Xiangqi Wang
Publications
SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation
Large language models often default to step-by-step computation even when efficient numerical shortcuts are available. This raises a basic question: do they exhibit number sense in a human-like behavioral sense, i.e., the ability to recognize numerical structure, apply shortcuts when appropriate, and avoid them when they are not? We introduce SenseMath, a controlled benchmark for evaluating structure-sensitive numerical reasoning in LLMs. SenseMath contains 4,800 items spanning eight shortcut categories and four digit scales, with matched strong-shortcut, weak-shortcut, and control variants. It supports three evaluation settings of increasing cognitive demand: Shortcut Use (whether models can apply shortcuts on shortcut-amenable problems); Applicability Judgment (whether they can recognize when a shortcut is appropriate or misleading); and Problem Generation (whether they can generate new problem items that correctly admit a given type of shortcut). Our evaluation across five LLMs, ranging from GPT-4o-mini to Llama-3.1-8B, shows a consistent pattern: when explicitly prompted, models readily adopt shortcut strategies and achieve substantial accuracy gains on shortcut-amenable items (up to 15%), yet under standard chain-of-thought prompting they spontaneously employ such strategies in fewer than 40% of cases, even when they demonstrably possess the requisite capability. Moreover, this competence is confined to the Use level; models systematically over-generalise shortcuts to problems where they do not apply, and fail to generate valid shortcut-bearing problems from scratch. Together, these results suggest that current LLMs exhibit procedural shortcut fluency without the structural understanding of when and why shortcuts work that underlies human number sense.
Dual Optimal: Make Your LLM Peer-like with Dignity
Current aligned language models exhibit a dual failure mode we term the Evasive Servant: they sycophantically validate flawed user beliefs while deflecting responsibility with boilerplate disclaimers. We propose the Dignified Peer framework, which counters servility with anti-sycophancy and trustworthiness, and mitigates evasiveness through empathy and creativity. Realizing this agent requires overcoming significant challenges in data supervision, objective collapse, and evaluation bias. We address these issues by introducing the PersonaKnob dataset which features a compositional partial order structure of multiple persona preference. This data is utilized alongside a tolerant constrained Lagrangian DPO algorithm that dynamically balances all persona dimensions to prevent behavioral collapse. Additionally, we employ a psychometrically calibrated Item Response Theory evaluation protocol to disentangle latent model persona capability from confounders like judge biases. Extensive empirical studies demonstrate that our approach successfully build a LLM agent with both dignity and peer.