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.

Input: Consider Input: Learning long-term dependencies is a key long-standing challenge of recurrent neural networks (RNNs). Hierarchical recurrent neural networks (HRNNs) have been considered a promising approach as long-term dependencies are resolved through shortcuts up and down the hierarchy. Yet, the memory requirements of Truncated Backpropagation Through Time (TBPTT) still prevent training them on very long sequences. In this paper, we empirically show that in (deep) HRNNs, propagating gradients back from higher to lower levels can be replaced by locally computable losses, without harming the learning capability of the network, over a wide range of tasks. This decoupling by local losses reduces the memory requirements of training by a factor exponential in the depth of the hierarchy in comparison to standard TBPTT.

Output: We replace some gradients paths in hierarchical RNN's by an auxiliary loss. We show that this can reduce the memory cost while preserving performance.


Input: Consider Input: Designing of search space is a critical problem for neural architecture search (NAS) algorithms. We propose a fine-grained search space comprised of atomic blocks, a minimal search unit much smaller than the ones used in recent NAS algorithms. This search space facilitates direct selection of channel numbers and kernel sizes in convolutions. In addition, we propose a resource-aware architecture search algorithm which dynamically selects atomic blocks during training. The algorithm is further accelerated by a dynamic network shrinkage technique.
 Instead of a  search-and-retrain two-stage paradigm, our method can simultaneously search and train the target architecture in an end-to-end manner. 
 Our method achieves state-of-the-art performance under several FLOPS configurations on ImageNet with a negligible searching cost.
 We open our entire codebase at: https://github.com/meijieru/AtomNAS.

Output: A new state-of-the-art on Imagenet for mobile setting


Input: Consider Input: Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show that even for such activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability. Deep and narrow NNs are encountered in solving partial differential equations with high-order derivatives. We demonstrate this collapse of such NNs both numerically and theoretically, and provide estimates of the probability of collapse. We also construct a diagram of a safe region for designing NNs that avoid the collapse to erroneous states. Finally, we examine different ways of initialization and normalization that may avoid the collapse problem. Asymmetric initializations may reduce the probability of collapse but do not totally eliminate it.


Output: Deep and narrow neural networks will converge to erroneous mean or median states of the target function depending on the loss with high probability.