Heterogeneous Graph Sparsification for Efficient Representation Learning

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically exploited to improve efficiency of learning tasks. In this work, we initiate the study on heterogeneous graph sparsification and develop sampling-based algorithms for constructing sparsifiers that are provably sparse and preserve important information in the original graphs. We have performed extensive experiments to confirm that the proposed method can improve time and space complexities of representation learning while achieving comparable, or even better performance in subsequent graph learning tasks based on the learned embedding.

Auto-Encoding Goodness of Fit

For generative autoencoders to learn a meaningful latent representation for data generation, a careful balance must be achieved between reconstruction error and how close the distribution in the latent space is to the prior. However, this balance is challenging to achieve due to a lack of criteria that work both at the mini-batch (local) and aggregated posterior (global) level. Goodness of fit (GoF) hypothesis tests provide a measure of statistical indistinguishability between the latent distribution and a target distribution class. In this work, we develop the Goodness of Fit Autoencoder (GoFAE), which incorporates hypothesis tests at two levels. At the mini-batch level, it uses GoF test statistics as regularization objectives. At a more global level, it selects a regularization coefficient based on higher criticism, i.e., a test on the uniformity of the local GoF p-values. We justify the use of GoF tests by providing a relaxed $L_2$-Wasserstein bound on the distance between the latent distribution and target prior. We propose to use GoF tests and prove that optimization based on these tests can be done with stochastic gradient (SGD) descent on a compact Riemannian manifold. Empirically, we show that our higher criticism parameter selection procedure balances reconstruction and generation using mutual information and uniformity of p-values respectively. Finally, we show that GoFAE achieves comparable FID scores and mean squared errors with competing deep generative models while retaining statistical indistinguishability from Gaussian in the latent space based on a variety of hypothesis tests.

A Length Adaptive Algorithm-Hardware Co-design of Transformer on FPGA Through Sparse Attention and Dynamic Pipelining

Transformers are considered one of the most important deep learning models since 2018, in part because it establishes state-of-the-art (SOTA) records and could potentially replace existing Deep Neural Networks (DNNs). Despite the remarkable triumphs, the prolonged turnaround time of Transformer models is a widely recognized roadblock. The variety of sequence lengths imposes additional computing overhead where inputs need to be zero-padded to the maximum sentence length in the batch to accommodate the parallel computing platforms. This paper targets the field-programmable gate array (FPGA) and proposes a coherent sequence length adaptive algorithm-hardware co-design for Transformer acceleration. Particularly, we develop a hardware-friendly sparse attention operator and a length-aware hardware resource scheduling algorithm. The proposed sparse attention operator brings the complexity of attention-based models down to linear complexity and alleviates the off-chip memory traffic. The proposed length-aware resource hardware scheduling algorithm dynamically allocates the hardware resources to fill up the pipeline slots and eliminates bubbles for NLP tasks. Experiments show that our design has very small accuracy loss and has 80.2 $\times$ and 2.6 $\times$ speedup compared to CPU and GPU implementation, and 4 $\times$ higher energy efficiency than state-of-the-art GPU accelerator optimized via CUBLAS GEMM.

An Efficient Algorithm for Deep Stochastic Contextual Bandits

In stochastic contextual bandit (SCB) problems, an agent selects an action based on certain observed context to maximize the cumulative reward over iterations. Recently there have been a few studies using a deep neural network (DNN) to predict the expected reward for an action, and the DNN is trained by a stochastic gradient based method. However, convergence analysis has been greatly ignored to examine whether and where these methods converge. In this work, we formulate the SCB that uses a DNN reward function as a non-convex stochastic optimization problem, and design a stage-wise stochastic gradient descent algorithm to optimize the problem and determine the action policy. We prove that with high probability, the action sequence chosen by this algorithm converges to a greedy action policy respecting a local optimal reward function. Extensive experiments have been performed to demonstrate the effectiveness and efficiency of the proposed algorithm on multiple real-world datasets.

Escaping Saddle Points with Stochastically Controlled Stochastic Gradient Methods

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic gradient descent (SGD) step introduces anistropic noise around saddle points for deep learning and non-convex half space learning problems, which indicates that SGD satisfies the correlated negative curvature (CNC) condition for these problems. Therefore, we propose to use a separate SGD step to help the SCSG method escape from strict saddle points, resulting in the CNC-SCSG method. The SGD step plays a role similar to noise injection but is more stable. We prove that the resultant algorithm converges to a second-order stationary point with a convergence rate of $\tilde{O}( \epsilon^{-2} log( 1/\epsilon))$ where $\epsilon$ is the pre-specified error tolerance. This convergence rate is independent of the problem dimension, and is faster than that of CNC-SGD. A more general framework is further designed to incorporate the proposed CNC-SCSG into any first-order method for the method to escape saddle points. Simulation studies illustrate that the proposed algorithm can escape saddle points in much fewer epochs than the gradient descent methods perturbed by either noise injection or a SGD step.

Discrete Graph Structure Learning for Forecasting Multiple Time Series

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.

Federated Nonconvex Sparse Learning

Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their capability of recovering true support and scalability with large datasets. Theoretical analysis of IHT is currently based on centralized IID data. In realistic large-scale situations, however, data are distributed, hardly IID, and private to local edge computing devices. It is thus necessary to examine the property of IHT in federated settings, which update in parallel on local devices and communicate with a central server only once in a while without sharing local data. In this paper, we propose two IHT methods: Federated Hard Thresholding (Fed-HT) and Federated Iterative Hard Thresholding (FedIter-HT). We prove that both algorithms enjoy a linear convergence rate and have strong guarantees to recover the optimal sparse estimator, similar to traditional IHT methods, but now with decentralized non-IID data. Empirical results demonstrate that the Fed-HT and FedIter-HT outperform their competitor - a distributed IHT, in terms of decreasing the objective values with lower requirements on communication rounds and bandwidth.

Effective Proximal Methods for Non-convex Non-smooth Regularized Learning

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions recently. We design a family of stochastic proximal gradient methods by applying arbitrary sampling to solve the empirical risk minimization problem with a non-convex and non-smooth regularizer. These methods draw mini-batches of training examples according to an arbitrary probability distribution when computing stochastic gradients. A unified analytic approach is developed to examine the convergence and computational complexity of these methods, allowing us to compare the different sampling schemes. We show that the independent sampling scheme tends to improve performance over the commonly-used uniform sampling scheme. Our new analysis also derives a tighter bound on convergence speed for the uniform sampling than the best one available so far. Empirical evaluations demonstrate that the proposed algorithms converge faster than the state of the art.