Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.
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Energy-Efficient Processing and Robust Wireless Cooperative Transmission for Edge Inference
Edge machine learning can deliver low-latency and private artificial intelligent (AI) services for mobile devices by leveraging computation and storage resources at the network edge. This paper presents an energy-efficient edge processing framework to execute deep learning inference tasks at the edge computing nodes whose wireless connections to mobile devices are prone to channel uncertainties. Aimed at minimizing the sum of computation and transmission power consumption with probabilistic quality-of-service (QoS) constraints, we formulate a joint inference tasking and downlink beamforming problem that is characterized by a group sparse objective function. We provide a statistical learning based robust optimization approach to approximate the highly intractable probabilistic-QoS constraints by nonconvex quadratic constraints, which are further reformulated as matrix inequalities with a rank-one constraint via matrix lifting. We design a reweighted power minimization approach by iteratively reweighted ℓ1 minimization with difference-of-convex-functions (DC) regularization and updating weights, where the reweighted approach is adopted for enhancing group sparsity whereas the DC regularization is designed for inducing rank-one solutions. Numerical results demonstrate that the proposed approach outperforms other state-of-the-art approaches.
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- Award ID(s):
- 1711823
- NSF-PAR ID:
- 10166317
- Date Published:
- Journal Name:
- IEEE Internet of Things Journal
- ISSN:
- 2372-2541
- Page Range / eLocation ID:
- 1 to 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Probabilistic graphical models have become an important unsupervised learning tool for detecting network structures for a variety of problems, including the estimation of functional neuronal connectivity from two‐photon calcium imaging data. However, in the context of calcium imaging, technological limitations only allow for partially overlapping layers of neurons in a brain region of interest to be jointly recorded. In this case, graph estimation for the full data requires inference for edge selection when many pairs of neurons have no simultaneous observations. This leads to the graph quilting problem, which seeks to estimate a graph in the presence of block‐missingness in the empirical covariance matrix. Solutions for the graph quilting problem have previously been studied for Gaussian graphical models; however, neural activity data from calcium imaging are often non‐Gaussian, thereby requiring a more flexible modelling approach. Thus, in our work, we study two approaches for nonparanormal graph quilting based on the Gaussian copula graphical model, namely, a maximum likelihood procedure and a low rank‐based framework. We provide theoretical guarantees on edge recovery for the former approach under similar conditions to those previously developed for the Gaussian setting, and we investigate the empirical performance of both methods using simulations as well as real data calcium imaging data. Our approaches yield more scientifically meaningful functional connectivity estimates compared to existing Gaussian graph quilting methods for this calcium imaging data set.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/JIOT.2020.2979523
