Multi-Step Knowledge Interaction Analysis via Rank-2 Subspace
  Disentanglement
Authors: name: Sekh Mainul Islam, name: Pepa Atanasova, name: Isabelle Augenstein

Natural Language Explanations (NLEs) describe how Large Language Models
(LLMs) make decisions, drawing on both external Context Knowledge (CK) and
Parametric Knowledge (PK) stored in model weights. Understanding their
interaction is key to assessing the grounding of NLEs, yet it remains
underexplored. Prior work has largely examined only single-step generation,
typically the final answer, and has modelled PK and CK interaction only as a
binary choice in a rank-1 subspace. This overlooks richer forms of interaction,
such as complementary or supportive knowledge. We propose a novel rank-2
projection subspace that disentangles PK and CK contributions more accurately
and use it for the first multi-step analysis of knowledge interactions across
longer NLE sequences. Experiments on four QA datasets and three open-weight
instruction-tuned LLMs show that diverse knowledge interactions are poorly
represented in a rank-1 subspace but are effectively captured in our rank-2
formulation. Our multi-step analysis reveals that hallucinated NLEs align
strongly with the PK direction, context-faithful ones balance PK and CK, and
Chain-of-Thought prompting for NLEs shifts generated NLEs toward CK by reducing
PK reliance. This work provides the first framework for systematic studies of
multi-step knowledge interactions in LLMs through a richer rank-2 subspace
disentanglement. Code and data:
https://github.com/copenlu/pk-ck-knowledge-disentanglement.