Zihao Zhu

The rapid growth of the large language model (LLM) ecosystem raises a critical question: are seemingly diverse models truly independent? Shared pretraining data, distillation, and alignment pipelines can induce hidden behavioral dependencies, latent entanglement, that undermine multi-model systems such as LLM-as-a-judge pipelines and ensemble verification, which implicitly assume independent signals. In practice, this manifests as correlated reasoning patterns and synchronized failures, where apparent agreement reflects shared error modes rather than independent validation. To address this, we develop a statistical framework for auditing behavioral entanglement among black-box LLMs. Our approach introduces a multi-resolution hierarchy that characterizes the joint failure manifold through two information-theoretic metrics: (i) a Difficulty-Weighted Behavioral Entanglement Index (BEI), which amplifies synchronized failures on easy tasks, and (ii) a Cumulative Information Gain (CIG) metric, which captures directional alignment in erroneous responses. Through experiments on 18 LLMs from six model families, we identify statistically significant behavioral entanglement. Such behavioral dependence is associated with judge over-endorsement bias on a disjoint MMLU-Pro evaluation set ($\rho=0.508$ for BEI and $\rho=0.520$ for CIG; $p<0.01$). The association further transfers to the MATH-500 benchmark ($\rho=0.441$ for BEI and $\rho=0.457$ for CIG; $p<0.05$), providing cross-benchmark evidence that the identified dependency structure generalizes beyond the data and response format used for its estimation. Finally, we demonstrate a practical use case of entanglement through de-entangled verifier ensemble reweighting, achieving 3.5 and 2.6 percentage-point gains in accuracy and precision, respectively, over majority voting.

As Large Language Models (LLMs) are increasingly deployed as autonomous agents in high-stakes domains, understanding contextual factors that may modulate their decision-making becomes critical. While LLMs are trained to perceive and resonate with users' emotions, it remains unclear whether induced emotion can influence their sequential decision-making. We investigate this question using the Iowa Gambling Task (IGT), a classic psychological paradigm for studying decision-making under uncertainty, combined with an imagination-based emotion induction procedure. We first validate the feasibility of this paradigm by confirming that LLMs can sense strong, distinguishable emotions from context and that LLM agents can learn from sequential interactions in a human-like pace. With the validated setup, we find that, different from humans, induced emotion does not significantly bias the decision dynamics of LLM agents on average. However, the effects of anger are conditioned: inducing anger makes LLM agents less sensitive to penalties for bad decisions, and in early stages of the game, anger can lower exploration, locking decisions into a few choices early. These findings reveal the subtle yet distinct effects of induced emotion on LLM decision-making compared to human behavior, and provide a tool for future research on affective modulation of LLM agents.