On the Universality of the Inner Product as a PMI Estimator in Embedding Models

Enrique Amigó; Fernando Giner; Julio Gonzalo

On the Universality of the Inner Product as a PMI Estimator in Embedding Models

Enrique Amigo, Fernando Giner, Julio Gonzalo

Correct Metadata for

Use this form to create a GitHub issue with structured data describing the correction. You will need a GitHub account. Once you create that issue, the correction will be reviewed by a staff member.

⚠️ Mobile Users: Submitting this form to create a new issue will only work with github.com, not the GitHub Mobile app.

Important: The Anthology treat PDFs as authoritative. Please use this form only to correct data that is out of line with the PDF. See our corrections guidelines if you need to change the PDF.

Title Adjust the title. Retain tags such as <fixed-case>.

Authors Adjust author names and order to match the PDF.

Abstract Correct abstract if needed. Retain XML formatting tags such as <tex-math>. You may use ... for bold, ... for italic, ... for underline, <sc>...</sc> for small-caps, <tt>...<tt> for typewriter text, <url>...</url> for URLs, <a href=...> for hyperlinks, and <par/> for paragraph breaks.

Verification against PDF Ensure that the new title/authors match the snapshot below. (If there is no snapshot or it is too small, consult the PDF.)

Authors concatenated from the text boxes above:

ALL author names match the snapshot above—including middle initials, hyphens, and accents.

Abstract

Embedding representations are widely used in natural language processing, yet their semantic interpretation depends on the operators used to compare them. Previous work has shown that, for certain embedding models, the inner product is linearly correlated with Pointwise Mutual Information (PMI). However, this relation has so far been established only empirically or analytically for specific models.

In this work, we formally show that, under certain assumptions about distributional semantic embedding models, the inner product between embeddings approaches PMI. This theoretical result provides a more general explanation for the observed relationship and enables the formulation of training criteria aimed at learning embedding spaces in which operations between embeddings are semantically interpretable.

Anthology ID:: 2026.findings-emnlp.1800
Volume:: Findings of the Association for Computational Linguistics: EMNLP 2026
Month:: October
Year:: 2026
Address:: Budapest, Hungary
Editors:: Hung-Yi Lee, Sunipa Dev, Jessy Li, Desmond Elliott
Venue:: Findings
SIG:: SIGDAT
Publisher:: Association for Computational Linguistics
Note:
Pages:: 38472–38480
Language:
URL:: https://aclanthology.org/2026.findings-emnlp.1800/
DOI:
Bibkey:
Cite (ACL):: Enrique Amigo, Fernando Giner, and Julio Gonzalo. 2026. On the Universality of the Inner Product as a PMI Estimator in Embedding Models. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 38472–38480, Budapest, Hungary. Association for Computational Linguistics.
Cite (Informal):: On the Universality of the Inner Product as a PMI Estimator in Embedding Models (Amigo et al., Findings 2026)
Copy Citation:
PDF:: https://aclanthology.org/2026.findings-emnlp.1800.pdf

PDF Cite Search Fix data

Export citation

BibTeX
MODS XML
Endnote
Preformatted

@inproceedings{amigo-etal-2026-universality,
    title = "On the Universality of the Inner Product as a {PMI} Estimator in Embedding Models",
    author = "Amigo, Enrique  and
      Giner, Fernando  and
      Gonzalo, Julio",
    editor = "Lee, Hung-Yi  and
      Dev, Sunipa  and
      Li, Jessy  and
      Elliott, Desmond",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
    month = oct,
    year = "2026",
    address = "Budapest, Hungary",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2026.findings-emnlp.1800/",
    pages = "38472--38480",
    ISBN = "979-8-89176-462-0",
    abstract = "Embedding representations are widely used in natural language processing, yet their semantic interpretation depends on the operators used to compare them. Previous work has shown that, for certain embedding models, the inner product is linearly correlated with Pointwise Mutual Information (PMI). However, this relation has so far been established only empirically or analytically for specific models.\par In this work, we formally show that, under certain assumptions about distributional semantic embedding models, the inner product between embeddings approaches PMI. This theoretical result provides a more general explanation for the observed relationship and enables the formulation of training criteria aimed at learning embedding spaces in which operations between embeddings are semantically interpretable."
}

Download as File

<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="amigo-etal-2026-universality">
    <titleInfo>
        <title>On the Universality of the Inner Product as a PMI Estimator in Embedding Models</title>
    </titleInfo>
    <name type="personal">
        <namePart type="given">Enrique</namePart>
        <namePart type="family">Amigo</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Fernando</namePart>
        <namePart type="family">Giner</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Julio</namePart>
        <namePart type="family">Gonzalo</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <originInfo>
        <dateIssued>2026-10</dateIssued>
    </originInfo>
    <typeOfResource>text</typeOfResource>
    <relatedItem type="host">
        <titleInfo>
            <title>Findings of the Association for Computational Linguistics: EMNLP 2026</title>
        </titleInfo>
        <name type="personal">
            <namePart type="given">Hung-Yi</namePart>
            <namePart type="family">Lee</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Sunipa</namePart>
            <namePart type="family">Dev</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Jessy</namePart>
            <namePart type="family">Li</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Desmond</namePart>
            <namePart type="family">Elliott</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <originInfo>
            <publisher>Association for Computational Linguistics</publisher>
            <place>
                <placeTerm type="text">Budapest, Hungary</placeTerm>
            </place>
        </originInfo>
        <genre authority="marcgt">conference publication</genre>
        <identifier type="isbn">979-8-89176-462-0</identifier>
    </relatedItem>
    <abstract>Embedding representations are widely used in natural language processing, yet their semantic interpretation depends on the operators used to compare them. Previous work has shown that, for certain embedding models, the inner product is linearly correlated with Pointwise Mutual Information (PMI). However, this relation has so far been established only empirically or analytically for specific models.\par In this work, we formally show that, under certain assumptions about distributional semantic embedding models, the inner product between embeddings approaches PMI. This theoretical result provides a more general explanation for the observed relationship and enables the formulation of training criteria aimed at learning embedding spaces in which operations between embeddings are semantically interpretable.</abstract>
    <identifier type="citekey">amigo-etal-2026-universality</identifier>
    <location>
        <url>https://aclanthology.org/2026.findings-emnlp.1800/</url>
    </location>
    <part>
        <date>2026-10</date>
        <extent unit="page">
            <start>38472</start>
            <end>38480</end>
        </extent>
    </part>
</mods>
</modsCollection>

Download as File

%0 Conference Proceedings
%T On the Universality of the Inner Product as a PMI Estimator in Embedding Models
%A Amigo, Enrique
%A Giner, Fernando
%A Gonzalo, Julio
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F amigo-etal-2026-universality
%X Embedding representations are widely used in natural language processing, yet their semantic interpretation depends on the operators used to compare them. Previous work has shown that, for certain embedding models, the inner product is linearly correlated with Pointwise Mutual Information (PMI). However, this relation has so far been established only empirically or analytically for specific models.\par In this work, we formally show that, under certain assumptions about distributional semantic embedding models, the inner product between embeddings approaches PMI. This theoretical result provides a more general explanation for the observed relationship and enables the formulation of training criteria aimed at learning embedding spaces in which operations between embeddings are semantically interpretable.
%U https://aclanthology.org/2026.findings-emnlp.1800/
%P 38472-38480

Download as File

Markdown (Informal)

[On the Universality of the Inner Product as a PMI Estimator in Embedding Models](https://aclanthology.org/2026.findings-emnlp.1800/) (Amigo et al., Findings 2026)

On the Universality of the Inner Product as a PMI Estimator in Embedding Models (Amigo et al., Findings 2026)

ACL

Enrique Amigo, Fernando Giner, and Julio Gonzalo. 2026. On the Universality of the Inner Product as a PMI Estimator in Embedding Models. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 38472–38480, Budapest, Hungary. Association for Computational Linguistics.