REMA: A Unified Reasoning Manifold Framework for Interpreting Large
  Language Model
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.
68d9f3650177a6054b013b1b
Bo Li
claimed_verified
2025-09-29T05:58:06.996Z
6582c482f3006507ea10302a
https://cdn-avatars.huggingface.co/v1/production/uploads/6582c482f3006507ea10302a/KbgSsq0FnbMngBcWPhIXi.jpeg
Bo Li
user
liboaccn
68d9f3650177a6054b013b1c
Guanzhi Deng
68d9f3650177a6054b013b1d
Ronghao Chen
68d9f3650177a6054b013b1e
Junrong Yue
68d9f3650177a6054b013b1f
Shuo Zhang
68d9f3650177a6054b013b20
Qinghua Zhao
68d9f3650177a6054b013b21
Linqi Song
68d9f3650177a6054b013b22
Lijie Wen
REMA: A Unified Reasoning Manifold Framework for Interpreting Large
  Language Model
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.
The Reasoning Manifold framework quantifies and localizes reasoning failures in Large Language Models by analyzing geometric deviations in internal representations.
Large Language Models Reasoning Manifold internal representations k-nearest neighbors geometric deviation reasoning failures REMA framework multimodal models low-dimensional nature separability