Соболева Вера Владиславовна

LoRA meets Riemannion: Muon Optimizer for Parametrization-independent Low-Rank Adapters

2026 · CHAPTER · en

This work presents a novel, fully Riemannian framework for Low-Rank Adaptation (LoRA) that geometrically treats low-rank adapters by optimizing them directly on the fixed-rank manifold. This formulation eliminates the parametrization ambiguity present in standard Euclidean optimizers. Our framework integrates three key components to achieve this: (1) we derive Riemannion, a new Riemannian optimizer on the fixed-rank matrix manifold that generalizes the recently proposed Muon optimizer; (2) we develop a Riemannian gradient-informed LoRA initialization, and (3) we provide an efficient implementation without prominent overhead that uses automatic differentiation to compute arising geometric operations while adhering to best practices in numerical linear algebra. Comprehensive experimental results on both LLM and diffusion model architectures demonstrate that our approach yields consistent and noticeable improvements in convergence speed and final task performance over both standard LoRA and its state-of-the-art modifications.

Beyond Fine-Tuning: A Systematic Study of Sampling Techniques in Personalized Image Generation

2025 · PREPRINT · en

Personalized text-to-image generation aims to create images tailored to user-defined concepts and textual descriptions. Balancing the fidelity of the learned concept with its ability for generation in various contexts presents a significant challenge. Existing methods often address this through diverse fine-tuning parameterizations and improved sampling strategies that integrate superclass trajectories during the diffusion process. While improved sampling offers a cost-effective, trainingfree solution for enhancing fine-tuned models, systematic analyses of these methods remain limited. Current approaches typically tie sampling strategies with fixed fine-tuning configurations, making it difficult to isolate their impact on generation outcomes. To address this issue, we systematically analyze sampling strategies beyond finetuning, exploring the impact of concept and superclass trajectories on the results. Building on this analysis, we propose a decision framework evaluating text alignment, computational constraints, and fidelity objectives to guide strategy selection. It integrates with diverse architectures and training approaches, systematically optimizing concept preservation, prompt adherence, and resource efficiency. The source code can be found at github.com/ControlGenAI/PersonGenSampler.

Group and Shuffle: Efficient Structured Orthogonal Parametrization

2024 · CHAPTER · en