FRUGAL: Memory-Efficient Optimization by Reducing State Overhead for Scalable Training

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the $\textit{effective rank of the weight updates remains low-rank}$, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce $\texttt{FRUGAL}$ ($\textbf{F}$ull-$\textbf{R}$ank $\textbf{U}$pdates with $\textbf{G}$r$\textbf{A}$dient sp$\textbf{L}$itting), a new memory-efficient optimization framework. $\texttt{FRUGAL}$ leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

Accelerated Stochastic ExtraGradient: Mixing Hessian and Gradient Similarity to Reduce Communication in Distributed and Federated Learning

Modern realities and trends in learning require more and more generalization ability of models, which leads to an increase in both models and training sample size. It is already difficult to solve such tasks in a single device mode. This is the reason why distributed and federated learning approaches are becoming more popular every day. Distributed computing involves communication between devices, which requires solving two key problems: efficiency and privacy. One of the most well-known approaches to combat communication costs is to exploit the similarity of local data. Both Hessian similarity and homogeneous gradients have been studied in the literature, but separately. In this paper, we combine both of these assumptions in analyzing a new method that incorporates the ideas of using data similarity and clients sampling. Moreover, to address privacy concerns, we apply the technique of additional noise and analyze its impact on the convergence of the proposed method. The theory is confirmed by training on real datasets.

Gradient Clipping Improves AdaGrad when the Noise Is Heavy-Tailed

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the high-probability convergence of AdaGrad/Adam has not been studied in this case. In this work, we prove that AdaGrad (and its delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. To fix this issue, we propose a new version of AdaGrad called Clip-RAdaGradD (Clipped Reweighted AdaGrad with Delay) and prove its high-probability convergence bounds with polylogarithmic dependence on the confidence level for smooth convex/non-convex stochastic optimization with heavy-tailed noise. Our empirical evaluations, including NLP model fine-tuning, highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.

Local Methods with Adaptivity via Scaling

The rapid development of machine learning and deep learning has introduced increasingly complex optimization challenges that must be addressed. Indeed, training modern, advanced models has become difficult to implement without leveraging multiple computing nodes in a distributed environment. Distributed optimization is also fundamental to emerging fields such as federated learning. Specifically, there is a need to organize the training process to minimize the time lost due to communication. A widely used and extensively researched technique to mitigate the communication bottleneck involves performing local training before communication. This approach is the focus of our paper. Concurrently, adaptive methods that incorporate scaling, notably led by Adam, have gained significant popularity in recent years. Therefore, this paper aims to merge the local training technique with the adaptive approach to develop efficient distributed learning methods. We consider the classical Local SGD method and enhance it with a scaling feature. A crucial aspect is that the scaling is described generically, allowing us to analyze various approaches, including Adam, RMSProp, and OASIS, in a unified manner. In addition to theoretical analysis, we validate the performance of our methods in practice by training a neural network.

Sparse Concept Bottleneck Models: Gumbel Tricks in Contrastive Learning

We propose a novel architecture and method of explainable classification with Concept Bottleneck Models (CBMs). While SOTA approaches to Image Classification task work as a black box, there is a growing demand for models that would provide interpreted results. Such a models often learn to predict the distribution over class labels using additional description of this target instances, called concepts. However, existing Bottleneck methods have a number of limitations: their accuracy is lower than that of a standard model and CBMs require an additional set of concepts to leverage. We provide a framework for creating Concept Bottleneck Model from pre-trained multi-modal encoder and new CLIP-like architectures. By introducing a new type of layers known as Concept Bottleneck Layers, we outline three methods for training them: with $\ell_1$-loss, contrastive loss and loss function based on Gumbel-Softmax distribution (Sparse-CBM), while final FC layer is still trained with Cross-Entropy. We show a significant increase in accuracy using sparse hidden layers in CLIP-based bottleneck models. Which means that sparse representation of concepts activation vector is meaningful in Concept Bottleneck Models. Moreover, with our Concept Matrix Search algorithm we can improve CLIP predictions on complex datasets without any additional training or fine-tuning. The code is available at: https://github.com/Andron00e/SparseCBM.

Optimal Data Splitting in Distributed Optimization for Machine Learning

The distributed optimization problem has become increasingly relevant recently. It has a lot of advantages such as processing a large amount of data in less time compared to non-distributed methods. However, most distributed approaches suffer from a significant bottleneck - the cost of communications. Therefore, a large amount of research has recently been directed at solving this problem. One such approach uses local data similarity. In particular, there exists an algorithm provably optimally exploiting the similarity property. But this result, as well as results from other works solve the communication bottleneck by focusing only on the fact that communication is significantly more expensive than local computing and does not take into account the various capacities of network devices and the different relationship between communication time and local computing expenses. We consider this setup and the objective of this study is to achieve an optimal ratio of distributed data between the server and local machines for any costs of communications and local computations. The running times of the network are compared between uniform and optimal distributions. The superior theoretical performance of our solutions is experimentally validated.

Activations and Gradients Compression for Model-Parallel Training

Large neural networks require enormous computational clusters of machines. Model-parallel training, when the model architecture is partitioned sequentially between workers, is a popular approach for training modern models. Information compression can be applied to decrease workers communication time, as it is often a bottleneck in such systems. This work explores how simultaneous compression of activations and gradients in model-parallel distributed training setup affects convergence. We analyze compression methods such as quantization and TopK compression, and also experiment with error compensation techniques. Moreover, we employ TopK with AQ-SGD per-batch error feedback approach. We conduct experiments on image classification and language model fine-tuning tasks. Our findings demonstrate that gradients require milder compression rates than activations. We observe that $K=10\%$ is the lowest TopK compression level, which does not harm model convergence severely. Experiments also show that models trained with TopK perform well only when compression is also applied during inference. We find that error feedback techniques do not improve model-parallel training compared to plain compression, but allow model inference without compression with almost no quality drop. Finally, when applied with the AQ-SGD approach, TopK stronger than with $ K=30\%$ worsens model performance significantly.

Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boosting

This work considers a rather general and broad class of Markov chains, Ito chains that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one, as in most related papers. Moreover, our chain's drift and diffusion coefficient can be inexact to cover a wide range of applications such as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent, or Stochastic Gradient Boosting. We prove an upper bound for $W_{2}$-distance between laws of the Ito chain and the corresponding Stochastic Differential Equation. These results improve or cover most of the known estimates. Moreover, for some particular cases, our analysis is the first.

First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities

This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our approach covers scenarios for both non-convex and strongly convex minimization problems. To achieve an optimal (linear) dependence on the mixing time of the underlying noise sequence, we use the randomized batching scheme, which is based on the multilevel Monte Carlo method. Moreover, our technique allows us to eliminate the limiting assumptions of previous research on Markov noise, such as the need for a bounded domain and uniformly bounded stochastic gradients. Our extension to variational inequalities under Markovian noise is original. Additionally, we provide lower bounds that match the oracle complexity of our method in the case of strongly convex optimization problems.

Sarah Frank-Wolfe: Methods for Constrained Optimization with Best Rates and Practical Features

The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient is prohibitively expensive. In this paper, we present two new variants of the FW algorithms for stochastic finite-sum minimization. Our algorithms have the best convergence guarantees of existing stochastic FW approaches for both convex and non-convex objective functions. Our methods do not have the issue of permanently collecting large batches, which is common to many stochastic projection-free approaches. Moreover, our second approach does not require either large batches or full deterministic gradients, which is a typical weakness of many techniques for finite-sum problems. The faster theoretical rates of our approaches are confirmed experimentally.