Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix decomposition or use the preconditioned conjugate gradient method. For relatively large instances, these methods cannot achieve the real-time requirement unless there is an effective preconditioner. Recently, graph neural networks (GNNs) opened new possibilities for QP. Some promising empirical studies of applying GNNs for QP tasks show that GNNs can capture key characteristics of an optimization instance and provide adaptive guidance accordingly to crucial configurations during the solving process, or directly provide an approximate solution. However, the theoretical understanding of GNNs in this context remains limited. Specifically, it is unclear what GNNs can and cannot achieve for QP tasks in theory. This work addresses this gap in the context of linearly constrained QP tasks. In the continuous setting, we prove that message-passing GNNs can universally represent fundamental properties of quadratic programs, including feasibility, optimal objective values, and optimal solutions. In the more challenging mixed-integer setting, while GNNs are not universal approximators, we identify a subclass of QP problems that GNNs can reliably represent.

Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching (SB), the most effective yet computationally expensive heuristic employed in the branch-and-bound algorithm. In the literature, message-passing GNN (MP-GNN), as the simplest GNN structure, is frequently used as a fast approximation of SB and we find that not all MILPs's SB can be represented with MP-GNN. We precisely define a class of "MP-tractable" MILPs for which MP-GNNs can accurately approximate SB scores. Particularly, we establish a universal approximation theorem: for any data distribution over the MP-tractable class, there always exists an MP-GNN that can approximate the SB score with arbitrarily high accuracy and arbitrarily high probability, which lays a theoretical foundation of the existing works on imitating SB with MP-GNN. For MILPs without the MP-tractability, unfortunately, a similar result is impossible, which can be illustrated by two MILP instances with different SB scores that cannot be distinguished by any MP-GNN, regardless of the number of parameters. Recognizing this, we explore another GNN structure called the second-order folklore GNN (2-FGNN) that overcomes this limitation, and the aforementioned universal approximation theorem can be extended to the entire MILP space using 2-FGNN, regardless of the MP-tractability. A small-scale numerical experiment is conducted to directly validate our theoretical findings.

Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provably solve these problems in an iterative fashion. On one hand, data-driven algorithms can "learn to optimize" (L2O) with much fewer iterations and similar cost per iteration as general-purpose optimization algorithms. On the other hand, unfortunately, many L2O algorithms lack converge guarantees. To fuse the advantages of these approaches, we present a Safe-L2O framework. Safe-L2O updates incorporate a safeguard to guarantee convergence for convex problems with proximal and/or gradient oracles. The safeguard is simple and computationally cheap to implement, and it is activated only when the data-driven L2O updates would perform poorly or appear to diverge. This yields the numerical benefits of employing machine learning to create rapid L2O algorithms while still guaranteeing convergence. Our numerical examples show convergence of Safe-L2O algorithms, even when the provided data is not from the distribution of training data.

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

The record-breaking performance of deep neural networks (DNNs) comes with heavy parameter budgets, which leads to external dynamic random access memory (DRAM) for storage. The prohibitive energy of DRAM accesses makes it nontrivial for DNN deployment on resource-constrained devices, calling for minimizing the movements of weights and data in order to improve the energy efficiency. Driven by this critical bottleneck, we present SmartDeal, a hardware-friendly algorithm framework to trade higher-cost memory storage/access for lower-cost computation, in order to aggressively boost the storage and energy efficiency, for both DNN inference and training. The core technique of SmartDeal is a novel DNN weight matrix decomposition framework with respective structural constraints on each matrix factor, carefully crafted to unleash the hardware-aware efficiency potential. Specifically, we decompose each weight tensor as the product of a small basis matrix and a large structurally sparse coefficient matrix whose nonzero elements are readily quantized to the power-of-2. The resulting sparse and readily quantized DNNs enjoy greatly reduced energy consumption in data movement as well as weight storage, while incurring minimal overhead to recover the original weights thanks to the required sparse bit-operations and cost-favorable computations. Beyond inference, we take another leap to embrace energy-efficient training, by introducing several customized techniques to address the unique roadblocks arising in training while preserving the SmartDeal structures. We also design a dedicated hardware accelerator to fully utilize the new weight structure to improve the real energy efficiency and latency performance. We conduct experiments on both vision and language tasks, with nine models, four datasets, and three settings (inference-only, adaptation, and fine-tuning). Our extensive results show that 1) being applied to inference, SmartDeal achieves up to 2.44× improvement in energy efficiency as evaluated using real hardware implementations and 2) being applied to training, SmartDeal can lead to 10.56× and 4.48× reduction in the storage and the training energy cost, respectively, with usually negligible accuracy loss, compared to state-of-the-art training baselines. Our source codes are available at: https://github.com/VITA-Group/SmartDeal.

Federated learning (FL) enables distribution of machine learning workloads from the cloud to resource-limited edge devices. Unfortunately, current deep networks remain not only too compute-heavy for inference and training on edge devices, but also too large for communicating updates over bandwidth-constrained networks. In this paper, we develop, implement, and experimentally validate a novel FL framework termed Federated Dynamic Sparse Training (FedDST) by which complex neural networks can be deployed and trained with substantially improved efficiency in both on-device computation and in-network communication. At the core of FedDST is a dynamic process that extracts and trains sparse sub-networks from the target full network. With this scheme, "two birds are killed with one stone:'' instead of full models, each client performs efficient training of its own sparse networks, and only sparse networks are transmitted between devices and the cloud. Furthermore, our results reveal that the dynamic sparsity during FL training more flexibly accommodates local heterogeneity in FL agents than the fixed, shared sparse masks. Moreover, dynamic sparsity naturally introduces an "in-time self-ensembling effect'' into the training dynamics, and improves the FL performance even over dense training. In a realistic and challenging non i.i.d. FL setting, FedDST consistently outperforms competing algorithms in our experiments: for instance, at any fixed upload data cap on non-iid CIFAR-10, it gains an impressive accuracy advantage of 10% over FedAvgM when given the same upload data cap; the accuracy gap remains 3% even when FedAvgM is given 2 times the upload data cap, further demonstrating efficacy of FedDST. Code is available at: https://github.com/bibikar/feddst.

Deep neural networks (DNNs) typically require massive data to train on, which is a hurdle for numerous practical domains. Facing the data shortfall, one viable option is to acquire domain-specific training data from external uncensored sources, such as open webs or third-party data collectors. However, the quality of such acquired data is often not rigorously scrutinized, and one cannot easily rule out the risk of `"poisoned" examples being included in such unreliable datasets, resulting in unreliable trained models which pose potential risks to many high-stake applications. While existing options usually suffer from high computational costs or assumptions on clean data access, this paper attempts to detect backdoors for potential victim models with minimal prior knowledge. In particular, provided with a trained model, users are assumed to (1) have no prior knowledge of whether it is already poisoned, or what the target class/percentage of samples is poisoned, and (2) have no access to a clean sample set from the same training distribution, nor any trusted model trained on such clean data. To tackle this challenging scenario, we first observe the contrasting channel-level statistics between the backdoor trigger and clean image features, and consequently, how they can be differentiated by progressive channel shuffling. We then propose the randomized channel shuffling method for backdoor-targeted class detection, which requires only a few feed-forward passes. It thus incurs minimal overheads and demands no clean sample nor prior knowledge. We further explore a “full” clean data-free setting, where neither the target class detection nor the trigger recovery can access the clean data. Extensive experiments are conducted with three datasets (CIFAR-10, GTSRB, Tiny ImageNet), three architectures (AlexNet, ResNet-20, SENet-18), and three attacks (BadNets, clean label attack, and WaNet). Results consistently endorse the effectiveness of our proposed technique in backdoor model detection, with margins of 0.291 ～ 0.640 AUROC over the current state-of-the-arts. Codes are available at https://github.com/VITA-Group/Random-Shuffling-BackdoorDetect.

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on its performance on a set of training problems. This data-driven procedure generates methods that can efficiently solve problems similar to those in training. In sharp contrast, the typical and traditional designs of optimization methods are theory-driven, so they obtain performance guarantees over the classes of problems specified by the theory. The difference makes L2O suitable for repeatedly solving a particular optimization problem over a specific distribution of data, while it typically fails on out-of-distribution problems. The practicality of L2O depends on the type of target optimization, the chosen architecture of the method to learn, and the training procedure. This new paradigm has motivated a community of researchers to explore L2O and report their findings. This article is poised to be the first comprehensive survey and benchmark of L2O for continuous optimization. We set up taxonomies, categorize existing works and research directions, present insights, and identify open challenges. We benchmarked many existing L2O approaches on a few representative optimization problems. For reproducible research and fair benchmarking purposes, we released our software implementation and data in the package Open-L2O at https://github.com/VITA-Group/Open-L2O.

Xiaohan Chen, Yu Cheng, Shuohang Wang, Zhe Gan, Zhangyang Wang, Jingjing Liu. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Lottery Ticket Hypothesis (LTH) raises keen attention to identifying sparse trainable subnetworks, or winning tickets, which can be trained in isolation to achieve similar or even better performance compared to the full models. Despite many efforts being made, the most effective method to identify such winning tickets is still Iterative Magnitude-based Pruning (IMP), which is computationally expensive and has to be run thoroughly for every different network. A natural question that comes in is: can we “transform” the winning ticket found in one network to another with a different architecture, yielding a winning ticket for the latter at the beginning, without re-doing the expensive IMP? Answering this question is not only practically relevant for efficient “once-for-all” winning ticket finding, but also theoretically appealing for uncovering inherently scalable sparse patterns in networks. We conduct extensive experiments on CIFAR-10 and ImageNet, and propose a variety of strategies to tweak the winning tickets found from different networks of the same model family (e.g., ResNets). Based on these results, we articulate the Elastic Lottery Ticket Hypothesis (E-LTH): by mindfully replicating (or dropping) and re-ordering layers for one network, its corresponding winning ticket could be stretched (or squeezed) into a subnetwork for another deeper (or shallower) network from the same family, whose performance is nearly the same competitive as the latter’s winning ticket directly found by IMP. We have also extensively compared E-LTH with pruning-at-initialization and dynamic sparse training methods, as well as discussed the generalizability of E-LTH to different model families, layer types, and across datasets. Code is available at https://github.com/VITA-Group/ElasticLTH.

Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the concept of unrolling an iterative algorithm and training it like a neural network. It has had great success on sparse recovery. In this paper, we show that adding momentum to intermediate variables in the LISTA network achieves a better convergence rate and, in particular, the network with instance-optimal parameters is superlinearly convergent. Moreover, our new theoretical results lead to a practical approach of automatically and adaptively calculating the parameters of a LISTA network layer based on its previous layers. Perhaps most surprisingly, such an adaptive-parameter procedure reduces the training of LISTA to tuning only three hyperparameters from data: a new record set in the context of the recent advances on trimming down LISTA complexity. We call this new ultra-light weight network HyperLISTA. Compared to state-of-the-art LISTA models, HyperLISTA achieves almost the same performance on seen data distributions and performs better when tested on unseen distributions (specifically, those with different sparsity levels and nonzero magnitudes). Code is available: https://github.com/VITA-Group/HyperLISTA.

Works on lottery ticket hypothesis (LTH) and single-shot network pruning (SNIP) have raised a lot of attention currently on post-training pruning (iterative magnitude pruning), and before-training pruning (pruning at initialization). The former method suffers from an extremely large computation cost and the latter usually struggles with insufficient performance. In comparison, during-training pruning, a class of pruning methods that simultaneously enjoys the training/inference efficiency and the comparable performance, temporarily, has been less explored. To better understand during-training pruning, we quantitatively study the effect of pruning throughout training from the perspective of pruning plasticity (the ability of the pruned networks to recover the original performance). Pruning plasticity can help explain several other empirical observations about neural network pruning in literature. We further find that pruning plasticity can be substantially improved by injecting a brain-inspired mechanism called neuroregeneration, i.e., to regenerate the same number of connections as pruned. We design a novel gradual magnitude pruning (GMP) method, named gradual pruning with zero-cost neuroregeneration (GraNet), that advances state of the art. Perhaps most impressively, its sparse-to-sparse version for the first time boosts the sparse-to-sparse training performance over various dense-to-sparse methods with ResNet-50 on ImageNet without extending the training time. We release all codes in https://github.com/Shiweiliuiiiiiii/GraNet.

There have been long-standing controversies and inconsistencies over the experiment setup and criteria for identifying the "winning ticket" in literature. To reconcile such, we revisit the definition of lottery ticket hypothesis, with comprehensive and more rigorous conditions. Under our new definition, we show concrete evidence to clarify whether the winning ticket exists across the major DNN architectures and/or applications. Through extensive experiments, we perform quantitative analysis on the correlations between winning tickets and various experimental factors, and empirically study the patterns of our observations. We find that the key training hyperparameters, such as learning rate and training epochs, as well as the architecture characteristics such as capacities and residual connections, are all highly correlated with whether and when the winning tickets can be identified. Based on our analysis, we summarize a guideline for parameter settings in regards of specific architecture characteristics, which we hope to catalyze the research progress on the topic of lottery ticket hypothesis. Our codes are publicly available at: https://github.com/boone891214/sanity-check-LTH.

Activity recognition in wearable computing faces two key challenges: i) activity characteristics may be context-dependent and change under different contexts or situations; ii) unknown contexts and activities may occur from time to time, requiring flexibility and adaptability of the algorithm. We develop a context-aware mixture of deep models termed the $\alpha$-$\beta$ network coupled with uncertainty quantification (UQ) based upon maximum entropy to enhance human activity recognition performance. We improve accuracy and F score by 10% by identifying high-level contexts in a data-driven way to guide model development. In order to ensure training stability, we have used a clustering-based pre-training in both public and in-house datasets, demonstrating improved accuracy through unknown context discovery.

We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruning, decomposition, and quantization, into one unified framework. The resulting sparse and readily-quantized DNN thus enjoys greatly reduced energy consumption in data movement as well as weight storage. On top of that, we further design a dedicated accelerator to fully utilize the SmartExchange-enforced weights to improve both energy efficiency and latency performance. Extensive experiments show that 1) on the algorithm level, SmartExchange outperforms stateof-the-art compression techniques, including merely sparsification or pruning, decomposition, and quantization, in various ablation studies based on nine models and four datasets; and 2) on the hardware level, SmartExchange can boost the energy efficiency by up to 6.7× and reduce the latency by up to 19.2× over four state-of-the-art DNN accelerators, when benchmarked on seven DNN models (including four standard DNNs, two compact DNN models, and one segmentation model) and three datasets.

Meta-learning improves generalization of machine learning models when faced with previously unseen tasks by leveraging experiences from different, yet related prior tasks. To allow for better generalization, we propose a novel task representation called model-aware task embedding (MATE) that incorporates not only the data distributions of different tasks, but also the complexity of the tasks through the models used. The task complexity is taken into account by a novel variant of kernel mean embedding, combined with an instance-adaptive attention mechanism inspired by an SVM-based feature selection algorithm. Together with conditioning layers in deep neural networks, MATE can be easily incorporated into existing meta learners as a plug-and-play module. While MATE is widely applicable to general tasks where the concept of task/environment is involved, we demonstrate its effectiveness in few-shot learning by improving a state-of-the-art model consistently on two benchmarks. Source codes for this paper are available at https://github.com/VITA-Group/MATE.

Multiplication (e.g., convolution) is arguably a cornerstone of modern deep neural networks (DNNs). However, intensive multiplications cause expensive resource costs that challenge DNNs' deployment on resource-constrained edge devices, driving several attempts for multiplication-less deep networks. This paper presented ShiftAddNet, whose main inspiration is drawn from a common practice in energy-efficient hardware implementation, that is, multiplication can be instead performed with additions and logical bit-shifts. We leverage this idea to explicitly parameterize deep networks in this way, yielding a new type of deep network that involves only bit-shift and additive weight layers. This hardware-inspired ShiftAddNet immediately leads to both energy-efficient inference and training, without compromising the expressive capacity compared to standard DNNs. The two complementary operation types (bit-shift and add) additionally enable finer-grained control of the model's learning capacity, leading to more flexible trade-off between accuracy and (training) efficiency, as well as improved robustness to quantization and pruning. We conduct extensive experiments and ablation studies, all backed up by our FPGA-based ShiftAddNet implementation and energy measurements. Compared to existing DNNs or other multiplication-less models, ShiftAddNet aggressively reduces over 80% hardware-quantified energy cost of DNNs training and inference, while offering comparable or better accuracies. Codes and pre-trained models are available at https://github.com/RICE-EIC/ShiftAddNet.

Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain Lipschitz condition on the denoisers. We then propose real spectral normalization, a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition. Finally, we present experimental results validating the theory.

Convolutional neural networks (CNNs) have been increasingly deployed to edge devices. Hence, many efforts have been made towards efficient CNN inference on resource-constrained platforms. This paper attempts to explore an orthogonal direction: how to conduct more energy-efficient training of CNNs, so as to enable on-device training? We strive to reduce the energy cost during training, by dropping unnecessary computations, from three complementary levels: stochastic mini-batch dropping on the data level; selective layer update on the model level; and sign prediction for low-cost, low-precision back-propagation, on the algorithm level. Extensive simulations and ablation studies, with real energy measurements from an FPGA board, confirm the superiority of our proposed strategies and demonstrate remarkable energy savings for training. For example, when training ResNet-74 on CIFAR-10, we achieve aggressive energy savings of >90% and >60%, while incurring a top-1 accuracy loss of only about 2% and 1.2%, respectively. When training ResNet-110 on CIFAR-100, an over 84% training energy saving is achieved without degrading inference accuracy.

This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop novel orthogonality regularizations on training deep CNNs, utilizing various advanced analytical tools such as mutual coherence and restricted isometry property. These plug-and-play regularizations can be conveniently incorporated into training almost any CNN without extra hassle. We then benchmark their effects on state-of-the-art models: ResNet, WideResNet, and ResNeXt, on several most popular computer vision datasets: CIFAR-10, CIFAR-100, SVHN and ImageNet. We observe consistent performance gains after applying those proposed regularizations, in terms of both the final accuracies achieved, and faster and more stable convergences. We have made our codes and pre-trained models publicly available: https://github.com/nbansal90/Can-we-Gain-More-from-Orthogonality.

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the power of neural networks. In this work, we study unfolded ISTA (Iterative Shrinkage Thresholding Algorithm) for sparse signal recovery. We introduce a weight structure that is necessary for asymptotic convergence to the true sparse signal. With this structure, unfolded ISTA can attain a linear convergence, which is better than the sublinear convergence of ISTA/FISTA in general cases. Furthermore, we propose to incorporate thresholding in the network to perform support selection, which is easy to implement and able to boost the convergence rate both theoretically and empirically. Extensive simulations, including sparse vector recovery and a compressive sensing experiment on real image data, corroborate our theoretical results and demonstrate their practical usefulness. We have made our codes publicly available: https://github.com/xchen-tamu/linear-lista-cpss.