations with a random matrix in search of a more biologically plausible credit assignment algorithm. In this work, we show that function changes in the  backpropagation procedure is equivalent to adding an implicit learning rate to an artificial neural network. Furthermore, we learn activation function derivatives in the backpropagation equations to demonstrate early convergence in these artificial neural networks. Our work reports competitive performances with early convergence on MNIST and CIFAR10 on sufficiently large deep neural network architectures.

A:
We demonstrate that function changes in the backpropagation is equivalent to an implicit learning rate
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