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.

The sign stochastic gradient descent method (signSGD) utilizes only the sign of the stochastic gradient in its updates. Since signSGD carries out one-bit quantization of the gradients, it is extremely practical for distributed optimization where gradients need to be aggregated from different processors. For the first time, we establish convergence rates for signSGD on general non-convex functions under transparent conditions. We show that the rate of signSGD to reach first-order critical points matches that of SGD in terms of number of stochastic gradient calls, up to roughly a linear factor in the dimension. We carry out simple experiments to explore the behaviour of sign gradient descent (without the stochasticity) close to saddle points and show that it often helps completely avoid them without using either stochasticity or curvature information.
We prove a non-convex convergence rate for the sign stochastic gradient method. The algorithm has links to algorithms like Adam and Rprop, as well as gradient quantisation schemes used in distributed machine learning.

We present a real-time method for synthesizing highly complex human motions using a novel training regime we call the auto-conditioned Recurrent Neural Network (acRNN). Recently, researchers have attempted to synthesize new motion by using autoregressive techniques, but existing methods tend to freeze or diverge after a couple of seconds due to an accumulation of errors that are fed back into the network. Furthermore, such methods have only been shown to be reliable for relatively simple human motions, such as walking or running. In contrast, our approach can synthesize arbitrary motions with highly complex styles, including dances or martial arts in addition to locomotion. The acRNN is able to accomplish this by explicitly accommodating for autoregressive noise accumulation during training. Our work is the first to our knowledge that demonstrates the ability to generate over 18,000 continuous frames (300 seconds) of new complex human motion w.r.t. different styles.
Synthesize complex and extended human motions using an auto-conditioned LSTM network

Recent advances have made it possible to create deep complex-valued neural networks. Despite this progress, many challenging learning tasks have yet to leverage the power of complex representations. Building on recent advances, we propose a new deep complex-valued method for signal retrieval and extraction in the frequency domain. As a case study, we perform audio source separation in the Fourier domain. Our new method takes advantage of the convolution theorem which states that the Fourier transform of two convolved signals is the elementwise product of their Fourier transforms. Our novel method is based on a complex-valued version of Feature-Wise Linear Modulation (FiLM) and serves as the keystone of our proposed signal extraction method. We also introduce a new and explicit amplitude and phase-aware loss, which is scale and time invariant, taking into account the complex-valued components of the spectrogram. Using the Wall Street Journal Dataset, we compared our phase-aware loss to several others that operate both in the time and frequency domains and demonstrate the effectiveness of our proposed signal extraction method and proposed loss.

New Signal Extraction Method in the Fourier Domain