TASK DEFINITION: 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.
PROBLEM: The allocation of computation resources in the backbone is a crucial issue in object detection. However, classification allocation pattern is usually adopted directly to object detector, which is proved to be sub-optimal. In order to reallocate the engaged computation resources in a more efficient way, we present CR-NAS (Computation Reallocation Neural Architecture Search) that can learn computation reallocation strategies across different feature resolution and spatial position diectly on the target detection dataset. A two-level reallocation space is proposed for both stage and spatial reallocation. A novel hierarchical search procedure is adopted to cope with the complex search space. We apply CR-NAS to multiple backbones and achieve consistent improvements. Our CR-ResNet50 and CR-MobileNetV2 outperforms the baseline by 1.9% and 1.7% COCO AP respectively without any additional computation budget. The models discovered by CR-NAS can be equiped to other powerful detection neck/head and be easily transferred to other dataset, e.g. PASCAL VOC, and other vision tasks, e.g. instance segmentation. Our CR-NAS can be used as a plugin to improve the performance of various networks, which is demanding.

SOLUTION: We propose CR-NAS to reallocate engaged  computation resources in different resolution and spatial position.

PROBLEM: Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further. 

 We present methods for training on small domains, while applying the trained models on larger domains, with consistency constraints ensuring the solutions are physically meaningful even at the boundary of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.

SOLUTION: We present RNNs for training surrogate models of PDEs, wherein consistency constraints ensure the solutions are physically meaningful, even when the training uses much smaller domains than the trained model is applied to.

PROBLEM: Neural networks have reached outstanding performance for solving various ill-posed inverse problems in imaging. However, drawbacks of end-to-end learning approaches in comparison to classical variational methods are the requirement of expensive retraining for even slightly different problem statements and the lack of provable error bounds during inference. Recent works tackled the first problem by using networks trained for Gaussian image denoising as generic plug-and-play regularizers in energy minimization algorithms. Even though this obtains state-of-the-art results on many tasks, heavy restrictions on the network architecture have to be made if provable convergence of the underlying fixed point iteration is a requirement. More recent work has proposed to train networks to output descent directions with respect to a given energy function with a provable guarantee of convergence to a minimizer of that energy. However, each problem and energy requires the training of a separate network.
 In this paper we consider the combination of both approaches by projecting the outputs of a plug-and-play denoising network onto the cone of descent directions to a given energy. This way, a single pre-trained network can be used for a wide variety of reconstruction tasks. Our results show improvements compared to classical energy minimization methods while still having provable convergence guarantees.

SOLUTION:
We use neural networks trained for image denoising as plug-and-play priors in energy minimization algorithms for image reconstruction problems with provable convergence.