Lu Cheng

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.

Identifying faithfulness hallucinations in LLM-generated outputs remains challenging due to the scarcity of high-quality annotated data. Recent work relies on advanced LLMs to synthesize training data, including rationales, labels, and hallucinated claims. However, these methods treat the generator as a static component, limiting iterative improvement of the detector. To address this limitation, we introduce Hallucination Self-Play (HSP), a novel framework that enables the detector to bootstrap with an evolved generator. HSP involves two roles initialized from the same base model, a detector that assesses the faithfulness of model outputs, and a generator that produces increasingly hard-to-detect hallucinated responses. Specifically, the detector is first fine-tuned on human-labeled data and then employed as a reward model to train the generator via reinforcement learning from AI feedback (RLAIF). In turn, the evolved generator synthesizes hallucination data to further optimize the detector through rule-based reinforcement learning. Experiments on RAGTruth and LLM-AggreFact across three model families demonstrate that the proposed framework can progressively enhance a small LLM to match or even outperform advanced LLMs without external supervision. Our code is available at https://github.com/maybenotime/Hallucination_Self-Play.