An Acceleration Technique for Matrix Completion using Deep Unfolding

This paper proposes an acceleration technique using deep unfolding for matrix completion problem, which is the problem of estimating the missing values of a matrix. To solve the problem, various methods have been proposed, which is based on matrix rank minimization. While these methods have iterative schemes to minimize the matrix rank on each step, they have poor estimation accuracy and convergence property when the parameters of the iterative schemes are not given appropriately. In order to provide appropriate parameters of iterative schemes, this paper focuses on a deep unfolding to accelerate matrix completion methods. The deep unfolding is a method of constructing more flexible derivation algorithms by embedding learnable parameters into existing iterative algorithms and by learning the parameters applying deep learning techniques to differentiable iterative algorithms with inputs and outputs. Algorithms which have adjustable parameters such as gradient descent are expected to accelerate by using deep unfolding. This paper proposes two matrix completion methods accelerated by deep unfolding which can optimize the iterative parameters via machine learning. Numerical experiments show the effectiveness of the proposed methods

Graph Convolutional Matrix Completion

We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we propose a graph auto-encoder framework based on differentiable message passing on the bipartite interaction graph. Our model shows competitive performance on standard collaborative filtering benchmarks. In settings where complimentary feature information or structured data such as a social network is available, our framework outperforms recent state-of-the-art methods.Comment: 9 pages, 3 figures, updated with additional experimental evaluatio

Implicit Regularization in Deep Matrix Factorization

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing, a model referred to as deep matrix factorization. Our first finding, supported by theory and experiments, is that adding depth to a matrix factorization enhances an implicit tendency towards low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we present theoretical and empirical arguments questioning a nascent view by which implicit regularization in matrix factorization can be captured using simple mathematical norms. Our results point to the possibility that the language of standard regularizers may not be rich enough to fully encompass the implicit regularization brought forth by gradient-based optimization.Comment: Published at the conference on Neural Information Processing Systems (NeurIPS) 201

Efficient machine learning: models and accelerations

One of the key enablers of the recent unprecedented success of machine learning is the adoption of very large models. Modern machine learning models typically consist of multiple cascaded layers such as deep neural networks, and at least millions to hundreds of millions of parameters (i.e., weights) for the entire model. The larger-scale model tend to enable the extraction of more complex high-level features, and therefore, lead to a significant improvement of the overall accuracy. On the other side, the layered deep structure and large model sizes also demand to increase computational capability and memory requirements. In order to achieve higher scalability, performance, and energy efficiency for deep learning systems, two orthogonal research and development trends have attracted enormous interests. The first trend is the acceleration while the second is the model compression. The underlying goal of these two trends is the high quality of the models to provides accurate predictions. In this thesis, we address these two problems and utilize different computing paradigms to solve real-life deep learning problems. To explore in these two domains, this thesis first presents the cogent confabulation network for sentence completion problem. We use Chinese language as a case study to describe our exploration of the cogent confabulation based text recognition models. The exploration and optimization of the cogent confabulation based models have been conducted through various comparisons. The optimized network offered a better accuracy performance for the sentence completion. To accelerate the sentence completion problem in a multi-processing system, we propose a parallel framework for the confabulation recall algorithm. The parallel implementation reduce runtime, improve the recall accuracy by breaking the fixed evaluation order and introducing more generalization, and maintain a balanced progress in status update among all neurons. A lexicon scheduling algorithm is presented to further improve the model performance. As deep neural networks have been proven effective to solve many real-life applications, and they are deployed on low-power devices, we then investigated the acceleration for the neural network inference using a hardware-friendly computing paradigm, stochastic computing. It is an approximate computing paradigm which requires small hardware footprint and achieves high energy efficiency. Applying this stochastic computing to deep convolutional neural networks, we design the functional hardware blocks and optimize them jointly to minimize the accuracy loss due to the approximation. The synthesis results show that the proposed design achieves the remarkable low hardware cost and power/energy consumption. Modern neural networks usually imply a huge amount of parameters which cannot be fit into embedded devices. Compression of the deep learning models together with acceleration attracts our attention. We introduce the structured matrices based neural network to address this problem. Circulant matrix is one of the structured matrices, where a matrix can be represented using a single vector, so that the matrix is compressed. We further investigate a more flexible structure based on circulant matrix, called block-circulant matrix. It partitions a matrix into several smaller blocks and makes each submatrix is circulant. The compression ratio is controllable. With the help of Fourier Transform based equivalent computation, the inference of the deep neural network can be accelerated energy efficiently on the FPGAs. We also offer the optimization for the training algorithm for block circulant matrices based neural networks to obtain a high accuracy after compression