Dual Traits in Probabilistic Reasoning of Large Language Models

TL;DR

The paper investigates how large language models judge posterior probabilities and finds coexistence of two reasoning modes: a normative $f_{\text{norm}}$ aligned with Bayes' rule and a representativeness $f_{\text{rep}}$ driven by similarity. Through three experiments with progressively limited information (structured, semi-structured, unstructured), it shows LLMs can adopt Bayes-like reasoning in structured settings but frequently default to similarity-based judgments when base rates or diagnosticity are not explicit. Prompt engineering can steer some models toward normative computation, but robustness is limited, and base-rate recall remains a core challenge. The authors link these dual traits to the contrastive loss used in supervised fine-tuning and RLHF, highlighting implications for bias mitigation and careful deployment in critical domains.

Abstract

We conducted three experiments to investigate how large language models (LLMs) evaluate posterior probabilities. Our results reveal the coexistence of two modes in posterior judgment among state-of-the-art models: a normative mode, which adheres to Bayes' rule, and a representative-based mode, which relies on similarity -- paralleling human System 1 and System 2 thinking. Additionally, we observed that LLMs struggle to recall base rate information from their memory, and developing prompt engineering strategies to mitigate representative-based judgment may be challenging. We further conjecture that the dual modes of judgment may be a result of the contrastive loss function employed in reinforcement learning from human feedback. Our findings underscore the potential direction for reducing cognitive biases in LLMs and the necessity for cautious deployment of LLMs in critical areas.