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 Input:
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball. We show that this is an effective regularizer; for example, it improves the test error of a deep residual network using batch normalization on CIFAR-10 from 6.2% to 5.3%.

Ex Output:
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation.

Ex Input:
We study the problem of learning and optimizing through physical simulations via differentiable programming. We present DiffSim, a new differentiable programming language tailored for building high-performance differentiable physical simulations. We demonstrate the performance and productivity of our language in gradient-based learning and optimization tasks on 10 different physical simulators. For example, a differentiable elastic object simulator written in our language is 4.6x faster than the hand-engineered CUDA version yet runs as fast, and is 188x faster than TensorFlow. Using our differentiable programs, neural network controllers are typically optimized within only tens of iterations. Finally, we share the lessons learned from our experience developing these simulators, that is, differentiating physical simulators does not always yield useful gradients of the physical system being simulated. We systematically study the underlying reasons and propose solutions to improve gradient quality.

Ex Output:
We study the problem of learning and optimizing through physical simulations via differentiable programming, using our proposed DiffSim programming language and compiler.

Ex Input:
In lifelong learning, the learner is presented with a sequence of tasks, incrementally building a data-driven prior which may be leveraged to speed up learning of a new task. In this work, we investigate the efficiency of current lifelong approaches, in terms of sample complexity, computational and memory cost. Towards this end, we first introduce a new and a more realistic evaluation protocol, whereby learners observe each example only once and hyper-parameter selection is done on a small and disjoint set of tasks, which is not used for the actual learning experience and evaluation. Second, we introduce a new metric measuring how quickly a learner acquires a new skill. Third, we propose an improved version of GEM (Lopez-Paz & Ranzato, 2017), dubbed Averaged GEM (A-GEM), which enjoys the same or even better performance as GEM, while being almost as computationally and memory efficient as EWC (Kirkpatrick et al., 2016) and other regularization-based methods. Finally, we show that all algorithms including A-GEM can learn even more quickly if they are provided with task descriptors specifying the classification tasks under consideration. Our experiments on several standard lifelong learning benchmarks demonstrate that A-GEM has the best trade-off between accuracy and efficiency

Ex Output:
An efficient lifelong learning algorithm that provides a better trade-off between accuracy and time/ memory complexity compared to other algorithms.