Martin Takáč

Naif Alkhunaizi, Dmitry Kamzolov, Martin Takáč et al.

Collaboration among multiple data-owning entities (e.g., hospitals) can accelerate the training process and yield better machine learning models due to the availability and diversity of data. However, privacy concerns make it challenging to exchange data while preserving confidentiality. Federated Learning (FL) is a promising solution that enables collaborative training through exchange of model parameters instead of raw data. However, most existing FL solutions work under the assumption that participating clients are \emph{honest} and thus can fail against poisoning attacks from malicious parties, whose goal is to deteriorate the global model performance. In this work, we propose a robust aggregation rule called Distance-based Outlier Suppression (DOS) that is resilient to byzantine failures. The proposed method computes the distance between local parameter updates of different clients and obtains an outlier score for each client using Copula-based Outlier Detection (COPOD). The resulting outlier scores are converted into normalized weights using a softmax function, and a weighted average of the local parameters is used for updating the global model. DOS aggregation can effectively suppress parameter updates from malicious clients without the need for any hyperparameter selection, even when the data distributions are heterogeneous. Evaluation on two medical imaging datasets (CheXpert and HAM10000) demonstrates the higher robustness of DOS method against a variety of poisoning attacks in comparison to other state-of-the-art methods. The code can be found here https://github.com/Naiftt/SPAFD.

Alexey Zemtsov, Maxim Bobrin, Alexander Nikulin et al.

Offline goal-conditioned reinforcement learning requires both long-horizon reachability estimates and local action comparisons. Dual goal representations provide value fields that capture global goal reachability, but they do not directly specify which action should be preferred at a given state. We propose Dual Advantage Fields, a policy-extraction method that turns a bilinear dual value model into a local advantage signal. Under bilinear dual parameterization, the goal embedding is the gradient of the value field with respect to the state representation. DAF learns an action-effect model that predicts the discounted feature displacement induced by an action and scores actions by the alignment between this displacement and the goal direction. In the realizable case, this score equals the goal-conditioned Bellman advantage, yielding a standard local policy-improvement guarantee. On OGBench locomotion, manipulation, and puzzle tasks, DAF improves aggregate RLiable metrics and performs strongly in settings where locally correct actions differ from direct movement toward the final goal.

Dávid Šuba, Marek Šuppa, Jozef Kubík et al.

Named Entity Recognition (NER) is a fundamental NLP tasks with a wide range of practical applications. The performance of state-of-the-art NER methods depends on high quality manually anotated datasets which still do not exist for some languages. In this work we aim to remedy this situation in Slovak by introducing WikiGoldSK, the first sizable human labelled Slovak NER dataset. We benchmark it by evaluating state-of-the-art multilingual Pretrained Language Models and comparing it to the existing silver-standard Slovak NER dataset. We also conduct few-shot experiments and show that training on a sliver-standard dataset yields better results. To enable future work that can be based on Slovak NER, we release the dataset, code, as well as the trained models publicly under permissible licensing terms at https://github.com/NaiveNeuron/WikiGoldSK.

Artem Riabinin, Andrey Veprikov, Arman Bolatov et al.

We study adaptive learning rate scheduling for norm-constrained optimizers (e.g., Muon and Lion). We introduce a generalized smoothness assumption under which local curvature decreases with the suboptimality gap and empirically verify that this behavior holds along optimization trajectories. Under this assumption, we establish convergence guarantees under an appropriate choice of learning rate, for which warm-up followed by decay arises naturally from the proof rather than being imposed heuristically. Building on this theory, we develop a practical learning rate scheduler that relies only on standard hyperparameters and adapts the warm-up duration automatically at the beginning of training. We evaluate this method on large language model pretraining with LLaMA architectures and show that our adaptive warm-up selection consistently outperforms or at least matches the best manually tuned warm-up schedules across all considered setups, without additional hyperparameter search. Our source code is available at https://github.com/brain-lab-research/llm-baselines/tree/warmup

Arman Bolatov, Artem Riabinin, Nikita Kornilov et al.

In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral matrix-sign update gives a much stronger direction at a substantially higher per-step cost. In this work, we propose LionMuon, which retains the effectiveness of Muon steps while considerably cutting the averaged iteration cost, similar to sign-based methods. It alternates between Lion's and Muon's updates on a fixed period P, sharing a single dual-EMA momentum buffer between them. The optimizer state memory therefore matches Lion and is exactly half of AdamW's. A simpler single-EMA variant, SignMuon, by itself already outperforms pure Muon. At P = 2, LionMuon Pareto-dominates Muon, Lion, Signum, and AdamW on every dataset and architecture we tested at 124M model size, reaching lower validation loss at lower compute, and the same advantage persists at 355M and 720M scale. On the theory side, we prove sharp complexity bounds under heavy-tailed noise which are governed by period-averaged smoothness and noise that interpolate between Muon's and Lion's constants. These bounds predict the compute-optimal period and the conditions under which LionMuon outruns Muon and Lion. Code: https://github.com/brain-lab-research/lion-muon

Shuang Li, William J. Swartworth, Martin Takáč et al.

Recently the "SP" (Stochastic Polyak step size) method has emerged as a competitive adaptive method for setting the step sizes of SGD. SP can be interpreted as a method specialized to interpolated models, since it solves the interpolation equations. SP solves these equation by using local linearizations of the model. We take a step further and develop a method for solving the interpolation equations that uses the local second-order approximation of the model. Our resulting method SP2 uses Hessian-vector products to speed-up the convergence of SP. Furthermore, and rather uniquely among second-order methods, the design of SP2 in no way relies on positive definite Hessian matrices or convexity of the objective function. We show SP2 is very competitive on matrix completion, non-convex test problems and logistic regression. We also provide a convergence theory on sums-of-quadratics.

Abdurakhmon Sadiev, Aleksandr Beznosikov, Abdulla Jasem Almansoori et al.

This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson's approach to approximating the diagonal of the Hessian, and couple it with several gradient-based methods to give new scaled algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work.

Egor Gladin, Maksim Lavrik-Karmazin, Karina Zainullina et al.

The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy regularized policy optimizer and Vaidya's dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.

Farshed Abdukhakimov, Chulu Xiang, Dmitry Kamzolov et al.

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning engineers with their simplicity. However, one of the weaknesses of this type of methods is the necessity to tune learning rate (step-size) for every loss function and dataset combination to solve an optimization problem and get an efficient performance in a given time budget. Stochastic Gradient Descent with Polyak Step-size (SPS) is a method that offers an update rule that alleviates the need of fine-tuning the learning rate of an optimizer. In this paper, we propose an extension of SPS that employs preconditioning techniques, such as Hutchinson's method, Adam, and AdaGrad, to improve its performance on badly scaled and/or ill-conditioned datasets.

Aleksandr Beznosikov, Aibek Alanov, Dmitry Kovalev et al.

Methods with adaptive scaling of different features play a key role in solving saddle point problems, primarily due to Adam's popularity for solving adversarial machine learning problems, including GANS training. This paper carries out a theoretical analysis of the following scaling techniques for solving SPPs: the well-known Adam and RmsProp scaling and the newer AdaHessian and OASIS based on Hutchison approximation. We use the Extra Gradient and its improved version with negative momentum as the basic method. Experimental studies on GANs show good applicability not only for Adam, but also for other less popular methods.

Eduard Gorbunov, Nazarii Tupitsa, Sayantan Choudhury et al.

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness (Zhang et al., 2020). In this paper, we focus on the class of (strongly) convex $(L_0,L_1)$-smooth functions and derive new convergence guarantees for several existing methods. In particular, we derive improved convergence rates for Gradient Descent with (Smoothed) Gradient Clipping and for Gradient Descent with Polyak Stepsizes. In contrast to the existing results, our rates do not rely on the standard smoothness assumption and do not suffer from the exponential dependency from the initial distance to the solution. We also extend these results to the stochastic case under the over-parameterization assumption, propose a new accelerated method for convex $(L_0,L_1)$-smooth optimization, and derive new convergence rates for Adaptive Gradient Descent (Malitsky and Mishchenko, 2020).

Artem Agafonov, Brahim Erraji, Martin Takáč

In the recent paper FLECS (Agafonov et al, FLECS: A Federated Learning Second-Order Framework via Compression and Sketching), the second-order framework FLECS was proposed for the Federated Learning problem. This method utilize compression of sketched Hessians to make communication costs low. However, the main bottleneck of FLECS is gradient communication without compression. In this paper, we propose the modification of FLECS with compressed gradient differences, which we call FLECS-CGD (FLECS with Compressed Gradient Differences) and make it applicable for stochastic optimization. Convergence guarantees are provided in strongly convex and nonconvex cases. Experiments show the practical benefit of proposed approach.

Aleksandr Beznosikov, Martin Takáč, Alexander Gasnikov

Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, and fixed point problems as special cases. Therefore, variational inequalities are used in various applications ranging from equilibrium search to adversarial learning. With the increasing size of data and models, today's instances demand parallel and distributed computing for real-world machine learning problems, most of which can be represented as variational inequalities. Meanwhile, most distributed approaches have a significant bottleneck - the cost of communications. The three main techniques to reduce the total number of communication rounds and the cost of one such round are the similarity of local functions, compression of transmitted information, and local updates. In this paper, we combine all these approaches. Such a triple synergy did not exist before for variational inequalities and saddle problems, nor even for minimization problems. The methods presented in this paper have the best theoretical guarantees of communication complexity and are significantly ahead of other methods for distributed variational inequalities. The theoretical results are confirmed by adversarial learning experiments on synthetic and real datasets.

Nazarii Tupitsa, Abdulla Jasem Almansoori, Yanlin Wu et al.

Robustness to Byzantine attacks is a necessity for various distributed training scenarios. When the training reduces to the process of solving a minimization problem, Byzantine robustness is relatively well-understood. However, other problem formulations, such as min-max problems or, more generally, variational inequalities, arise in many modern machine learning and, in particular, distributed learning tasks. These problems significantly differ from the standard minimization ones and, therefore, require separate consideration. Nevertheless, only one work (Adibi et al., 2022) addresses this important question in the context of Byzantine robustness. Our work makes a further step in this direction by providing several (provably) Byzantine-robust methods for distributed variational inequality, thoroughly studying their theoretical convergence, removing the limitations of the previous work, and providing numerical comparisons supporting the theoretical findings.

Asma Ahmed Hashmi, Aigerim Zhumabayeva, Nikita Kotelevskii et al.

The success of Deep Neural Network (DNN) models significantly depends on the quality of provided annotations. In medical image segmentation, for example, having multiple expert annotations for each data point is common to minimize subjective annotation bias. Then, the goal of estimation is to filter out the label noise and recover the ground-truth masks, which are not explicitly given. This paper proposes a probabilistic model for noisy observations that allows us to build a confident classification and segmentation models. To accomplish it, we explicitly model label noise and introduce a new information-based regularization that pushes the network to recover the ground-truth labels. In addition, for segmentation task we adjust the loss function by prioritizing learning in high-confidence regions where all the annotators agree on labeling. We evaluate the proposed method on a series of classification tasks such as noisy versions of MNIST, CIFAR-10, Fashion-MNIST datasets as well as CIFAR-10N, which is real-world dataset with noisy human annotations. Additionally, for segmentation task, we consider several medical imaging datasets, such as, LIDC and RIGA that reflect real-world inter-variability among multiple annotators. Our experiments show that our algorithm outperforms state-of-the-art solutions for the considered classification and segmentation problems.

Rachael Tappenden, Martin Takáč

This work shows that applying Gradient Descent (GD) with a fixed step size to minimize a (possibly nonconvex) quadratic function is equivalent to running the Power Method (PM) on the gradients. The connection between GD with a fixed step size and the PM, both with and without fixed momentum, is thus established. Consequently, valuable eigen-information is available via GD. Recent examples show that GD with a fixed step size, applied to locally quadratic nonconvex functions, can take exponential time to escape saddle points (Simon S. Du, Chi Jin, Jason D. Lee, Michael I. Jordan, Aarti Singh, and Barnabas Poczos: "Gradient descent can take exponential time to escape saddle points"; S. Paternain, A. Mokhtari, and A. Ribeiro: "A newton-based method for nonconvex optimization with fast evasion of saddle points"). Here, those examples are revisited and it is shown that eigenvalue information was missing, so that the examples may not provide a complete picture of the potential practical behaviour of GD. Thus, ongoing investigation of the behaviour of GD on nonconvex functions, possibly with an \emph{adaptive} or \emph{variable} step size, is warranted. It is shown that, in the special case of a quadratic in $R^2$, if an eigenvalue is known, then GD with a fixed step size will converge in two iterations, and a complete eigen-decomposition is available. By considering the dynamics of the gradients and iterates, new step size strategies are proposed to improve the practical performance of GD. Several numerical examples are presented, which demonstrate the advantages of exploiting the GD--PM connection.

Meir Roketlishvili, Semyon Semenov, Maksim Bobrin et al.

Compositional energy-based models can generalize to larger combinatorial reasoning problems by reusing a learned factor energy across many local constraints. In our paper, we show that a key bottleneck in compositional reasoning is not composition itself, but the non-convex geometry of the learned energy landscape. To solve this problem, we introduce Convex Compositional Energy Minimization (CCEM), a framework that parameterizes each factor with an input-convex neural network and optimizes the composed energy over a tight convex relaxation of the feasible set. Because convexity is preserved under summation, the global relaxed objective remains convex, enabling deterministic projected first-order optimization. CCEM is trained in two stages: factor-level contrastive learning to shape local energy basins, followed by end-to-end refinement through an unrolled projected solver. Our experiments show that our models trained on small subproblems or a single problem size transfer to larger instances without retraining.

Aleksandr Beznosikov, Georgiy Kormakov, Alexander Grigorievskiy et al.

The objective of Vertical Federated Learning (VFL) is to collectively train a model using features available on different devices while sharing the same users. This paper focuses on the saddle point reformulation of the VFL problem via the classical Lagrangian function. We first demonstrate how this formulation can be solved using deterministic methods. More importantly, we explore various stochastic modifications to adapt to practical scenarios, such as employing compression techniques for efficient information transmission, enabling partial participation for asynchronous communication, and utilizing coordinate selection for faster local computation. We show that the saddle point reformulation plays a key role and opens up possibilities to use mentioned extension that seem to be impossible in the standard minimization formulation. Convergence estimates are provided for each algorithm, demonstrating their effectiveness in addressing the VFL problem. Additionally, alternative reformulations are investigated, and numerical experiments are conducted to validate performance and effectiveness of the proposed approach.

Yanda Li, Yuhan Liu, Zirui Song et al.

Large audio-language models (LALMs) generalize across speech, sound, and music, but unified decoders can exhibit a \emph{temporal smoothing bias}: transient acoustic cues may be underutilized in favor of temporally smooth context that is better supported by language priors, leading to less specific audio-grounded outputs. We propose \emph{Temporal Contrastive Decoding} (TCD), a training-free decoding method for unified LALMs that mitigates this effect at inference time. TCD constructs a temporally blurred slow-path view by smoothing the input waveform and re-encoding it, then contrasts next-token logits from the original and slow-path views. The contrastive signal is applied as a token-level logit update restricted to a small candidate set. A self-normalized stability score sets the blur window and update scale, and a step-wise gate based on uncertainty and audio reliance activates the update only when needed. Experiments on MMAU and AIR-Bench show consistent improvements on strong unified LALMs. We further conduct ablations and an architectural applicability study to analyze the contributions of key components and how TCD behaves across large audio-language model designs.

Abdulla Jasem Almansoori, Maria Ivanova, Andrey Veprikov et al.

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. In this work, we address the gap between training with full steps with low-rank projections (SVDLoRA) and LoRA fine-tuning. We propose LoRSum, a memory-efficient subroutine that closes this gap for gradient descent by casting LoRA optimization as a proximal sub-problem and solving it efficiently with alternating least squares updates, which we prove to be an implicit block power method. We recover several recently proposed preconditioning methods for LoRA as special cases, and show that LoRSum can also be used for updating a low-rank momentum. In order to address full steps with preconditioned gradient descent, we propose a scaled variant of LoRSum that uses structured metrics such as K-FAC and Shampoo, and we show that storing the diagonal of these metrics still allows them to perform well while remaining memory-efficient. Experiments on a synthetic task, CIFAR-100, and language-model fine-tuning on GLUE, SQuAD v2, and WikiText-103, show that our method can match or improve LoRA baselines given modest compute overhead, while avoiding full-matrix SVD projections and retaining LoRA-style parameter efficiency.

Abdulla Jasem Almansoori, Samuel Horváth, Martin Takáč

Federated learning has become a popular machine learning paradigm with many potential real-life applications, including recommendation systems, the Internet of Things (IoT), healthcare, and self-driving cars. Though most current applications focus on classification-based tasks, learning personalized generative models remains largely unexplored, and their benefits in the heterogeneous setting still need to be better understood. This work proposes a novel architecture combining global client-agnostic and local client-specific generative models. We show that using standard techniques for training federated models, our proposed model achieves privacy and personalization by implicitly disentangling the globally consistent representation (i.e. content) from the client-dependent variations (i.e. style). Using such decomposition, personalized models can generate locally unseen labels while preserving the given style of the client and can predict the labels for all clients with high accuracy by training a simple linear classifier on the global content features. Furthermore, disentanglement enables other essential applications, such as data anonymization, by sharing only the content. Extensive experimental evaluation corroborates our findings, and we also discuss a theoretical motivation for the proposed approach.

Omar Choukrani, Idriss Malek, Daniil Orel et al.

Assessing the capacity of Large Language Models (LLMs) to plan and reason within the constraints of interactive environments is crucial for developing capable AI agents. We introduce $\textbf{LLM-BabyBench}$, a new benchmark suite designed specifically for this purpose. Built upon a textual adaptation of the procedurally generated BabyAI grid world, this suite evaluates LLMs on three fundamental aspects of grounded intelligence: (1) predicting the consequences of actions on the environment state ($\textbf{Predict}$ task), (2) generating sequences of low-level actions to achieve specified objectives ($\textbf{Plan}$ task), and (3) decomposing high-level instructions into coherent subgoal sequences ($\textbf{Decompose}$ task). We detail the methodology for generating the three corresponding datasets ($\texttt{LLM-BabyBench-Predict}$, $\texttt{-Plan}$, $\texttt{-Decompose}$) by extracting structured information from an expert agent operating within the text-based environment. Furthermore, we provide a standardized evaluation harness and metrics, including environment interaction for validating generated plans, to facilitate reproducible assessment of diverse LLMs. Initial baseline results highlight the challenges posed by these grounded reasoning tasks. The benchmark suite, datasets, data generation code, and evaluation code are made publicly available ($\href{https://github.com/choukrani/llm-babybench}{\text{GitHub}}$, $\href{https://huggingface.co/datasets/salem-mbzuai/LLM-BabyBench}{\text{HuggingFace}}$).

Mohannad Takrouri, Nicolás M. Cuadrado, Martin Takáč

Machine learning (ML) is increasingly vital for smart-grid research, yet restricted access to realistic, diverse data - often due to privacy concerns - slows progress and fuels doubts within the energy sector about adopting ML-based strategies. We propose integrating Large Language Models (LLMs) in energy modeling to generate realistic, culturally sensitive, and behavior-specific data for household energy usage across diverse geographies. In this study, we employ and compare five different LLMs to systematically produce family structures, weather patterns, and daily consumption profiles for households in six distinct countries. A four-stage methodology synthesizes contextual daily data, including culturally nuanced activities, realistic weather ranges, HVAC operations, and distinct `energy signatures' that capture unique consumption footprints. Additionally, we explore an alternative strategy where external weather datasets can be directly integrated, bypassing intermediate weather modeling stages while ensuring physically consistent data inputs. The resulting dataset provides insights into how cultural, climatic, and behavioral factors converge to shape carbon emissions, offering a cost-effective avenue for scenario-based energy optimization. This approach underscores how prompt engineering, combined with knowledge distillation, can advance sustainable energy research and climate mitigation efforts. Source code is available at https://github.com/Singularity-AI-Lab/LLM-Energy-Knowledge-Distillation .

Alexander Yukhimchuk, Mladen Kolar, Martin Takáč et al.

Gradient clipping is a standard safeguard for training neural networks under noisy, heavy-tailed stochastic gradients; yet, most clipping rules treat all parameters as vectors and ignore the matrix structure of modern architectures. We show empirically that data outliers often amplify only a small number of leading singular values in layer-wise gradient matrices, while the rest of the spectrum remains largely unchanged. Motivated by this phenomenon, we propose spectral clipping, which stabilizes training by clamping singular values that exceed a threshold while preserving the singular directions. This framework generalizes classical gradient norm clipping and can be easily integrated into existing optimizers. We provide a convergence analysis for non-convex optimization with spectrally clipped SGD, yielding the optimal $\mathcal{O}\left(K^{\frac{2 - 2α}{3α- 2}}\right)$ rate for heavy-tailed noise. To minimize hyperparameter tuning, we introduce layer-wise adaptive thresholds based on moving averages or sliding-window quantiles of the top singular values. Finally, we develop efficient implementations that clip only the top $r$ singular values via randomized truncated SVD, avoiding full decompositions for large layers. We demonstrate competitive performance across synthetic heavy-tailed settings and neural network training tasks.

Sayantan Choudhury, Xiaoran Cheng, Martin Takáč et al.

Most first-order optimizers treat matrix-valued parameters as vectors, ignoring the intrinsic geometry of hidden-layer weights in neural networks. Muon addresses this mismatch by updating along the polar factor of a momentum matrix, but its theoretical understanding has lagged behind practice. In particular, practical implementations incorporate Nesterov momentum, compute the polar factor only approximately, and operate with stochastic gradients that may be heavy-tailed. We close this gap by developing a convergence theory for Muon with Nesterov momentum and inexact polar decomposition in non-convex matrix optimization under heavy-tailed noise. Our analysis builds on a unified framework for inexact polar decomposition that captures practical iterative approximations such as Newton-Schulz and quantifies how their errors propagate through the optimization dynamics. Under this framework, we establish an optimal iteration and sample complexity of $O \left(\varepsilon^{\frac{-(3α-2)}{(α-1)}} \right)$ for finding an $\varepsilon$-stationary point, where $α\in(1,2]$ denotes the heavy-tail index. For the inexact-polar setting with $σ_1=0$, we also provide guarantees that do not require prior knowledge of $α$. We analyze a randomized low-rank polar decomposition that is substantially more efficient than full-space methods while remaining compatible with our theory. Numerical experiments further demonstrate the effectiveness of the proposed inexact and randomized variants.

Andrey Veprikov, Arman Bolatov, Samuel Horváth et al.

Optimization lies at the core of modern deep learning, yet existing methods often face a fundamental trade-off between adapting to problem geometry and leveraging curvature utilization. Steepest descent algorithms adapt to different geometries through norm choices but remain strictly first-order, whereas quasi-Newton and adaptive optimizers incorporate curvature information but are restricted to Frobenius geometry, limiting their applicability across diverse architectures. In this work, we propose a unified framework generalizing steepest descent, quasi-Newton methods, and adaptive methods through the novel notion of preconditioned matrix norms. This abstraction reveals that widely used optimizers such as SGD and Adam, as well as more advanced approaches like Muon and KL-Shampoo, and recent hybrids including SOAP and SPlus, all emerge as special cases of the same principle. Within this framework, we provide the first systematic treatment of affine and scale invariance in the matrix-parameterized setting, establishing necessary and sufficient conditions under generalized norms. Building on this foundation, we introduce two new methods, $\texttt{MuAdam}$ and $\texttt{MuAdam-SANIA}$, which combine the spectral geometry of Muon with Adam-style preconditioning. Our experiments demonstrate that these optimizers are competitive with, and in some cases outperform, existing state-of-the-art methods. Our code is available at https://github.com/brain-lab-research/LIB/tree/quasi_descent

Ivo Gollini Navarrete, Nicolas Mauricio Cuadrado, Jose Renato Restom et al.

Pruning offers a promising solution to mitigate the associated costs and environmental impact of deploying large deep neural networks (DNNs). Traditional approaches rely on computationally expensive trained models or time-consuming iterative prune-retrain cycles, undermining their utility in resource-constrained settings. To address this issue, we build upon the established principles of saliency (LeCun et al., 1989) and connection sensitivity (Lee et al., 2018) to tackle the challenging problem of one-shot pruning neural networks (NNs) before training (PBT) at initialization. We introduce Fisher-Taylor Sensitivity (FTS), a computationally cheap and efficient pruning criterion based on the empirical Fisher Information Matrix (FIM) diagonal, offering a viable alternative for integrating first- and second-order information to identify a model's structurally important parameters. Although the FIM-Hessian equivalency only holds for convergent models that maximize the likelihood, recent studies (Karakida et al., 2019) suggest that, even at initialization, the FIM captures essential geometric information of parameters in overparameterized NNs, providing the basis for our method. Finally, we demonstrate empirically that layer collapse, a critical limitation of data-dependent pruning methodologies, is easily overcome by pruning within a single training epoch after initialization. We perform experiments on ResNet18 and VGG19 with CIFAR-10 and CIFAR-100, widely used benchmarks in pruning research. Our method achieves competitive performance against state-of-the-art techniques for one-shot PBT, even under extreme sparsity conditions. Our code is made available to the public.

Munachiso Nwadike, Zangir Iklassov, Toluwani Aremu et al.

We introduce the concept of the self-referencing causal cycle (abbreviated RECALL) - a mechanism that enables large language models (LLMs) to bypass the limitations of unidirectional causality, which underlies a phenomenon known as the reversal curse. When an LLM is prompted with sequential data, it often fails to recall preceding context. For example, when we ask an LLM to recall the line preceding "O say does that star-spangled banner yet wave" in the U.S. National Anthem, it often fails to correctly return "Gave proof through the night that our flag was still there" - this is due to the reversal curse. It occurs because language models such as ChatGPT and Llama generate text based on preceding tokens, requiring facts to be learned and reproduced in a consistent token order. While the reversal curse is often viewed as a limitation, we offer evidence of an alternative view: it is not always an obstacle in practice. We find that RECALL is driven by what we designate as cycle tokens - sequences that connect different parts of the training data, enabling recall of preceding tokens from succeeding ones. Through rigorous probabilistic formalization and controlled experiments, we demonstrate how the cycles they induce influence a model's ability to reproduce information. To facilitate reproducibility, we provide our code and experimental details at https://anonymous.4open.science/r/remember-B0B8/.

Nicolas M Cuadrado Avila, Samuel Horváth, Martin Takáč

This work studies the challenge of optimal energy management in building-based microgrids through a collaborative and privacy-preserving framework. We evaluated two common RL algorithms (PPO and TRPO) in different collaborative setups to manage distributed energy resources (DERs) efficiently. Using a customized version of the CityLearn environment and synthetically generated data, we simulate and design net-zero energy scenarios for microgrids composed of multiple buildings. Our approach emphasizes reducing energy costs and carbon emissions while ensuring privacy. Experimental results demonstrate that Federated TRPO is comparable with state-of-the-art federated RL methodologies without hyperparameter tuning. The proposed framework highlights the feasibility of collaborative learning for achieving optimal control policies in energy systems, advancing the goals of sustainable and efficient smart grids. Our code is accessible \href{https://github.com/Optimization-and-Machine-Learning-Lab/energy_fed_trpo.git}{\textit{this repo}}.

Jozef Kubík, Marek Šuppa, Martin Takáč

Limited data for low-resource languages typically yield weaker language models (LMs). Since pre-training is compute-intensive, it is more pragmatic to target improvements during fine-tuning. In this work, we examine the use of Active Learning (AL) methods augmented by structured data selection strategies which we term 'Active Learning schedulers', to boost the fine-tuning process with a limited amount of training data. We connect the AL to data clustering and propose an integrated fine-tuning pipeline that systematically combines AL, clustering, and dynamic data selection schedulers to enhance model's performance. Experiments in the Slovak, Maltese, Icelandic and Turkish languages show that the use of clustering during the fine-tuning phase together with AL scheduling can simultaneously produce annotation savings up to 30% and performance improvements up to four F1 score points, while also providing better fine-tuning stability.

Nikita Kotelevskii, Vladimir Kondratyev, Martin Takáč et al.

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources of predictive uncertainty, namely aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods, applied as an approximation, we build a framework that allows one to generate different predictive uncertainty measures. We validate our method on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.

Nikita Kotelevskii, Samuel Horváth, Karthik Nandakumar et al.

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.

Farshed Abdukhakimov, Chulu Xiang, Dmitry Kamzolov et al.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.

Yury Demidovich, Petr Ostroukhov, Grigory Malinovsky et al.

Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0, L_1)$-smoothness assumption, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. However, in the context of Federated Learning, only a few works address this problem but rely on additional limiting assumptions. In this paper, we address this gap in the literature: we propose and analyze new methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. The proposed methods are based on the proper interplay between clients' and server's stepsizes and gradient clipping. Furthermore, we perform the first analysis of these methods under the Polyak-Ł ojasiewicz condition. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.

Philip Zmushko, Aleksandr Beznosikov, Martin Takáč et al.

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.

Klea Ziu, Slavomír Hanzely, Loka Li et al.

Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined this problem as a continuous optimization task by incorporating differentiable acyclicity constraints. These methods commonly rely on algebraic characterizations of DAGs, such as matrix exponentials, to enable the use of gradient-based optimization techniques. Despite these innovations, existing methods often face optimization difficulties due to the highly non-convex nature of DAG constraints and the per-iteration computational complexity. In this work, we present a novel framework for learning DAGs, employing a Stochastic Approximation approach integrated with Stochastic Gradient Descent (SGD)-based optimization techniques. Our framework introduces new projection methods tailored to efficiently enforce DAG constraints, ensuring that the algorithm converges to a feasible local minimum. With its low iteration complexity, the proposed method is well-suited for handling large-scale problems with improved computational efficiency. We demonstrate the effectiveness and scalability of our framework through comprehensive experimental evaluations, which confirm its superior performance across various settings.

Nazarii Tupitsa, Samuel Horváth, Martin Takáč et al.

In Federated Learning (FL), the distributed nature and heterogeneity of client data present both opportunities and challenges. While collaboration among clients can significantly enhance the learning process, not all collaborations are beneficial; some may even be detrimental. In this study, we introduce a novel algorithm that assigns adaptive aggregation weights to clients participating in FL training, identifying those with data distributions most conducive to a specific learning objective. We demonstrate that our aggregation method converges no worse than the method that aggregates only the updates received from clients with the same data distribution. Furthermore, empirical evaluations consistently reveal that collaborations guided by our algorithm outperform traditional FL approaches. This underscores the critical role of judicious client selection and lays the foundation for more streamlined and effective FL implementations in the coming years.

Nicolas Mauricio Cuadrado, Roberto Alejandro Gutierrez, Martin Takáč

The rise in renewable energy is creating new dynamics in the energy grid that promise to create a cleaner and more participative energy grid, where technology plays a crucial part in making the required flexibility to achieve the vision of the next-generation grid. This work presents FRESCO, a framework that aims to ease the implementation of energy markets using a hierarchical control architecture of reinforcement learning agents trained using federated learning. The core concept we are proving is that having greedy agents subject to changing conditions from a higher level agent creates a cooperative setup that will allow for fulfilling all the individual objectives. This paper presents a general overview of the framework, the current progress, and some insights we obtained from the recent results.

Petr Ostroukhov, Aigerim Zhumabayeva, Chulu Xiang et al.

This paper presents a novel adaptation of the Stochastic Gradient Descent (SGD), termed AdaBatchGrad. This modification seamlessly integrates an adaptive step size with an adjustable batch size. An increase in batch size and a decrease in step size are well-known techniques to tighten the area of convergence of SGD and decrease its variance. A range of studies by R. Byrd and J. Nocedal introduced various testing techniques to assess the quality of mini-batch gradient approximations and choose the appropriate batch sizes at every step. Methods that utilized exact tests were observed to converge within $O(LR^2/\varepsilon)$ iterations. Conversely, inexact test implementations sometimes resulted in non-convergence and erratic performance. To address these challenges, AdaBatchGrad incorporates both adaptive batch and step sizes, enhancing the method's robustness and stability. For exact tests, our approach converges in $O(LR^2/\varepsilon)$ iterations, analogous to standard gradient descent. For inexact tests, it achieves convergence in $O(\max\lbrace LR^2/\varepsilon, σ^2 R^2/\varepsilon^2 \rbrace )$ iterations. This makes AdaBatchGrad markedly more robust and computationally efficient relative to prevailing methods. To substantiate the efficacy of our method, we experimentally show, how the introduction of adaptive step size and adaptive batch size gradually improves the performance of regular SGD. The results imply that AdaBatchGrad surpasses alternative methods, especially when applied to inexact tests.

Ruben Solozabal, Velibor Bojkovic, Hilal AlQuabeh et al.

Current methods for initializing state space models (SSMs) parameters mainly rely on the \textit{HiPPO framework}, which is based on an online approximation of orthogonal polynomials. Recently, diagonal alternatives have shown to reach a similar level of performance while being significantly more efficient due to the simplification in the kernel computation. However, the \textit{HiPPO framework} does not explicitly study the role of its diagonal variants. In this paper, we take a further step to investigate the role of diagonal SSM initialization schemes from the frequency perspective. Our work seeks to systematically understand how to parameterize these models and uncover the learning biases inherent in such diagonal state-space models. Based on our observations, we propose a diagonal initialization on the discrete Fourier domain \textit{S4D-DFouT}. The insights in the role of pole placing in the initialization enable us to further scale them and achieve state-of-the-art results on the Long Range Arena benchmark, allowing us to train from scratch on very large datasets as PathX-256.

Artem Agafonov, Vladislav Ryspayev, Samuel Horváth et al.

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established only under specific line search strategies and the assumption of strong convexity. In this work, we extend the theoretical understanding of Quasi-Newton methods by introducing a simple stepsize schedule that guarantees a global convergence rate of ${O}(1/k)$ for the convex functions. Furthermore, we show that when the inexactness of the Hessian approximation is controlled within a prescribed relative accuracy, the method attains an accelerated convergence rate of ${O}(1/k^2)$ -- matching the best-known rates of both Nesterov's accelerated gradient method and cubically regularized Newton methods. We validate our theoretical findings through empirical comparisons, demonstrating clear improvements over standard Quasi-Newton baselines. To further enhance robustness, we develop an adaptive variant that adjusts to the function's curvature while retaining the global convergence guarantees of the non-adaptive algorithm.

Nicolas M. Cuadrado A., Mohannad Takrouri, Jiří Němeček et al.

Investment planning in power utilities, such as generation and transmission expansion, requires decade-long forecasts under profound uncertainty. Forecasting of energy mix and energy use decades ahead is nontrivial. Classical approaches focus on generating a finite number of scenarios (modeled as a mixture of Diracs in statistical theory terms), which limits insight into scenario-specific volatility and hinders robust decision-making. We propose an alternative using tractable probabilistic models (TPMs), particularly sum-product networks (SPNs). These models enable exact, scalable inference of key quantities such as scenario likelihoods, marginals, and conditional probabilities, supporting robust scenario expansion and risk assessment. This framework enables direct embedding of chance-constrained optimization into investment planning, enforcing safety or reliability with prescribed confidence levels. TPMs allow both scenario analysis and volatility quantification by compactly representing high-dimensional uncertainties. We demonstrate the approach's effectiveness through a representative power system planning case study, illustrating computational and reliability advantages over traditional scenario-based models.

Abdulla Jasem Almansoori, Maria Ivanova, Andrey Veprikov et al.

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. However, there is still a gap between full training with low-rank projections (SVDLoRA) and LoRA fine-tuning, indicating that LoRA steps can be further improved. In this study, we propose OPLoRA, a memory-efficient optimizer that closes this gap by casting LoRA optimization as an interpretable sub-problem and solving it efficiently with alternating least squares updates, where 1-2 alternating steps are empirically found to be sufficient to closely match truncated SVD without ever forming the full matrix. We also retrieve the recently proposed preconditioning methods for LoRA as a special case. OPLoRA supports momentum by maintaining a low-rank estimate using the same subroutine (LoRSum) for computing the step, with a memory budget of 3 times the number of LoRA parameters (i.e., same as Adam). We also propose an experimental scaled variant that uses the K-FAC metric, which could be of interest. Across a linear task, MNIST, CIFAR-100, and RoBERTa-base (MNLI), OPLoRA consistently approaches SVDLoRA's performance using significantly less memory.

Viktor Kovalchuk, Nikita Kotelevskii, Maxim Panov et al.

Federated learning (FL) usually shares model weights or gradients, which is costly for large models. Logit-based FL reduces this cost by sharing only logits computed on a public proxy dataset. However, aggregating information from heterogeneous clients is still challenging. This paper studies this problem, introduces and compares three logit aggregation methods: simple averaging, uncertainty-weighted averaging, and a learned meta-aggregator. Evaluated on MNIST and CIFAR-10, these methods reduce communication overhead, improve robustness under non-IID data, and achieve accuracy competitive with centralized training.

Farkhad Akimov, Munachiso Samuel Nwadike, Zangir Iklassov et al.

Imagine decision-makers uploading data and, within minutes, receiving clear, actionable insights delivered straight to their fingertips. That is the promise of the AI Data Scientist, an autonomous Agent powered by large language models (LLMs) that closes the gap between evidence and action. Rather than simply writing code or responding to prompts, it reasons through questions, tests ideas, and delivers end-to-end insights at a pace far beyond traditional workflows. Guided by the scientific tenet of the hypothesis, this Agent uncovers explanatory patterns in data, evaluates their statistical significance, and uses them to inform predictive modeling. It then translates these results into recommendations that are both rigorous and accessible. At the core of the AI Data Scientist is a team of specialized LLM Subagents, each responsible for a distinct task such as data cleaning, statistical testing, validation, and plain-language communication. These Subagents write their own code, reason about causality, and identify when additional data is needed to support sound conclusions. Together, they achieve in minutes what might otherwise take days or weeks, enabling a new kind of interaction that makes deep data science both accessible and actionable.

Dmitry Pasechnyuk-Vilensky, Martin Takáč

We develop a unified theoretical framework for neural architectures whose internal representations evolve as stationary states of dissipative Schrödinger-type dynamics on learned latent graphs. Each layer is defined by a fixed-point Schrödinger-type equation depending on a weighted Laplacian encoding latent geometry and a convex local potential. We prove existence, uniqueness, and smooth dependence of equilibria, and show that the dynamics are equivalent under the Bloch map to norm-preserving Landau--Lifshitz flows. Training over graph weights and topology is formulated as stochastic optimization on a stratified moduli space of graphs equipped with a natural Kähler--Hessian metric, ensuring convergence and differentiability across strata. We derive generalization bounds -- PAC-Bayes, stability, and Rademacher complexity -- in terms of geometric quantities such as edge count, maximal degree, and Gromov--Hausdorff distortion, establishing that sparsity and geometric regularity control capacity. Feed-forward composition of stationary layers is proven equivalent to a single global stationary diffusion on a supra-graph; backpropagation is its adjoint stationary system. Finally, directed and vector-valued extensions are represented as sheaf Laplacians with unitary connections, unifying scalar graph, directed, and sheaf-based architectures. The resulting model class provides a compact, geometrically interpretable, and analytically tractable foundation for learning latent graph geometry via fixed-point Schrödinger-type activations.

Gleb Molodtsov, Daniil Medyakov, Sergey Skorik et al.

Recent advancements in machine learning have improved performance while also increasing computational demands. While federated and distributed setups address these issues, their structure is vulnerable to malicious influences. In this paper, we address a specific threat, Byzantine attacks, where compromised clients inject adversarial updates to derail global convergence. We combine the trust scores concept with trial function methodology to dynamically filter outliers. Our methods address the critical limitations of previous approaches, allowing functionality even when Byzantine nodes are in the majority. Moreover, our algorithms adapt to widely used scaled methods like Adam and RMSProp, as well as practical scenarios, including local training and partial participation. We validate the robustness of our methods by conducting extensive experiments on both synthetic and real ECG data collected from medical institutions. Furthermore, we provide a broad theoretical analysis of our algorithms and their extensions to aforementioned practical setups. The convergence guarantees of our methods are comparable to those of classical algorithms developed without Byzantine interference.

Ruichen Luo, Sebastian U Stich, Samuel Horváth et al.

LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical advantages over simpler methods, such as minibatch SGD (MbSGD), has proven challenging, as existing analyses often rely on strong assumptions, unrealistic premises, or overly restrictive scenarios. In this work, we revisit the convergence properties of LocalSGD and SCAFFOLD under a variety of existing or weaker conditions, including gradient similarity, Hessian similarity, weak convexity, and Lipschitz continuity of the Hessian. Our analysis shows that (i) LocalSGD achieves faster convergence compared to MbSGD for weakly convex functions without requiring stronger gradient similarity assumptions; (ii) LocalSGD benefits significantly from higher-order similarity and smoothness; and (iii) SCAFFOLD demonstrates faster convergence than MbSGD for a broader class of non-quadratic functions. These theoretical insights provide a clearer understanding of the conditions under which LocalSGD and SCAFFOLD outperform MbSGD.

Samar Fares, Klea Ziu, Toluwani Aremu et al.

Vision-Language Models (VLMs) are becoming increasingly vulnerable to adversarial attacks as various novel attack strategies are being proposed against these models. While existing defenses excel in unimodal contexts, they currently fall short in safeguarding VLMs against adversarial threats. To mitigate this vulnerability, we propose a novel, yet elegantly simple approach for detecting adversarial samples in VLMs. Our method leverages Text-to-Image (T2I) models to generate images based on captions produced by target VLMs. Subsequently, we calculate the similarities of the embeddings of both input and generated images in the feature space to identify adversarial samples. Empirical evaluations conducted on different datasets validate the efficacy of our approach, outperforming baseline methods adapted from image classification domains. Furthermore, we extend our methodology to classification tasks, showcasing its adaptability and model-agnostic nature. Theoretical analyses and empirical findings also show the resilience of our approach against adaptive attacks, positioning it as an excellent defense mechanism for real-world deployment against adversarial threats.

Savelii Chezhegov, Yaroslav Klyukin, Andrei Semenov et al.

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 current understanding of the high-probability convergence of AdaGrad/Adam-type methods is limited in this case. In this work, we prove that AdaGrad/Adam (and their delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. We also show that gradient clipping fixes this issue, i.e., we derive new high-probability convergence bounds with polylogarithmic dependence on the confidence level for AdaGrad-Norm and Adam-Norm with clipping and with/without delay for smooth convex/non-convex stochastic optimization with heavy-tailed noise. We extend our results to the case of AdaGrad/Adam with delayed stepsizes. Our empirical evaluations highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.