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.

Example Input: Music relies heavily on repetition to build structure and meaning.   Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure.   The Transformer (Vaswani et al., 2017), a sequence model based on self-attention, has achieved compelling results in many generation tasks that require maintaining long-range coherence. This suggests that self-attention might also be well-suited to modeling music. In musical composition and performance, however, relative timing is critically important.   Existing approaches for representing relative positional information in the Transformer modulate attention based on pairwise distance (Shaw et al., 2018).   This is impractical for long sequences such as musical compositions since their memory complexity is quadratic in the sequence length.   We propose an algorithm that reduces the intermediate memory requirements to linear in the sequence length. This enables us to demonstrate that a Transformer with our modified relative attention mechanism can generate minute-long (thousands of steps) compositions with compelling structure, generate continuations that coherently elaborate on a given motif, and in a seq2seq setup generate accompaniments conditioned on melodies.    We evaluate the Transformer with our relative attention mechanism on two datasets, JSB Chorales and Piano-e-competition, and obtain state-of-the-art results on the latter.
Example Output: We show the first successful use of Transformer in generating music that exhibits long-term structure. 

Example Input: 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.
Example Output: We show that robust GAN priors work better than GAN priors for limited angle CT reconstruction which is a highly under-determined inverse problem.

Example Input: In this work, we aim to solve data-driven optimization problems, where the goal is to find an input that maximizes an unknown score function given access to a dataset of input, score pairs. Inputs may lie on extremely thin manifolds in high-dimensional spaces, making the optimization prone to falling-off the manifold. Further, evaluating the unknown function may be expensive, so the algorithm should be able to exploit static, offline data. We propose model inversion networks (MINs) as an approach to solve such problems. Unlike prior work, MINs scale to extremely high-dimensional input spaces and can efficiently leverage offline logged datasets for optimization in both contextual and non-contextual settings. We show that MINs can also be extended to the active setting, commonly studied in prior work, via a simple, novel and effective scheme for active data collection. Our experiments show that MINs act as powerful optimizers on a range of contextual/non-contextual, static/active problems including optimization over images and protein designs and learning from logged bandit feedback.
Example Output:
We propose a novel approach to solve data-driven model-based optimization problems in both passive and active settings that can scale to high-dimensional input spaces.

