<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-2353</article-id>
      <title-group>
        <article-title>Entropy evolution in multilingual transformer models : An information-theoretic perspective</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Bansode</surname>
            <given-names>Arti</given-names>
          </name>
          <aff>Department of Computer Science, SNDT Women’s University, Juhu Campus, Mumbai, Maharashtra, 400049, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Chaware</surname>
            <given-names>Anita</given-names>
          </name>
          <aff>Department of Computer Science, SNDT Women’s University, Juhu Campus, Mumbai, Maharashtra, 400049, India</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>9-A</issue>
      <fpage>3143</fpage>
      <lpage>3151</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>09</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Entropy is used to quantify uncertainty in probabilistic representations. Hence, studying how uncertainty evolves across layers in LLMs can help us understand how these models process different languages. This paper presents a layer-wise entropy analysis of how information is processed across layers of four different Transformer models using parallel data in English, Hindi, Marathi, and Gujarati. The Shannon entropy is computed for each layer and several information-theoretic metrics are derived, including entropy change, CR, JSD and LDI. In addition, four scalar measures like NLC, ACD, ES, and CLAS are used to summarise overall compression behaviour. The results show that autoregressive models exhibit largely monotonic entropy compression, whereas the multilingual model shows oscillatory compression and expansion patterns. English undergoes stronger and more efficient entropy reduction than Indic Languages, while Hindi and Marathi show closely aligned entropy trajectories. These findings support the use of entropy-based analysis as a diagnostic tool for analysing architectural behaviour and cross-lingual representational disparities in transformer models.</p>
      </abstract>
      <kwd-group>
        <kwd>Entropy</kwd>
        <kwd>LLMs</kwd>
        <kwd>Information theory</kwd>
        <kwd>Entropy analysis</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
