Low-rank adaptation (LoRA) is commonly used in both supervised fine-tuning (SFT) and reinforcement learning (RL), often under similar optimizer settings. Yet, how the different dynamics of the two stages manifest in the low-rank increment that LoRA optimizes remains unclear. Tracking the singular spectrum and subspaces of LoRA updates on mathematical reasoning tasks, we find that RL concentrates the spectrum at every learning rate, while SFT expands it at moderate learning rates; moreover, RL rotates the singular subspaces much faster than SFT at small learning rates. Interpolating between SFT and RL one ingredient at a time, we pinpoint group-mean baseline subtraction as the source of both contrasts. A quadratic multi-index model updated via LoRA unveils the underlying mechanism: group-mean baseline subtraction tilts the balance between two competing forces, coherent fitting and gradient noise, toward spectral concentration and faster subspace rotation, while forcing the risk-favorable learning rate to be low. Guided by these dynamics, we tailor LoRA updates to each stage: in SFT, we flatten the spectrum of the full update to spread adaptation across singular directions, whereas in RL, we flatten the part of the update outside the current LoRA increment span to promote subspace rotation. Experiments on mathematical reasoning tasks across multiple models show that the respective configurations for SFT and RL yield the best performance among the compared methods in most evaluated settings.
Unified Multimodal Models (UMMs) integrate visual understanding, generation, and editing within a single unified framework. However, existing unified multimodal datasets and benchmarks remain dominated by single-turn tasks. Even in recent multi-turn datasets, many turns can be solved independently without tracking information across turns. Consequently, they provide limited supervision and evaluation for multimodal stateful interaction, which requires models to understand, maintain, update, and faithfully realize evolving dialogue states across turns. To address this gap, we introduce YANAMI, the first large-scale multimodal dialogue dataset and benchmark for stateful interaction, comprising YANAMI-400K and YANAMI-Bench. YANAMI-400K contains 400K multi-turn multimodal dialogues, with more than 2M images and 2.6M dialogue turns. The dialogues span four representative scenarios: Multi-Image Fusion, Image Editing, World Modeling, and Visual Reasoning, and require models to continuously track, preserve, and revise evolving multimodal dialogue states across turns. YANAMI-Bench comprises 400 multi-turn dialogues for systematically evaluating multimodal stateful interaction. It jointly evaluates Dialogue State Understanding and Visual Realization, characterizing the gap between models' ability to understand evolving dialogue states and their ability to faithfully realize them in visual outputs. Experiments show that fine-tuning BAGEL on YANAMI-400K improves image editing, generation, and multimodal stateful interaction by 10.3%, 2.0%, and 13.23%, respectively, while preserving its general visual understanding capabilities. Evaluations on YANAMI-Bench further reveal that existing UMMs still struggle to maintain, update, and visually realize evolving multimodal dialogue states.