https://arxiv.org/abs/2407.02678

Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2407.02678
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv logo
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Computer Science > Artificial Intelligence

arXiv:2407.02678 (cs)
[Submitted on 2 Jul 2024]

Title:Reasoning in Large Language Models: A Geometric Perspective

Authors:Romain Cosentino, Sarath Shekkizhar
View a PDF of the paper titled Reasoning in Large Language Models: A
Geometric Perspective, by Romain Cosentino and 1 other authors
View PDF HTML (experimental)

    Abstract:The advancement of large language models (LLMs) for
    real-world applications hinges critically on enhancing their
    reasoning capabilities. In this work, we explore the reasoning
    abilities of large language models (LLMs) through their
    geometrical understanding. We establish a connection between the
    expressive power of LLMs and the density of their self-attention
    graphs. Our analysis demonstrates that the density of these
    graphs defines the intrinsic dimension of the inputs to the MLP
    blocks. We demonstrate through theoretical analysis and toy
    examples that a higher intrinsic dimension implies a greater
    expressive capacity of the LLM. We further provide empirical
    evidence linking this geometric framework to recent advancements
    in methods aimed at enhancing the reasoning capabilities of LLMs.

Subjects: Artificial Intelligence (cs.AI); Computation and Language
          (cs.CL)
Cite as:  arXiv:2407.02678 [cs.AI]
          (or arXiv:2407.02678v1 [cs.AI] for this version)
          https://doi.org/10.48550/arXiv.2407.02678
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Romain Cosentino Dr [view email]
[v1] Tue, 2 Jul 2024 21:39:53 UTC (1,611 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Reasoning in Large Language
    Models: A Geometric Perspective, by Romain Cosentino and 1 other
    authors
  * View PDF
  * HTML (experimental)
  * TeX Source
  * Other Formats

view license
Current browse context:
cs.AI
< prev   |   next >
new | recent | 2024-07
Change to browse by:
cs
cs.CL

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

a export BibTeX citation Loading...

BibTeX formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Reddit logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
[ ] scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
( ) Code, Data, Media

Code, Data and Media Associated with this Article

[ ] Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
[ ] DagsHub Toggle
DagsHub (What is DagsHub?)
[ ] GotitPub Toggle
Gotit.pub (What is GotitPub?)
[ ] Links to Code Toggle
Papers with Code (What is Papers with Code?)
[ ] ScienceCast Toggle
ScienceCast (What is ScienceCast?)
( ) Demos

Demos

[ ] Replicate Toggle
Replicate (What is Replicate?)
[ ] Spaces Toggle
Hugging Face Spaces (What is Spaces?)
[ ] Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
( ) Related Papers

Recommenders and Search Tools

[ ] Link to Influence Flower
Influence Flower (What are Influence Flowers?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)

  * Author
  * Venue
  * Institution
  * Topic

( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status
    Get status notifications via email or slack