arXiv subjects

Anastasios Kyrillidis

Publications and source records attributed to Anastasios Kyrillidis.

At least 55 records · Page 3Linked to original sources

arXiv2023

How much pre-training is enough to discover a good subnetwork?

Neural network pruning is useful for discovering efficient, high-performing subnetworks within pre-trained, dense network architectures. More often than not, it involves a three-step process -- pre-training, pruning, and re-training -- that is computationally expensive, as the dense model must be fully pre-trained. While previous work has revealed through experiments the relationship between the amount of pre-training and the performance of the pruned network, a theoretical characterization of such dependency is still missing. Aiming to mathematically analyze the amount of dense network pre-training needed for a pruned network to perform well, we discover a simple theoretical bound in the number of gradient descent pre-training iterations on a two-layer, fully-connected network, beyond which pruning via greedy forward selection [61] yields a subnetwork that achieves good training error. Interestingly, this threshold is shown to be logarithmically dependent upon the size of the dataset, meaning that experiments with larger datasets require more pre-training for subnetworks obtained via pruning to perform well. Lastly, we empirically validate our theoretical results on a multi-layer perceptron trained on MNIST.

stat.ML↗

arXiv2023

Convergence and Stability of the Stochastic Proximal Point Algorithm with Momentum

Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes with gradient noise, often leading to specific step size and momentum choices in order to guarantee convergence, set aside acceleration. Proximal point methods, on the other hand, have gained much attention due to their numerical stability and elasticity against imperfect tuning. Their stochastic accelerated variants though have received limited attention: how momentum interacts with the stability of (stochastic) proximal point methods remains largely unstudied. To address this, we focus on the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM), and show that SPPAM allows a faster linear convergence to a neighborhood compared to the stochastic proximal point algorithm (SPPA) with a better contraction factor, under proper hyperparameter tuning. In terms of stability, we show that SPPAM depends on problem constants more favorably than SGDM, allowing a wider range of step size and momentum that lead to convergence.

math.OC↗

arXiv2023

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT and Max-hybrid-SAT, are fundamental optimization problems in Boolean reasoning. Existing methods for MaxSAT have been successful in solving benchmarks in CNF format. They lack, however, the ability to handle 1) (non-CNF) hybrid constraints, such as XORs and 2) generalized MaxSAT problems natively. To address this issue, we propose a novel dynamic-programming approach for solving generalized MaxSAT problems with hybrid constraints -- called \emph{Dynamic-Programming-MaxSAT} or DPMS for short -- based on Algebraic Decision Diagrams (ADDs). With the power of ADDs and the (graded) project-join-tree builder, our versatile framework admits many generalizations of CNF-MaxSAT, such as MaxSAT, Min-MaxSAT, and MinSAT with hybrid constraints. Moreover, DPMS scales provably well on instances with low width. Empirical results indicate that DPMS is able to solve certain problems quickly, where other algorithms based on various techniques all fail. Hence, DPMS is a promising framework and opens a new line of research that invites more investigation in the future.

cs.AI↗

arXiv2022

Cold Start Streaming Learning for Deep Networks

The ability to dynamically adapt neural networks to newly-available data without performance deterioration would revolutionize deep learning applications. Streaming learning (i.e., learning from one data example at a time) has the potential to enable such real-time adaptation, but current approaches i) freeze a majority of network parameters during streaming and ii) are dependent upon offline, base initialization procedures over large subsets of data, which damages performance and limits applicability. To mitigate these shortcomings, we propose Cold Start Streaming Learning (CSSL), a simple, end-to-end approach for streaming learning with deep networks that uses a combination of replay and data augmentation to avoid catastrophic forgetting. Because CSSL updates all model parameters during streaming, the algorithm is capable of beginning streaming from a random initialization, making base initialization optional. Going further, the algorithm's simplicity allows theoretical convergence guarantees to be derived using analysis of the Neural Tangent Random Feature (NTRF). In experiments, we find that CSSL outperforms existing baselines for streaming learning in experiments on CIFAR100, ImageNet, and Core50 datasets. Additionally, we propose a novel multi-task streaming learning setting and show that CSSL performs favorably in this domain. Put simply, CSSL performs well and demonstrates that the complicated, multi-step training pipelines adopted by most streaming methodologies can be replaced with a simple, end-to-end learning approach without sacrificing performance.

cs.LG↗

arXiv2022

Strong Lottery Ticket Hypothesis with $\varepsilon$--perturbation

The strong Lottery Ticket Hypothesis (LTH) claims the existence of a subnetwork in a sufficiently large, randomly initialized neural network that approximates some target neural network without the need of training. We extend the theoretical guarantee of the strong LTH literature to a scenario more similar to the original LTH, by generalizing the weight change in the pre-training step to some perturbation around initialization. In particular, we focus on the following open questions: By allowing an $\varepsilon$-scale perturbation on the random initial weights, can we reduce the over-parameterization requirement for the candidate network in the strong LTH? Furthermore, does the weight change by SGD coincide with a good set of such perturbation? We answer the first question by first extending the theoretical result on subset sum to allow perturbation on the candidates. Applying this result to the neural network setting, we show that such $\varepsilon$-perturbation reduces the over-parameterization requirement of the strong LTH. To answer the second question, we show via experiments that the perturbed weight achieved by the projected SGD shows better performance under the strong LTH pruning.

cs.LG↗

arXiv2022

Efficient and Light-Weight Federated Learning via Asynchronous Distributed Dropout

Asynchronous learning protocols have regained attention lately, especially in the Federated Learning (FL) setup, where slower clients can severely impede the learning process. Herein, we propose \texttt{AsyncDrop}, a novel asynchronous FL framework that utilizes dropout regularization to handle device heterogeneity in distributed settings. Overall, \texttt{AsyncDrop} achieves better performance compared to state of the art asynchronous methodologies, while resulting in less communication and training time overheads. The key idea revolves around creating ``submodels'' out of the global model, and distributing their training to workers, based on device heterogeneity. We rigorously justify that such an approach can be theoretically characterized. We implement our approach and compare it against other asynchronous baselines, both by design and by adapting existing synchronous FL algorithms to asynchronous scenarios. Empirically, \texttt{AsyncDrop} reduces the communication cost and training time, while matching or improving the final test accuracy in diverse non-i.i.d. FL scenarios.

cs.LG↗

arXiv2022

LOFT: Finding Lottery Tickets through Filter-wise Training

Recent work on the Lottery Ticket Hypothesis (LTH) shows that there exist ``\textit{winning tickets}'' in large neural networks. These tickets represent ``sparse'' versions of the full model that can be trained independently to achieve comparable accuracy with respect to the full model. However, finding the winning tickets requires one to \emph{pretrain} the large model for at least a number of epochs, which can be a burdensome task, especially when the original neural network gets larger. In this paper, we explore how one can efficiently identify the emergence of such winning tickets, and use this observation to design efficient pretraining algorithms. For clarity of exposition, our focus is on convolutional neural networks (CNNs). To identify good filters, we propose a novel filter distance metric that well-represents the model convergence. As our theory dictates, our filter analysis behaves consistently with recent findings of neural network learning dynamics. Motivated by these observations, we present the \emph{LOttery ticket through Filter-wise Training} algorithm, dubbed as \textsc{LoFT}. \textsc{LoFT} is a model-parallel pretraining algorithm that partitions convolutional layers by filters to train them independently in a distributed setting, resulting in reduced memory and communication costs during pretraining. Experiments show that \textsc{LoFT} $i)$ preserves and finds good lottery tickets, while $ii)$ it achieves non-trivial computation and communication savings, and maintains comparable or even better accuracy than other pretraining methods.

cs.LG↗

arXiv2022

On the Convergence of Shallow Neural Network Training with Randomly Masked Neurons

With the motive of training all the parameters of a neural network, we study why and when one can achieve this by iteratively creating, training, and combining randomly selected subnetworks. Such scenarios have either implicitly or explicitly emerged in the recent literature: see e.g., the Dropout family of regularization techniques, or some distributed ML training protocols that reduce communication/computation complexities, such as the Independent Subnet Training protocol. While these methods are studied empirically and utilized in practice, they often enjoy partial or no theoretical support, especially when applied on neural network-based objectives. In this manuscript, our focus is on overparameterized single hidden layer neural networks with ReLU activations in the lazy training regime. By carefully analyzing $i)$ the subnetworks' neural tangent kernel, $ii)$ the surrogate functions' gradient, and $iii)$ how we sample and combine the surrogate functions, we prove linear convergence rate of the training error -- up to a neighborhood around the optimal point -- for an overparameterized single-hidden layer perceptron with a regression loss. Our analysis reveals a dependency of the size of the neighborhood around the optimal point on the number of surrogate models and the number of local training steps for each selected subnetwork. Moreover, the considered framework generalizes and provides new insights on dropout training, multi-sample dropout training, as well as Independent Subnet Training; for each case, we provide convergence results as corollaries of our main theorem.

cs.LG↗

arXiv2022

No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for visualization or summarization of a dataset. Real world datasets often contain inherent abnormalities, e.g., repeated samples and sampling bias, that manifest imbalanced clustering. We propose to remedy such a scenario by introducing a maximal radius constraint $r$ on the clusters formed by the centroids, i.e., samples from the same cluster should not be more than $2r$ apart in terms of $\ell_2$ distance. We achieve this constraint by solving a semi-definite program, followed by a linear assignment problem with quadratic constraints. Through qualitative results, we show that our proposed method is robust towards dataset imbalances and sampling artifacts. To the best of our knowledge, ours is the first constrained k-means clustering method with hard radius constraints. Codes at https://bit.ly/kmeans-constrained

cs.LG↗

arXiv2022

Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography

We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure to characterize the state of a quantum system, which we formulate as a stochastic nonconvex smooth optimization problem. Physically, the estimation of a low-rank density matrix helps characterizing the amount of noise introduced by quantum computation. Theoretically, we prove the local convergence of Local SFGD for a general class of restricted strongly convex/smooth loss functions, i.e., Local SFGD converges locally to a small neighborhood of the global optimum at a linear rate with a constant step size, while it locally converges exactly at a sub-linear rate with diminishing step sizes. With a proper initialization, local convergence results imply global convergence. We validate our theoretical findings with numerical simulations of QST on the Greenberger-Horne-Zeilinger (GHZ) state.

quant-ph↗

arXiv2022

Distributed Learning of Deep Neural Networks using Independent Subnet Training

Distributed machine learning (ML) can bring more computational resources to bear than single-machine learning, thus enabling reductions in training time. Distributed learning partitions models and data over many machines, allowing model and dataset sizes beyond the available compute power and memory of a single machine. In practice though, distributed ML is challenging when distribution is mandatory, rather than chosen by the practitioner. In such scenarios, data could unavoidably be separated among workers due to limited memory capacity per worker or even because of data privacy issues. There, existing distributed methods will utterly fail due to dominant transfer costs across workers, or do not even apply. We propose a new approach to distributed fully connected neural network learning, called independent subnet training (IST), to handle these cases. In IST, the original network is decomposed into a set of narrow subnetworks with the same depth. These subnetworks are then trained locally before parameters are exchanged to produce new subnets and the training cycle repeats. Such a naturally "model parallel" approach limits memory usage by storing only a portion of network parameters on each device. Additionally, no requirements exist for sharing data between workers (i.e., subnet training is local and independent) and communication volume and frequency are reduced by decomposing the original network into independent subnets. These properties of IST can cope with issues due to distributed data, slow interconnects, or limited device memory, making IST a suitable approach for cases of mandatory distribution. We show experimentally that IST results in training times that are much lower than common distributed learning approaches.

cs.LG↗

arXiv2022

i-SpaSP: Structured Neural Pruning via Sparse Signal Recovery

We propose a novel, structured pruning algorithm for neural networks -- the iterative, Sparse Structured Pruning algorithm, dubbed as i-SpaSP. Inspired by ideas from sparse signal recovery, i-SpaSP operates by iteratively identifying a larger set of important parameter groups (e.g., filters or neurons) within a network that contribute most to the residual between pruned and dense network output, then thresholding these groups based on a smaller, pre-defined pruning ratio. For both two-layer and multi-layer network architectures with ReLU activations, we show the error induced by pruning with i-SpaSP decays polynomially, where the degree of this polynomial becomes arbitrarily large based on the sparsity of the dense network's hidden representations. In our experiments, i-SpaSP is evaluated across a variety of datasets (i.e., MNIST, ImageNet, and XNLI) and architectures (i.e., feed forward networks, ResNet34, MobileNetV2, and BERT), where it is shown to discover high-performing sub-networks and improve upon the pruning efficiency of provable baseline methodologies by several orders of magnitude. Put simply, i-SpaSP is easy to implement with automatic differentiation, achieves strong empirical results, comes with theoretical convergence guarantees, and is efficient, thus distinguishing itself as one of the few computationally efficient, practical, and provable pruning algorithms.

cs.LG↗

arXiv2022

Fast quantum state reconstruction via accelerated non-convex programming

We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, \texttt{MiFGD} converges \emph{provably} close to the true density matrix at an accelerated linear rate, in the absence of experimental and statistical noise, and under common assumptions. With this manuscript, we present the method, prove its convergence property and provide Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real experiments performed on an IBM's quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than state of the art approaches, with the same or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.

quant-ph↗

arXiv2022

PipeGCN: Efficient Full-Graph Training of Graph Convolutional Networks with Pipelined Feature Communication

Graph Convolutional Networks (GCNs) is the state-of-the-art method for learning graph-structured data, and training large-scale GCNs requires distributed training across multiple accelerators such that each accelerator is able to hold a partitioned subgraph. However, distributed GCN training incurs prohibitive overhead of communicating node features and feature gradients among partitions for every GCN layer during each training iteration, limiting the achievable training efficiency and model scalability. To this end, we propose PipeGCN, a simple yet effective scheme that hides the communication overhead by pipelining inter-partition communication with intra-partition computation. It is non-trivial to pipeline for efficient GCN training, as communicated node features/gradients will become stale and thus can harm the convergence, negating the pipeline benefit. Notably, little is known regarding the convergence rate of GCN training with both stale features and stale feature gradients. This work not only provides a theoretical convergence analysis but also finds the convergence rate of PipeGCN to be close to that of the vanilla distributed GCN training without any staleness. Furthermore, we develop a smoothing method to further improve PipeGCN's convergence. Extensive experiments show that PipeGCN can largely boost the training throughput (1.7x~28.5x) while achieving the same accuracy as its vanilla counterpart and existing full-graph training methods. The code is available at https://github.com/RICE-EIC/PipeGCN.

cs.LG↗

arXiv2022

GIST: Distributed Training for Large-Scale Graph Convolutional Networks

The graph convolutional network (GCN) is a go-to solution for machine learning on graphs, but its training is notoriously difficult to scale both in terms of graph size and the number of model parameters. Although some work has explored training on large-scale graphs (e.g., GraphSAGE, ClusterGCN, etc.), we pioneer efficient training of large-scale GCN models (i.e., ultra-wide, overparameterized models) with the proposal of a novel, distributed training framework. Our proposed training methodology, called GIST, disjointly partitions the parameters of a GCN model into several, smaller sub-GCNs that are trained independently and in parallel. In addition to being compatible with all GCN architectures and existing sampling techniques for efficient GCN training, GIST i) improves model performance, ii) scales to training on arbitrarily large graphs, iii) decreases wall-clock training time, and iv) enables the training of markedly overparameterized GCN models. Remarkably, with GIST, we train an astonishgly-wide 32,768-dimensional GraphSAGE model, which exceeds the capacity of a single GPU by a factor of 8x, to SOTA performance on the Amazon2M dataset.

cs.LG↗

arXiv2022

ResIST: Layer-Wise Decomposition of ResNets for Distributed Training

We propose ResIST, a novel distributed training protocol for Residual Networks (ResNets). ResIST randomly decomposes a global ResNet into several shallow sub-ResNets that are trained independently in a distributed manner for several local iterations, before having their updates synchronized and aggregated into the global model. In the next round, new sub-ResNets are randomly generated and the process repeats until convergence. By construction, per iteration, ResIST communicates only a small portion of network parameters to each machine and never uses the full model during training. Thus, ResIST reduces the per-iteration communication, memory, and time requirements of ResNet training to only a fraction of the requirements of full-model training. In comparison to common protocols, like data-parallel training and data-parallel training with local SGD, ResIST yields a decrease in communication and compute requirements, while being competitive with respect to model performance.

cs.LG↗

arXiv2021

Federated Multiple Label Hashing (FedMLH): Communication Efficient Federated Learning on Extreme Classification Tasks

Federated learning enables many local devices to train a deep learning model jointly without sharing the local data. Currently, most of federated training schemes learns a global model by averaging the parameters of local models. However, most of these training schemes suffer from high communication cost resulted from transmitting full local model parameters. Moreover, directly averaging model parameters leads to a significant performance degradation, due to the class-imbalanced non-iid data on different devices. Especially for the real life federated learning tasks involving extreme classification, (1) communication becomes the main bottleneck since the model size increases proportionally to the number of output classes; (2) extreme classification (such as user recommendation) normally have extremely imbalanced classes and heterogeneous data on different devices. To overcome this problem, we propose federated multiple label hashing (FedMLH), which leverages label hashing to simultaneously reduce the model size (up to 3.40X decrease) with communication cost (up to 18.75X decrease) and achieves significant better accuracy (up to 35.5%} relative accuracy improvement) and faster convergence rate (up to 5.5X increase) for free on the federated extreme classification tasks compared to federated average algorithm.

cs.LG↗

arXiv2021

REX: Revisiting Budgeted Training with an Improved Schedule

Deep learning practitioners often operate on a computational and monetary budget. Thus, it is critical to design optimization algorithms that perform well under any budget. The linear learning rate schedule is considered the best budget-aware schedule, as it outperforms most other schedules in the low budget regime. On the other hand, learning rate schedules -- such as the \texttt{30-60-90} step schedule -- are known to achieve high performance when the model can be trained for many epochs. Yet, it is often not known a priori whether one's budget will be large or small; thus, the optimal choice of learning rate schedule is made on a case-by-case basis. In this paper, we frame the learning rate schedule selection problem as a combination of $i)$ selecting a profile (i.e., the continuous function that models the learning rate schedule), and $ii)$ choosing a sampling rate (i.e., how frequently the learning rate is updated/sampled from this profile). We propose a novel profile and sampling rate combination called the Reflected Exponential (REX) schedule, which we evaluate across seven different experimental settings with both SGD and Adam optimizers. REX outperforms the linear schedule in the low budget regime, while matching or exceeding the performance of several state-of-the-art learning rate schedules (linear, step, exponential, cosine, step decay on plateau, and OneCycle) in both high and low budget regimes. Furthermore, REX requires no added computation, storage, or hyperparameters.

cs.LG↗