Ge Liu

Training tool-augmented large language models has evolved from supervised fine-tuning (SFT) to reinforcement learning with verifiable rewards (RLVR). Yet existing methods rarely examine whether intermediate execution logic---specifically, the procedural fidelity of multi-turn tool invocations---requires explicit supervision. We hypothesize that enforcing sequential validity at the turn level is a prerequisite for robust multi-turn task completion. To this end, we introduce a Procedure-Aware Reinforcement Learning Framework that explicitly evaluates procedural validity through both invocation chain quality and final system state correctness. Using Group Relative Policy Optimization (GRPO) with KL regularization to fine-tune Qwen2.5-3B-Instruct, we demonstrate on API-Bank, Bamboogle, and BFCL-V3 that our approach consistently outperforms correctness-only baselines. Despite operating at a substantially smaller scale, our 3B model achieves average accuracy competitive with proprietary models such as GPT-5-mini, GPT-4.1-mini, Claude-Haiku-4.5, and Gemini-2.5-Flash-Lite, whose scores are obtained under BFCL's official per-model evaluation protocols. Qualitative analysis reveals that optimizing tool sequencing yields emergent benefits, simultaneously enhancing multi-turn performance and error recovery from failed tool calls.

Time series reasoning is essential for real-world problem-solving. While both Large Language Models (LLMs) and Vision-Language Models (VLMs) can reason about time-series data, their capabilities are complementary: LLMs process time series as text sequences and thus preserve exact numerical understanding, but struggle with global patterns, whereas VLMs efficiently capture these patterns by visualizing time series but may lose fine-grained details. Moreover, models vary significantly in task-specific expertise and inference costs. Dynamically selecting the most suitable modality and model for each query is therefore crucial, yet challenging because it requires modeling the complex interactions among tasks, queries, modalities, and models, which carry rich contextual signals. To this end, we introduce TSRouter, a graph-based dynamic routing framework. TSRouter constructs a heterogeneous graph of task, query, modality, and model nodes to contextualize the interactions among query characteristics, modality attributes, and model capabilities. TSRouter formulates routing as a candidate scoring problem, where each modality-model pair is evaluated based on user-defined performance-cost preferences to select the optimal candidate. Comprehensive evaluations on 4 distinct time series reasoning tasks reveal that TSRouter substantially outperforms diverse baselines with 16\% to 46\% relative improvements. Furthermore, TSRouter demonstrates robust zero-shot plug-and-play generalization to unseen models and novel tasks and preserves high performance while reducing computational overhead through cost-aware optimization. Our code is available at https://github.com/tianyi-lab/TSRouter.