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A Bayesian-latent model of large language model sycophancy
Partha Pratim Ray (Sikkim University)
Résumé : Large language models (LLMs) have become ubiquitous tools across numerous domains such as education, healthcare, and professional advisory services. However, their susceptibility to sycophancy-a bias toward echoing user prompts over independently reasoning-poses a critical threat to model reliability. We present a Bayesian-latent variable framework that introduces a hidden sycophancy score Si,m,u,p ∼ N (0, σ 2 S) to quantify such behavior. The framework defines a flip indicator ∆i,m,u,p ∈ {−1, 0, +1} to distinguish regressive (accuracydecreasing) from progressive (accuracy-increasing) shifts. Our generative logistic model ties correctness probabilities to latent agreement pressure via Pr(ŷ (1) = 1) = σ(x ⊤ β + γmSi,m,u,p), enabling rigorous posterior inference. Empirically, we find an average sycophancy-induced shift of E[|S|] ≈ 0.8σS, and a model susceptibility factor γ that directly controls response volatility. Simulated results show that nearly 50% of responses flip under user cues, with regressive flips dominating when γ < 0. Our approach provides a statistically grounded diagnostic for auditing and improving trustworthiness in LLM behavior under social influence. Simulation code for this study is available at: https://github.com/ParthaPRay/Sycophancy_in_LLM_model.