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: Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in existing GPUs. MPT is typically used in combination with a technique called loss scaling, that works by scaling up the loss value up before the start of backpropagation in order to minimize the impact of numerical underflow on training. Unfortunately, existing methods make this loss scale value a hyperparameter that needs to be tuned per-model, and a single scale cannot be adapted to different layers at different training stages. We introduce a loss scaling-based training method called adaptive loss scaling that makes MPT easier and more practical to use, by removing the need to tune a model-specific loss scale hyperparameter. We achieve this by introducing layer-wise loss scale values which are automatically computed during training to deal with underflow more effectively than existing methods. We present experimental results on a variety of networks and tasks that show our approach can shorten the time to convergence and improve accuracy, compared with using the existing state-of-the-art MPT and single-precision floating point.
Example solution: We devise adaptive loss scaling to improve mixed precision training that surpass the state-of-the-art results.
Example explanation: The abstract focusses on designing an adaptive loss scaling method, hence the generated output is correct.

Problem: We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector
$ heta_0\in\mathbb{R}^d$ \emph{uniformly} from $m$ quantized noisy measurements. Under the assumption that the measurements are sub-Gaussian, to recover any $k$-sparse $ heta_0$ ($k\ll d$) \emph{uniformly} up to an error $arepsilon$ with high probability, the best known computationally tractable algorithm requires
ootnote{Here, an algorithm is ''computationally tractable'' if it has provable convergence guarantees. The notation $ ilde{\mathcal{O}}(\cdot)$ omits a logarithm factor of $arepsilon^{-1}$. } $m\geq ilde{\mathcal{O}}(k\log d/arepsilon^4)$. In this paper, we consider a new framework for the one-bit sensing problem where the sparsity is implicitly enforced via mapping a low dimensional representation $x_0$ through a known $n$-layer ReLU generative network $G:\mathbb{R}^k
ightarrow\mathbb{R}^d$. Such a framework poses low-dimensional priors on $ heta_0$ without a known basis. We propose to recover the target $G(x_0)$ via an unconstrained empirical risk minimization (ERM) problem under a much weaker \emph{sub-exponential measurement assumption}. For such a problem, we establish a joint statistical and computational analysis . In particular, we prove that the ERM estimator in this new framework achieves an improved statistical rate of $m= ilde{\mathcal{O}} (kn\log d /\epsilon^2)$ recovering any $G(x_0)$ uniformly up to an error $arepsilon$. Moreover, from the lens of computation, we prove that under proper conditions on the ReLU weights, our proposed empirical risk, despite non-convexity, has no stationary point outside of small neighborhoods around the true representation $x_0$ and its negative multiple. Furthermore, we show that the global minimizer of the empirical risk stays within the neighborhood around $x_0$ rather than its negative multiple. Our analysis sheds some light on the possibility of inverting a deep generative model under partial and quantized measurements, complementing the recent success of using deep generative models for inverse problems.
Solution: We provide statistical and computational analysis of one-bit compressed sensing problem with a generative prior.