Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include \textit{graph sparsification} that samples a subgraph to reduce the amount of data aggregation and \textit{model sparsification} that prunes the neural network to reduce the number of trainable weights. Despite the empirical successes in reducing the training cost while maintaining the test accuracy, the theoretical generalization analysis of sparse learning for GNNs remains elusive. To the best of our knowledge, this paper provides the first theoretical characterization of joint edge-model sparse learning from the perspective of sample complexity and convergence rate in achieving zero generalization error. It proves analytically that both sampling important nodes and pruning neurons with the lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy. Although the analysis is centered on two-layer GNNs with structural constraints on data, the insights are applicable to more general setups and justified by both synthetic and practical citation datasets.
Advanced visual localization techniques encompass image retrieval challenges and 6 Degree-of-Freedom (DoF) camera pose estimation, such as hierarchical localization. Thus, they must extract global and local features from input images. Previous methods have achieved this through resource-intensive or accuracy-reducing means, such as combinatorial pipelines or multi-task distillation. In this study, we present a novel method called SuperGF, which effectively unifies local and global features for visual localization, leading to a higher trade-off between localization accuracy and computational efficiency. Specifically, SuperGF is a transformer-based aggregation model that operates directly on image-matching-specific local features and generates global features for retrieval. We conduct experimental evaluations of our method in terms of both accuracy and efficiency, demonstrating its advantages over other methods. We also provide implementations of SuperGF using various types of local features, including dense and sparse learning-based or hand-crafted descriptors.
$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to solve this problem. However, first-order gradients of the objective function may be either unavailable or expensive to calculate in a lot of real-world problems, where zeroth-order (ZO) gradients could be a good surrogate. Unfortunately, whether ZO gradients can work with the hard-thresholding operator is still an unsolved problem. To solve this puzzle, in this paper, we focus on the $\ell_0$ constrained black-box stochastic optimization problems, and propose a new stochastic zeroth-order gradient hard-thresholding (SZOHT) algorithm with a general ZO gradient estimator powered by a novel random support sampling. We provide the convergence analysis of SZOHT under standard assumptions. Importantly, we reveal a conflict between the deviation of ZO estimators and the expansivity of the hard-thresholding operator, and provide a theoretical minimal value of the number of random directions in ZO gradients. In addition, we find that the query complexity of SZOHT is independent or weakly dependent on the dimensionality under different settings. Finally, we illustrate the utility of our method on a portfolio optimization problem as well as black-box adversarial attacks.
Recently, convolutional auto-encoders (CAE) were introduced for image coding. They achieved performance improvements over the state-of-the-art JPEG2000 method. However, these performances were obtained using massive CAEs featuring a large number of parameters and whose training required heavy computational power.\\ In this paper, we address the problem of lossy image compression using a CAE with a small memory footprint and low computational power usage. In order to overcome the computational cost issue, the majority of the literature uses Lagrangian proximal regularization methods, which are time consuming themselves.\\ In this work, we propose a constrained approach and a new structured sparse learning method. We design an algorithm and test it on three constraints: the classical $\ell_1$ constraint, the $\ell_{1,\infty}$ and the new $\ell_{1,1}$ constraint. Experimental results show that the $\ell_{1,1}$ constraint provides the best structured sparsity, resulting in a high reduction of memory and computational cost, with similar rate-distortion performance as with dense networks.
Edge devices can benefit remarkably from federated learning due to their distributed nature; however, their limited resource and computing power poses limitations in deployment. A possible solution to this problem is to utilize off-the-shelf sparse learning algorithms at the clients to meet their resource budget. However, such naive deployment in the clients causes significant accuracy degradation, especially for highly resource-constrained clients. In particular, our investigations reveal that the lack of consensus in the sparsity masks among the clients may potentially slow down the convergence of the global model and cause a substantial accuracy drop. With these observations, we present \textit{federated lottery aware sparsity hunting} (FLASH), a unified sparse learning framework for training a sparse sub-model that maintains the performance under ultra-low parameter density while yielding proportional communication benefits. Moreover, given that different clients may have different resource budgets, we present \textit{hetero-FLASH} where clients can take different density budgets based on their device resource limitations instead of supporting only one target parameter density. Experimental analysis on diverse models and datasets shows the superiority of FLASH in closing the gap with an unpruned baseline while yielding up to $\mathord{\sim}10.1\%$ improved accuracy with $\mathord{\sim}10.26\times$ fewer communication, compared to existing alternatives, at similar hyperparameter settings. Code is available at \url{https://github.com/SaraBabakN/flash_fl}.
Extracting governing physics from data is a key challenge in many areas of science and technology. The existing techniques for equations discovery are dependent on both input and state measurements; however, in practice, we only have access to the output measurements only. We here propose a novel framework for learning governing physics of dynamical system from output only measurements; this essentially transfers the physics discovery problem from the deterministic to the stochastic domain. The proposed approach models the input as a stochastic process and blends concepts of stochastic calculus, sparse learning algorithms, and Bayesian statistics. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data. The resulting model is highly efficient and works with sparse, noisy, and incomplete output measurements. The efficacy and robustness of the proposed approach is illustrated on several numerical examples involving both complete and partial state measurements. The results obtained indicate the potential of the proposed approach in identifying governing physics from output only measurement.
The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus on the task of controlling the level of sparsity when performing sparse learning. Existing methods based on sparsity-inducing penalties involve expensive trial-and-error tuning of the penalty factor, thus lacking direct control of the resulting model sparsity. In response, we adopt a constrained formulation: using the gate mechanism proposed by Louizos et al. (2018), we formulate a constrained optimization problem where sparsification is guided by the training objective and the desired sparsity target in an end-to-end fashion. Experiments on CIFAR-{10, 100}, TinyImageNet, and ImageNet using WideResNet and ResNet{18, 50} models validate the effectiveness of our proposal and demonstrate that we can reliably achieve pre-determined sparsity targets without compromising on predictive performance.
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of precomputed basis functions that can be used to approximate the quantity of interest. We then design a neural network architecture to learn the coefficients of solutions in the spaces which are spanned by these basis functions. The information of the basis functions are incorporated in the loss function, which minimizes the differences between the downscaled reduced order solutions and reference solutions at multiple time steps. The network contains multiple submodules and the solutions at different time steps can be learned simultaneously. We propose some strategies in the learning framework to identify important degrees of freedom. To find a sparse solution representation, a soft thresholding operator is applied to enforce the sparsity of the output coefficient vectors of the neural network. To avoid over-simplification and enrich the approximation space, some degrees of freedom can be added back to the system through a greedy algorithm. In both scenarios, that is, removing and adding degrees of freedom, the corresponding network connections are pruned or reactivated guided by the magnitude of the solution coefficients obtained from the network outputs. The proposed adaptive learning process is applied to some toy case examples to demonstrate that it can achieve a good basis selection and accurate approximation. More numerical tests are performed on two-phase multiscale flow problems to show the capability and interpretability of the proposed method on complicated applications.
Training generative models that capture rich semantics of the data and interpreting the latent representations encoded by such models are very important problems in un-/self-supervised learning. In this work, we provide a simple algorithm that relies on perturbation experiments on latent codes of a pre-trained generative autoencoder to uncover an attribute graph that is implied by the generative model. We perform perturbation experiments to check for influence of a given latent variable on a subset of attributes. Given this, we show that one can fit an effective graphical model that models a structural equation model between latent codes taken as exogenous variables and attributes taken as observed variables. One interesting aspect is that a single latent variable controls multiple overlapping subsets of attributes unlike conventional approaches that try to impose full independence. Using a pre-trained generative autoencoder trained on a large dataset of small molecules, we demonstrate that the graphical model between various molecular attributes and latent codes learned by our algorithm can be used to predict a specific property for molecules which are drawn from a different distribution. We compare prediction models trained on various feature subsets chosen by simple baselines, as well as existing causal discovery and sparse learning/feature selection methods, with the ones in the derived Markov blanket from our method. Results show empirically that the predictor that relies on our Markov blanket attributes is robust to distribution shifts when transferred or fine-tuned with a few samples from the new distribution, especially when training data is limited.
Binary neural networks (BNNs) have demonstrated their ability to solve complex tasks with comparable accuracy as full-precision deep neural networks (DNNs), while also reducing computational power and storage requirements and increasing the processing speed. These properties make them an attractive alternative for the development and deployment of DNN-based applications in Internet-of-Things (IoT) devices. Despite the recent improvements, they suffer from a fixed and limited compression factor that may result insufficient for certain devices with very limited resources. In this work, we propose sparse binary neural networks (SBNNs), a novel model and training scheme which introduces sparsity in BNNs and a new quantization function for binarizing the network's weights. The proposed SBNN is able to achieve high compression factors and it reduces the number of operations and parameters at inference time. We also provide tools to assist the SBNN design, while respecting hardware resource constraints. We study the generalization properties of our method for different compression factors through a set of experiments on linear and convolutional networks on three datasets. Our experiments confirm that SBNNs can achieve high compression rates, without compromising generalization, while further reducing the operations of BNNs, making SBNNs a viable option for deploying DNNs in cheap, low-cost, limited-resources IoT devices and sensors.
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms of a family of $\ell_0$-regularized problems. An efficient primal-dual method has been developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.
The nervous system, more specifically, the brain, is capable of solving complex problems simply and efficiently, far surpassing modern computers. In this regard, neuromorphic engineering is a research field that focuses on mimicking the basic principles that govern the brain in order to develop systems that achieve such computational capabilities. Within this field, bio-inspired learning and memory systems are still a challenge to be solved, and this is where the hippocampus is involved. It is the region of the brain that acts as a short-term memory, allowing the learning and unstructured and rapid storage of information from all the sensory nuclei of the cerebral cortex and its subsequent recall. In this work, we propose a novel bio-inspired memory model based on the hippocampus with the ability to learn memories, recall them from a cue (a part of the memory associated with the rest of the content) and even forget memories when trying to learn others with the same cue. This model has been implemented on the SpiNNaker hardware platform using Spiking Neural Networks, and a set of experiments and tests were performed to demonstrate its correct and expected operation. The proposed spike-based memory model generates spikes only when it receives an input, being energy efficient, and it needs 7 timesteps for the learning step and 6 timesteps for recalling a previously-stored memory. This work presents the first hardware implementation of a fully functional bio-inspired spike-based hippocampus memory model, paving the road for the development of future more complex neuromorphic systems.
The paper has two major themes. The first part of the paper establishes certain general results for infinite-dimensional optimization problems on Hilbert spaces. These results cover the classical representer theorem and many of its variants as special cases and offer a wider scope of applications. The second part of the paper then develops a systematic approach for learning the drift function of a stochastic differential equation by integrating the results of the first part with Bayesian hierarchical framework. Importantly, our Baysian approach incorporates low-cost sparse learning through proper use of shrinkage priors while allowing proper quantification of uncertainty through posterior distributions. Several examples at the end illustrate the accuracy of our learning scheme.
Standard fine-tuning of large pre-trained language models (PLMs) for downstream tasks requires updating hundreds of millions to billions of parameters, and storing a large copy of the PLM weights for every task resulting in increased cost for storing, sharing and serving the models. To address this, parameter-efficient fine-tuning (PEFT) techniques were introduced where small trainable components are injected in the PLM and updated during fine-tuning. We propose AdaMix as a general PEFT method that tunes a mixture of adaptation modules -- given the underlying PEFT method of choice -- introduced in each Transformer layer while keeping most of the PLM weights frozen. For instance, AdaMix can leverage a mixture of adapters like Houlsby or a mixture of low rank decomposition matrices like LoRA to improve downstream task performance over the corresponding PEFT methods for fully supervised and few-shot NLU and NLG tasks. Further, we design AdaMix such that it matches the same computational cost and the number of tunable parameters as the underlying PEFT method. By only tuning 0.1-0.2% of PLM parameters, we show that AdaMix outperforms SOTA parameter-efficient fine-tuning and full model fine-tuning for both NLU and NLG tasks.
Federated learning (FL) enables edge devices to collaboratively learn a model in a distributed fashion. Many existing researches have focused on improving communication efficiency of high-dimensional models and addressing bias caused by local updates. However, most of FL algorithms are either based on reliable communications or assume fixed and known unreliability characteristics. In practice, networks could suffer from dynamic channel conditions and non-deterministic disruptions, with time-varying and unknown characteristics. To this end, in this paper we propose a sparsity enabled FL framework with both communication efficiency and bias reduction, termed as SAFARI. It makes novel use of a similarity among client models to rectify and compensate for bias that is resulted from unreliable communications. More precisely, sparse learning is implemented on local clients to mitigate communication overhead, while to cope with unreliable communications, a similarity-based compensation method is proposed to provide surrogates for missing model updates. We analyze SAFARI under bounded dissimilarity and with respect to sparse models. It is demonstrated that SAFARI under unreliable communications is guaranteed to converge at the same rate as the standard FedAvg with perfect communications. Implementations and evaluations on CIFAR-10 dataset validate the effectiveness of SAFARI by showing that it can achieve the same convergence speed and accuracy as FedAvg with perfect communications, with up to 80% of the model weights being pruned and a high percentage of client updates missing in each round.
With the latest advances in deep learning, there has been a lot of focus on the online learning paradigm due to its relevance in practical settings. Although many methods have been investigated for optimal learning settings in scenarios where the data stream is continuous over time, sparse networks training in such settings have often been overlooked. In this paper, we explore the problem of training a neural network with a target sparsity in a particular case of online learning: the anytime learning at macroscale paradigm (ALMA). We propose a novel way of progressive pruning, referred to as \textit{Anytime Progressive Pruning} (APP); the proposed approach significantly outperforms the baseline dense and Anytime OSP models across multiple architectures and datasets under short, moderate, and long-sequence training. Our method, for example, shows an improvement in accuracy of $\approx 7\%$ and a reduction in the generalization gap by $\approx 22\%$, while being $\approx 1/3$ rd the size of the dense baseline model in few-shot restricted imagenet training. We further observe interesting nonmonotonic transitions in the generalization gap in the high number of megabatches-based ALMA. The code and experiment dashboards can be accessed at \url{https://github.com/landskape-ai/Progressive-Pruning} and \url{https://wandb.ai/landskape/APP}, respectively.
Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm regularization decomposes the transfer function into first-order atomic models and solves a group lasso problem that selects a sparse set of poles and identifies the corresponding coefficients. The difficulty in solving the problem lies in the fact that there are an infinite number of possible atomic models. This work proposes a greedy algorithm that generates new candidate atomic models maximizing the violation of the optimality condition of the existing problem. This algorithm is able to solve the infinite-dimensional group lasso problem with high precision. The algorithm is further extended to reduce the bias and reject false positives in pole location estimation by iteratively reweighted adaptive group lasso and complementary pairs stability selection respectively. Numerical results demonstrate that the proposed algorithm performs better than benchmark parameterized and regularized methods in terms of both impulse response fitting and pole location estimation.
Sparse Transformer has recently attracted a lot of attention since the ability for reducing the quadratic dependency on the sequence length. We argue that two factors, information bottleneck sensitivity and inconsistency between different attention topologies, could affect the performance of the Sparse Transformer. This paper proposes a well-designed model named ERNIE-Sparse. It consists of two distinctive parts: (i) Hierarchical Sparse Transformer (HST) to sequentially unify local and global information. (ii) Self-Attention Regularization (SAR) method, a novel regularization designed to minimize the distance for transformers with different attention topologies. To evaluate the effectiveness of ERNIE-Sparse, we perform extensive evaluations. Firstly, we perform experiments on a multi-modal long sequence modeling task benchmark, Long Range Arena (LRA). Experimental results demonstrate that ERNIE-Sparse significantly outperforms a variety of strong baseline methods including the dense attention and other efficient sparse attention methods and achieves improvements by 2.77% (57.78% vs. 55.01%). Secondly, to further show the effectiveness of our method, we pretrain ERNIE-Sparse and verified it on 3 text classification and 2 QA downstream tasks, achieve improvements on classification benchmark by 0.83% (92.46% vs. 91.63%), on QA benchmark by 3.24% (74.67% vs. 71.43%). Experimental results continue to demonstrate its superior performance.
We present L0Learn: an open-source package for sparse linear regression and classification using $\ell_0$ regularization. L0Learn implements scalable, approximate algorithms, based on coordinate descent and local combinatorial optimization. The package is built using C++ and has user-friendly R and Python interfaces. L0Learn can address problems with millions of features, achieving competitive run times and statistical performance with state-of-the-art sparse learning packages. L0Learn is available on both CRAN and GitHub (https://cran.r-project.org/package=L0Learn and https://github.com/hazimehh/L0Learn).
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for nonconvex and nonsmooth objectives in possibly high dimensions. For sparse learning problems with a composite objective, under some regularity conditions, the obtained estimators as the surrogate's fixed points, though not necessarily local minimizers, enjoy provable statistical guarantees, and the sequence of iterates can be shown to approach the statistical truth within the desired accuracy geometrically fast. The paper also studies how to design adaptive momentum based accelerations without assuming convexity or smoothness by carefully controlling stepsize and relaxation parameters.