REMA: A Unified Reasoning Manifold Framework for Interpreting Large
  Language Model
Authors: name: Bo Li, name: Guanzhi Deng, name: Ronghao Chen, name: Junrong Yue, name: Shuo Zhang, name: Qinghua Zhao, name: Linqi Song, name: Lijie Wen

Understanding how Large Language Models (LLMs) perform complex reasoning and
their failure mechanisms is a challenge in interpretability research. To
provide a measurable geometric analysis perspective, we define the concept of
the Reasoning Manifold, a latent low-dimensional geometric structure formed by
the internal representations corresponding to all correctly reasoned
generations. This structure can be conceptualized as the embodiment of the
effective thinking paths that the model has learned to successfully solve a
given task. Based on this concept, we build REMA, a framework that explains the
origins of failures by quantitatively comparing the spatial relationships of
internal model representations corresponding to both erroneous and correct
reasoning samples. Specifically, REMA first quantifies the geometric deviation
of each erroneous representation by calculating its k-nearest neighbors
distance to the approximated manifold formed by correct representations,
thereby providing a unified failure signal. It then localizes the divergence
points where these deviations first become significant by tracking this
deviation metric across the model's layers and comparing it against a baseline
of internal fluctuations from correct representations, thus identifying where
the reasoning chain begins to go off-track. Our extensive experiments on
diverse language and multimodal models and tasks demonstrate the
low-dimensional nature of the reasoning manifold and the high separability
between erroneous and correct reasoning representations. The results also
validate the effectiveness of the REMA framework in analyzing the origins of
reasoning failures. This research connects abstract reasoning failures to
measurable geometric deviations in representations, providing new avenues for
in-depth understanding and diagnosis of the internal computational processes of
black-box models.