arXiv subjects

Tetiana Parshakova

Publications and source records attributed to Tetiana Parshakova.

11 recordsLinked to original sources

arXiv2026

SoftServe: A Scalable Quasi-Newton Method for Deep Learning

Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limited their use in deep learning: non-convexity and enormous parameter sizes. We introduce SoftServe, a family of QN methods designed to overcome these obstacles without line searches or ad hoc curvature corrections. SoftServe derives positivedefinite curvature estimates from the variational objective of Berglund et al. (2025), even in the presence of negative curvature. We develop diagonal and Kroneckerfactored variants that preserve positive definiteness by construction and scale to massive neural networks. Finally, SoftServe relies on the stable coupled Newton-Schulz iteration for the required matrix operations, replacing costly matrix decompositions with GPU-friendly matrix multiplications. SoftServe excels on problems that are severely ill-conditioned, including tasks such as recurrent networks, deep autoencoders, physics-informed neural networks, and a 136M-parameter physics-informed diffusion model, often achieving lower losses than established baselines including Adam, Muon, and SOAP.

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arXiv2026

PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer

Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices. These matrices are usually trained with Adam, which treats them as a single flat vector of parameters and ignores both the matrix and product structure of LoRA. Applying a matrix-aware optimizer such as Muon to each factor does not consistently improve over Adam, and neither do the product-aware Muon variants proposed in concurrent works. To realize consistent gains, we introduce PoLoRA, a Preconditioned Orthogonalized LoRA optimizer built from three ingredients: a product-aware spectral update direction, curvature preconditioning derived from controlling the per-sample loss change, and a magnitude rule that controls the sizes of both the factor and merged updates. We evaluate PoLoRA on instruction-tuning datasets for code and math across models from 1B to 8B parameters, and find that it reaches the final held-out loss achieved by tuned Adam in 1.2-1.7 times fewer steps, while adding at most 3% per-step overhead. Compared to Adam, PoLoRA is also less sensitive to the learning rate, and its optimal learning rate is stable across ranks.

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arXiv2026

Muon Does Not Converge on Convex Lipschitz Functions

Muon and its variants have shown strong empirical performance in a variety of deep learning tasks. Existing convergence analyses of Muon rely on smoothness assumptions, though arguably the most successful function class for developing deep learning methods (such as AdaGrad, Shampoo, Schedule-Free and more) has been the class of convex and Lipschitz functions. In this paper we question whether the classical convex Lipschitz model is a useful one for understanding Muon. Our answer is no. We show that Muon does not converge on the class of convex and Lipschitz functions, regardless of the choice of learning rate schedule. We also show that error feedback restores convergence of Muon and all the non-Euclidean subgradient methods with momentum. However, this theoretical fix using error feedback degrades the performance of Muon in two representative settings for image classification (CIFAR-10) and language modeling (nanoGPT on FineWeb-Edu 10B). Our conclusion is that convex Lipschitz theory, despite having a prominent role in the design of practical methods for deep learning, is not the most suited one for Muon. This suggests that Muon's success must come from structure absent from this model, most plausibly related to smoothness.

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arXiv2026

Multiple Approximate-Response Agents (MARA): Fast Near-Optimal Primal Recovery for Distributed Optimization

Dual methods are useful for distributed optimization because they allow agent-level subproblems to be solved in parallel. However, achieving primal feasibility with dual methods is a challenge; it can take many iterations to find prices that recover primal feasibility, and even with optimal dual prices primal feasibility is not guaranteed unless special conditions like strict convexity hold. To address this limitation, we propose a simple primal recovery method, multiple approximate-response agents (MARA), that is able to rapidly reduce primal infeasibility, tolerating some degree of suboptimality. The method is agnostic to how dual prices are computed, so MARA can be applied to enhance any dual algorithm. Rather than returning a single primal response to each price query, MARA requires agents to generate multiple primal responses, each of which has bounded suboptimality. Because these multiple responses can be computed in parallel, there is no increase in the wall-clock time of the underlying dual algorithm. MARA then constructs a convex combination of the multiple responses by minimizing the sum of the primal and complementary slackness residuals to produce a high-quality primal solution. Tests of MARA using both a price localization method and a dual subgradient method show that it typically converges to a feasible, near-optimal solution in a few tens of iterations. Moreover, hyperparameters of MARA can be flexibly tuned to control the trade-off among speed, computational budget, and degree of suboptimality of the feasible solutions.

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arXiv2025

Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices

We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low rank matrices but share many of their properties, such as the total storage required and complexity of matrix-vector multiplication. We address three problems that arise in fitting a given matrix by an MLR matrix in the Frobenius norm. The first problem is factor fitting, where we adjust the factors of the MLR matrix. The second is rank allocation, where we choose the ranks of the blocks in each level, subject to the total rank having a given value, which preserves the total storage needed for the MLR matrix. The final problem is to choose the hierarchical partition of rows and columns, along with the ranks and factors. This paper is accompanied by an open source package that implements the proposed methods.

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arXiv2025

Fitting Multilevel Factor Models

We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization algorithm, tailored for multilevel factor models, to maximize the likelihood of the observed data. This method accommodates any hierarchical structure and maintains linear time and storage complexities per iteration. This is achieved through a new efficient technique for computing the inverse of the positive definite MLR matrix. We show that the inverse of positive definite MLR matrix is also an MLR matrix with the same sparsity in factors, and we use the recursive Sherman-Morrison-Woodbury matrix identity to obtain the factors of the inverse. Additionally, we present an algorithm that computes the Cholesky factorization of an expanded matrix with linear time and space complexities, yielding the covariance matrix as its Schur complement. This paper is accompanied by an open-source package that implements the proposed methods.

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arXiv2025

Optimization Algorithm Design via Electric Circuits

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynamics converge to the solution of the optimization problem at hand. Then, the second stage is an automated, computer-assisted discretization of the continuous-time dynamics, yielding a provably convergent discrete-time algorithm. Our methodology recovers many classical (distributed) optimization algorithms and enables users to quickly design and explore a wide range of new algorithms with convergence guarantees.

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arXiv2023

Efficient Graph Field Integrators Meet Point Clouds

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

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arXiv2023

Implementation of an Oracle-Structured Bundle Method for Distributed Optimization

We consider the problem of minimizing a function that is a sum of convex agent functions plus a convex common public function that couples them. The agent functions can only be accessed via a subgradient oracle; the public function is assumed to be structured and expressible in a domain specific language (DSL) for convex optimization. We focus on the case when the evaluation of the agent oracles can require significant effort, which justifies the use of solution methods that carry out significant computation in each iteration. To solve this problem we integrate multiple known techniques (or adaptations of known techniques) for bundle-type algorithms, obtaining a method which has a number of practical advantages over other methods that are compatible with our access methods, such as proximal subgradient methods. First, it is reliable, and works well across a number of applications. Second, it has very few parameters that need to be tuned, and works well with sensible default values. Third, it typically produces a reasonable approximate solution in just a few tens of iterations. This paper is accompanied by an open-source implementation of the proposed solver, available at \url{https://github.com/cvxgrp/OSBDO}.

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arXiv2019

Distributional Reinforcement Learning for Energy-Based Sequential Models

Global Autoregressive Models (GAMs) are a recent proposal [Parshakova et al., CoNLL 2019] for exploiting global properties of sequences for data-efficient learning of seq2seq models. In the first phase of training, an Energy-Based model (EBM) over sequences is derived. This EBM has high representational power, but is unnormalized and cannot be directly exploited for sampling. To address this issue [Parshakova et al., CoNLL 2019] proposes a distillation technique, which can only be applied under limited conditions. By relating this problem to Policy Gradient techniques in RL, but in a \emph{distributional} rather than \emph{optimization} perspective, we propose a general approach applicable to any sequential EBM. Its effectiveness is illustrated on GAM-based experiments.

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arXiv2019

Global Autoregressive Models for Data-Efficient Sequence Learning

Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an autoregressive component with a log-linear component, allowing the use of global \textit{a priori} features to compensate for lack of data. We train these models in two steps. In the first step, we obtain an \emph{unnormalized} GAM that maximizes the likelihood of the data, but is improper for fast inference or evaluation. In the second step, we use this GAM to train (by distillation) a second autoregressive model that approximates the \emph{normalized} distribution associated with the GAM, and can be used for fast inference and evaluation. Our experiments focus on language modelling under synthetic conditions and show a strong perplexity reduction of using the second autoregressive model over the standard one.

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