Andrey Veprikov

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

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.

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

Andrey Veprikov, Vladimir Solodkin, Alexander Zyl et al.

The widespread utilization of language models in modern applications is inconceivable without Parameter-Efficient Fine-Tuning techniques, such as low-rank adaptation ($\texttt{LoRA}$), which adds trainable adapters to selected layers. Although $\texttt{LoRA}$ may obtain accurate solutions, it requires significant memory to train large models and intuition on which layers to add adapters. In this paper, we propose a novel method, $\texttt{WeightLoRA}$, which overcomes this issue by adaptive selection of the most critical $\texttt{LoRA}$ heads throughout the optimization process. As a result, we can significantly reduce the number of trainable parameters while maintaining the capability to obtain consistent or even superior metric values. We conduct experiments for a series of competitive benchmarks and DeBERTa, BART, and Llama models, comparing our method with different adaptive approaches. The experimental results demonstrate the efficacy of $\texttt{WeightLoRA}$ and the superior performance of $\texttt{WeightLoRA+}$ in almost all cases.