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]: Limited angle CT reconstruction is an under-determined linear inverse problem that requires appropriate regularization techniques to be solved. In this work we study how pre-trained generative adversarial networks (GANs) can be used to clean noisy, highly artifact laden reconstructions from conventional techniques, by effectively projecting onto the inferred image manifold. In particular, we use a robust version of the popularly used GAN prior for inverse problems, based on a recent technique called corruption mimicking, that significantly improves the reconstruction quality. The proposed approach operates in the image space directly, as a result of which it does not need to be trained or require access to the measurement model, is scanner agnostic, and can work over a wide range of sensing scenarios.
[A]: We show that robust GAN priors work better than GAN priors for limited angle CT reconstruction which is a highly under-determined inverse problem.


[Q]: We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.
[A]: We introduce a statistical approach to assessing neural network robustness that provides an informative notion of how robust a network is, rather than just the conventional binary assertion of whether or not of property is violated.


[Q]: Many biological learning systems such as the mushroom body, hippocampus, and cerebellum are built from sparsely connected networks of neurons. For a new understanding of such networks, we study the function spaces induced by sparse random features and characterize what functions may and may not be learned. A network with d inputs per neuron is found to be equivalent to an additive model of order d, whereas with a degree distribution the network combines additive terms of different orders. We identify three specific advantages of sparsity: additive function approximation is a powerful inductive bias that limits the curse of dimensionality, sparse networks are stable to outlier noise in the inputs, and sparse random features are scalable. Thus, even simple brain architectures can be powerful function approximators. Finally, we hope that this work helps popularize kernel theories of networks among computational neuroscientists.
[A]:
We advocate for random features as a theory of biological neural networks, focusing on sparsely connected networks