Towards Theoretical Understanding of Transformer Test-Time Computing: Investigation on In-Context Linear Regression
This work offers a theoretical foundation for understanding practical inference techniques in transformers, though it is incremental as it builds on existing transformer analysis frameworks.
The paper investigates how test-time computation with randomness and sampling affects transformer performance, focusing on in-context linear regression with continuous/binary coefficients. It provides theoretical analyses and empirical results showing potential insights into real-world language model inference behaviors.
Using more test-time computation during language model inference, such as generating more intermediate thoughts or sampling multiple candidate answers, has proven effective in significantly improving model performance. This paper takes an initial step toward bridging the gap between practical language model inference and theoretical transformer analysis by incorporating randomness and sampling. We focus on in-context linear regression with continuous/binary coefficients, where our framework simulates language model decoding through noise injection and binary coefficient sampling. Through this framework, we provide detailed analyses of widely adopted inference techniques. Supported by empirical results, our theoretical framework and analysis demonstrate the potential for offering new insights into understanding inference behaviors in real-world language models.