Tianyi Zhou

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.

Reinforcement learning (RL) with verifiable rewards has become a standard post-training stage for boosting visual reasoning in vision-language models, yet it remains unclear what capabilities RL actually improves compared with supervised fine-tuning as cold-start initialization (IN). End-to-end benchmark gains conflate multiple factors, making it difficult to attribute improvements to specific skills. To bridge the gap, we propose a Frankenstein-style analysis framework, including: (i) functional localization via causal probing; (ii) update characterization via parameter comparison; and (iii) transferability test via model merging. Across multiple public IN+RL training recipes, we find that benchmark accuracy improves monotonically, but fine-grained metrics show that vision ability and pure language-side reasoning do not. Instead, RL induces a consistent inference-time shift primarily in mid-to-late layers, and these mid-to-late refinements are both transferable (via merging) and necessary (via freezing) for RL gains. Overall, our results suggest that RL’s reliable contribution in visual reasoning is not a uniform enhancement of visual perception, but a systematic refinement of mid-to-late transformer computation that improves vision-to-reasoning alignment and reasoning performance, highlighting the limitations of benchmark-only evaluation for understanding multimodal reasoning improvements.

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules—particularly in corner cases—is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM contributes candidate-level scores through log-linear reranking, without requiring the LLM to interpret rule text. Rule-guided sampling prioritizes transitions that are weakly covered by symbolic rules, using 35--60% of the training pairs while outperforming full-data supervised fine-tuning in five of six settings. Experiments on ScienceWorld, WebShop, and PlanCraft demonstrate consistent gains in WM prediction accuracy and data efficiency; one-step lookahead on open-ended WebShop also improves agent reward. Our models, rules, and code are available at https://github.com/tianyi-lab/NeSyS.

Modern LLMs are observed to be overconfident in their own outputs, making them poor self-verifiers. We found that for mixture-of-experts (MoE) LLMs, the Routing Entropy (RE) is a more reliable self-verifier than output confidence (OC). In other words, more confident expert choices in MoE usually lead to higher-quality outputs. We examined RE for self-verification on multiple recent MoE LLMs. While RE consistently outperforms OC, combining them leads to the best performance. Moreover, our RE-based analysis shows that better MoEs are usually more confident in expert choices. These novel insights further motivate an RE-regularizer for post-training of MoE routers. Our extensive experiments demonstrate the superiority of RE for self-verification across diverse reasoning and knowledge benchmarks. Furthermore, RE-regularization in post-training significantly enhances MoE’s internal calibration and self-awareness, yielding a more reliable model without sacrificing its core generative performance.