User information needs are often highly diverse and varied. A key challenge in current research is how to achieve controllable multi-objective generation while enabling rapid adaptation to accommodate diverse user demands during test time. Existing solutions, such as Rewarded Soup, focus on merging language models individually tuned on single objectives. While easy to implement and widely used, these approaches face limitations in achieving optimal performance due to their disregard for the impacts of competing objectives on model tuning. To address this issue, we propose **Bone Soup**, a novel model merging approach that first seeks a series of back**bone** models by considering the impacts of multiple objectives and then makes the **soup** (i.e., merge the backbone models). Specifically, Bone Soup begins by training multiple backbone models for different objectives using multi-objective reinforcement learning. Each backbone model is guided by a combination of backbone reward signals. To ensure that these models are optimal for the Pareto front, the backbone rewards are crafted by combining standard reward functions into basis vectors, which can then be modified through a rule-based construction method. Bone Soup leverages a symmetric circulant matrix mapping to generate the merging coefficients, which are used to merge the backbone models according to user preferences.Extensive experimental results demonstrate that Bone Soup exhibits strong controllability and Pareto optimality in controllable multi-objective generation, providing a more effective and efficient approach to addressing diverse user needs at test time.

Legal mathematical reasoning is essential for applying large language models (LLMs) in high-stakes legal contexts, where outputs must be both mathematically accurate and procedurally compliant. However, existing legal LLMs lack structured numerical reasoning, and open-domain models, though capable of calculations, often overlook mandatory legal steps. To address this, we present LexNum, the first Chinese legal mathematical reasoning benchmark, covering three representative scenarios where each instance reflects legally grounded procedural flows. We further propose LexPam, a two-stage reinforcement learning framework for efficient legal reasoning training. Leveraging curriculum learning, we use a stronger teacher model to partition data into basic and challenging subsets. A lightweight 1.5B student model is then fine-tuned with Group Relative Policy Optimization, which avoids costly value networks and enables stable training from sparse, end-of-sequence rewards. The first stage improves accuracy and format; the second introduces a novel reward to guide procedural alignment via task-specific legal elements. Experiments show that existing models perform poorly on LexNum, while LexPam enhances both mathematical accuracy and legal coherence, and generalizes effectively across tasks and domains.