https://arxiv.org/abs/2510.15511

close this message
arXiv smileybones

Happy Open Access Week from arXiv!

YOU make open access possible! Tell us why you support #openaccess
and give to arXiv this week to help keep science open for all.

Donate!
Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2510.15511
[                    ]

Help | Advanced Search

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

  * Login
  * Help Pages
  * About

Computer Science > Machine Learning

arXiv:2510.15511 (cs)
[Submitted on 17 Oct 2025 (v1), last revised 21 Oct 2025 (this
version, v3)]

Title:Language Models are Injective and Hence Invertible

Authors:Giorgos Nikolaou, Tommaso Mencattini, Donato Crisostomi,
Andrea Santilli, Yannis Panagakis, Emanuele Rodola
View a PDF of the paper titled Language Models are Injective and
Hence Invertible, by Giorgos Nikolaou and 5 other authors
View PDF HTML (experimental)

    Abstract:Transformer components such as non-linear activations
    and normalization are inherently non-injective, suggesting that
    different inputs could map to the same output and prevent exact
    recovery of the input from a model's representations. In this
    paper, we challenge this view. First, we prove mathematically
    that transformer language models mapping discrete input sequences
    to their corresponding sequence of continuous representations are
    injective and therefore lossless, a property established at
    initialization and preserved during training. Second, we confirm
    this result empirically through billions of collision tests on
    six state-of-the-art language models, and observe no collisions.
    Third, we operationalize injectivity: we introduce SipIt, the
    first algorithm that provably and efficiently reconstructs the
    exact input text from hidden activations, establishing
    linear-time guarantees and demonstrating exact invertibility in
    practice. Overall, our work establishes injectivity as a
    fundamental and exploitable property of language models, with
    direct implications for transparency, interpretability, and safe
    deployment.

Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:  arXiv:2510.15511 [cs.LG]
          (or arXiv:2510.15511v3 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2510.15511
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Andrea Santilli [view email]
[v1] Fri, 17 Oct 2025 10:25:30 UTC (3,980 KB)
[v2] Mon, 20 Oct 2025 07:29:02 UTC (3,980 KB)
[v3] Tue, 21 Oct 2025 14:44:49 UTC (3,980 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Language Models are Injective and
    Hence Invertible, by Giorgos Nikolaou and 5 other authors
  * View PDF
  * HTML (experimental)
  * TeX Source

license icon view license
Current browse context:
cs.LG
< prev   |   next >
new | recent | 2025-10
Change to browse by:
cs
cs.AI

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

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?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] 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

[ ] alphaXiv Toggle
alphaXiv (What is alphaXiv?)
[ ] 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?)
[ ] Huggingface Toggle
Hugging Face (What is Huggingface?)
[ ] 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?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)
[ ] IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)

  * 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