HighDimensional Stochastic Gradient Quantization for CommunicationEfficient Edge Learning Edge machine learning involves the deployment of machine learning algorithms at the network edge so as to leverage massive mobile data and distributed computation resources. Many edge learning frameworks (e.g., federated learning) have been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for aggregation for updating a global AI model. Since each gradient is typically highdimensional (with millions to billions of coefficients), communication overhead may become a bottleneck for edge learning. In this work, we propose a novel gradient compression scheme to reduce the aforementioned overhead. Specifically, in the proposed scheme, the norm of the stochastic gradient is quantized using a uniform quantizer while the normalized stochastic gradient is decomposed into block gradients. A Grassmannian codebook is applied to quantizing each normalized block gradients. Their quantized versions are assembled using a socalled hinge vector, which is quantized using another Grassmannian codebook. Furthermore, a practical bitallocation strategy is developed. By simulations, we show that similar learning performance can be achieved with substantially lower communication overhead as compared to the onebit scalar quantization schemes used in the stateoftheart design, namely signed SGD.

Collaborative Machine Learning at the Wireless Edge with Blind Transmitters We study wireless collaborative machine learning (ML), where mobile edge devices, each with its own dataset, carry out distributed stochastic gradient descent (DSGD) overtheair with the help of a wireless access point acting as the parameter server (PS). At each iteration of the DSGD algorithm wireless devices compute gradient estimates with their local datasets, and send them to the PS over a wireless fading multiple access channel (MAC). Motivated by the additive nature of the wireless MAC, we propose an analog DSGD scheme, in which the devices transmit scaled versions of their gradient estimates in an uncoded fashion. We assume that the channel state information (CSI) is available only at the PS. We instead allow the PS to employ multiple antennas to alleviate the destructive fading effect, which cannot be cancelled by the transmitters due to the lack of CSI. Theoretical analysis indicates that, with the proposed DSGD scheme, increasing the number of PS antennas mitigates the fading effect, and, in the limit, the effects of fading and noise disappear, and the PS receives aligned signals used to update the model parameter. The theoretical results are then corroborated with the experimental ones.