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 NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay. In our experiments on neural networks for image classification, speech recognition, machine translation, and language modeling, it performs on par or better than well tuned SGD with momentum and Adam/AdamW. 
 Additionally, NovoGrad (1) is robust to the choice of learning rate and weight initialization, (2) works well in a large batch setting, and (3) has two times smaller memory footprint than Adam.
Example Output: NovoGrad -  an adaptive SGD method with layer-wise gradient normalization and decoupled weight decay. 

Example Input: Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets easier with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions.
Example Output: We investigate ReLU networks in the Fourier domain and demonstrate peculiar behaviour.

Example Input: In this paper, we propose an arbitrarily-conditioned data imputation framework built upon variational autoencoders and normalizing flows. The proposed model is capable of mapping any partial data to a multi-modal latent variational distribution. Sampling from such a distribution leads to stochastic imputation. Preliminary evaluation on MNIST dataset shows promising stochastic imputation conditioned on partial images as input.
Example Output:
We propose an arbitrarily-conditioned data imputation framework built upon variational autoencoders and normalizing flows