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.

Input: Consider Input: We present a hybrid framework that leverages the trade-off between temporal and frequency precision in audio representations to improve the performance of speech enhancement task. We first show that conventional approaches using specific representations such as raw-audio and spectrograms are each effective at targeting different types of noise.
By integrating both approaches, our model can learn multi-scale and multi-domain features, effectively removing noise existing on different regions on the time-frequency space in a complementary way. Experimental results show that the proposed hybrid model yields better performance and robustness than using each model individually.

Output: A hybrid model utilizing both raw-audio and spectrogram information for speech enhancement tasks.

Input: Consider Input: We present a deep generative model, named Monge-Amp\'ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\'ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\'ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\'ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.

Output: A gradient flow based dynamical system for invertible generative modeling

Input: Consider Input: We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network.
Output: Redistributing and growing weights according to the momentum magnitude enables the training of sparse networks from random initializations that can reach dense performance levels with 5% to 50% weights while accelerating training by up to 5.6x.