User simulators are essential for the scalable training and evaluation of interactive AI systems. However, existing approaches often rely on shallow user profiling, struggle to maintain persona consistency over long interactions, and are largely limited to English or single-domain settings. We present MUSE, a multi-domain Chinese user simulation framework designed to generate human-like, controllable, and behaviorally consistent responses. First, we propose Iterative Profile Self-Evolution (IPSE), which gradually optimizes user profiles by comparing and reasoning discrepancies between simulated trajectories and real dialogue behaviors. We then apply Role-Reversal Supervised Fine-Tuning to improve local response realism and human-like expression. To enable fine-grained behavioral alignment, we further train a specialized rubric-based reward model and incorporate it into rubric-guided multi-turn reinforcement learning, which optimizes the simulator at the dialogue level and enhances long-horizon behavioral consistency. Experiments show that MUSE consistently outperforms strong baselines in both utterance-level and session-level evaluations, generating responses that are more realistic, coherent, and persona-consistent over extended interactions.

Reinforcement Learning with Verifiable Rewards (RLVR) is a key paradigm for improving large-scale reasoning models. Unlike supervised fine-tuning (SFT), RLVR exhibits distinct optimization dynamics and are sensitive to the preservation of pre-trained geometric structures. However, existing parameter-efficient methods face key limitations in this regime. Low-rank adaptation methods, such as PiSSA, are primarily designed for Supervised Fine-Tuning (SFT) and do not account for the distinct optimization dynamics and geometric structures of RLVR. Conversely, directly fine-tuning the unstructured sparse parameter subspace favored by RLVR encounters efficiency bottlenecks on modern hardware. To address these challenges, we propose GeoRA (Geometry-Aware Low-Rank Adaptation), a low-rank adaptation method tailored for RLVR. Specifically, GeoRA exploits the anisotropic and compressible structure of RL update subspace, and extracts its principal directions via Singular Value Decomposition (SVD) to initialize low-rank adapters, while freezing residual components as a structural anchor during training. This design preserves the pre-trained structure and enables efficient dense computation. Experiments on Qwen and Llama models from 1.5B to 32B parameters show that GeoRA consistently outperforms strong low-rank baselines across RLVR settings in mathematics, medicine, and coding, while showing stronger generalization and less forgetting on out-of-domain tasks.