This paper presents an initial step toward bridging the gap between practical language model inference and theoretical transformer analysis, building on research demonstrating that using more operations (e.g., intermediate thought generation and sampling multiple candidate answers) effectively improves performance in language model inference. Focusing on contextual linear regression with continuous/binary coefficients, we present a framework that simulates language model decoding through noise injection and binary coefficient sampling. This framework provides a detailed analysis of widely used inference techniques, and experimental results demonstrate its potential to provide new insights into the inference behavior of practical language models.
