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: We propose a framework for extreme learned image compression based on Generative Adversarial Networks (GANs), obtaining visually pleasing images at significantly lower bitrates than previous methods. This is made possible through our GAN formulation of learned compression combined with a generator/decoder which operates on the full-resolution image and is trained in combination with a multi-scale discriminator. Additionally, if a semantic label map of the original image is available, our method can fully synthesize unimportant regions in the decoded image such as streets and trees from the label map, therefore only requiring the storage of the preserved region and the semantic label map. A user study confirms that for low bitrates, our approach is preferred to state-of-the-art methods, even when they use more than double the bits.
Example Output: GAN-based extreme image compression method using less than half the bits of the SOTA engineered codec while preserving visual quality

Example Input: We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases.
Example Output: A theoretical algorithm for testing local optimality and extracting descent directions at nondifferentiable points of empirical risks of one-hidden-layer ReLU networks.

Example Input: There exists a plethora of techniques for inducing structured sparsity in parametric models during the optimization process, with the final goal of resource-efficient inference. However, to the best of our knowledge, none target a specific number of floating-point operations (FLOPs) as part of a single end-to-end optimization objective, despite reporting FLOPs as part of the results. Furthermore, a one-size-fits-all approach ignores realistic system constraints, which differ significantly between, say, a GPU and a mobile phone -- FLOPs on the former incur less latency than on the latter; thus, it is important for practitioners to be able to specify a target number of FLOPs during model compression. In this work, we extend a state-of-the-art technique to directly incorporate FLOPs as part of the optimization objective and show that, given a desired FLOPs requirement, different neural networks can be successfully trained for image classification.
Example Output:
We extend a state-of-the-art technique to directly incorporate FLOPs as part of the optimization objective, and we show that, given a desired FLOPs requirement, different neural networks are successfully trained.