Low-dimensionality of cores for complex multi-step reasoning

Determine whether low-dimensional algorithmic core subspaces persist for complex multi-step reasoning tasks in transformer-based language models, as opposed to only simpler settings such as Markov-chain prediction, modular addition, and subject–verb agreement.

Background

The paper introduces Algorithmic Core Extraction (ACE) and shows that transformers trained on Markov chains and modular addition, as well as GPT-2 models performing subject–verb agreement, exhibit compact core subspaces that are causally necessary and sufficient for task performance.

While these findings demonstrate low-dimensional cores for relatively simple or localized computations (e.g., a one-dimensional agreement axis across GPT-2 scales), the authors explicitly note that it has not yet been tested whether such low dimensionality holds for complex multi-step reasoning tasks. This gap motivates a concrete scaling and generality question about the dimensionality of cores in more demanding settings.