High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has 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 updating a global AI model. Since each stochastic gradient is typically high-dimensional (with millions to billions of coefficients), communication overhead becomes a bottleneck for edge learning. To address this issue, we propose in this work a novel framework of hierarchical stochastic gradient quantization and study its effect on the learning performance. First, the framework features a practical hierarchical architecture for decomposing the stochastic gradient into its norm and normalized block gradients, and efficiently quantizes them using a uniform quantizer and a low-dimensional codebook on a Grassmann manifold, respectively. Subsequently, the quantized normalized block gradients are scaled and cascaded to yield the quantized normalized stochastic gradient using a so-called hinge vector designed under the criterion of minimum distortion. The hinge vector is also efficiently compressed using another low-dimensional Grassmannian quantizer. The other feature of the framework is a bit-allocation scheme for reducing the quantization error. The scheme determines the resolutions of the low-dimensional quantizers in the proposed framework. The framework is proved to guarantee model convergency by analyzing the convergence rate as a function of the quantization bits. Furthermore, by simulation, our design is shown to substantially reduce the communication overhead compared with the state-of-the-art signSGD scheme, while both achieve similar learning accuracies

Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal Output Distributions

In many real-world applications, from robotics to pedestrian trajectory prediction, there is a need to predict multiple real-valued outputs to represent several potential scenarios. Current deep learning techniques to address multiple-output problems are based on two main methodologies: (1) mixture density networks, which suffer from poor stability at high dimensions, or (2) multiple choice learning (MCL), an approach that uses $M$ single-output functions, each only producing a point estimate hypothesis. This paper presents a Mixture of Multiple-Output functions (MoM) approach using a novel variant of dropout, Multiple Hypothesis Dropout. Unlike traditional MCL-based approaches, each multiple-output function not only estimates the mean but also the variance for its hypothesis. This is achieved through a novel stochastic winner-take-all loss which allows each multiple-output function to estimate variance through the spread of its subnetwork predictions. Experiments on supervised learning problems illustrate that our approach outperforms existing solutions for reconstructing multimodal output distributions. Additional studies on unsupervised learning problems show that estimating the parameters of latent posterior distributions within a discrete autoencoder significantly improves codebook efficiency, sample quality, precision and recall.Comment: To appear in Proceedings of the 38th AAAI Conference on Artificial Intelligence (AAAI-24). 13 pages (9 main, 4 appendix