The Matrix: A Bayesian learning model for LLMs

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  "title": "The Matrix: A Bayesian learning model for LLMs",
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  "url": "https://arxiv.org/abs/2402.03175"
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{
  "author": "Siddhartha Dalal",
  "date": "2024-02-05T12:00:00.000Z",
  "description": "This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs), focusing on their core optimization metric of next token prediction. We develop a theoretical framework based on an ideal generative text model represented by a multinomial transition probability matrix with a prior, and examine how LLMs approximate this matrix. Key contributions include: (i) a continuity theorem relating embeddings to multinomial distributions, (ii) a demonstration that LLM text generation aligns with Bayesian learning principles, (iii) an explanation for the emergence of in-context learning in larger models, (iv) empirical validation using visualizations of next token probabilities from an instrumented Llama model Our findings provide new insights into LLM functioning, offering a statistical foundation for understanding their capabilities and limitations. This framework has implications for LLM design, training, and application, potentially guiding future developments in the field.",
  "image": "https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png",
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  "publisher": "arXiv.org",
  "title": "Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference",
  "url": "https://arxiv.org/abs/2402.03175v2"
}

{
  "url": "https://arxiv.org/abs/2402.03175",
  "title": "Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference",
  "description": "This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs), focusing on their core optimization metric of next token prediction. We develop a...",
  "links": [
    "https://arxiv.org/abs/2402.03175v2",
    "https://arxiv.org/abs/2402.03175"
  ],
  "image": "https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png",
  "content": "<div>\n  <div>\n    <p>\n      </p><h2>Computer Science &gt; Machine Learning</h2>\n    <p></p>\n    <p><strong>arXiv:2402.03175</strong> (cs)\n    </p>\n<div>\n                <p>View a PDF of the paper titled Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference, by Siddhartha Dalal and Vishal Misra</p>\n    <p><a target=\"_blank\" href=\"https://arxiv.org/pdf/2402.03175\">View PDF</a></p><blockquote>\n            <span>Abstract:</span>This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs), focusing on their core optimization metric of next token prediction. We develop a theoretical framework based on an ideal generative text model represented by a multinomial transition probability matrix with a prior, and examine how LLMs approximate this matrix. Key contributions include: (i) a continuity theorem relating embeddings to multinomial distributions, (ii) a demonstration that LLM text generation aligns with Bayesian learning principles, (iii) an explanation for the emergence of in-context learning in larger models, (iv) empirical validation using visualizations of next token probabilities from an instrumented Llama model Our findings provide new insights into LLM functioning, offering a statistical foundation for understanding their capabilities and limitations. This framework has implications for LLM design, training, and application, potentially guiding future developments in the field.\n    </blockquote>\n  </div>\n    <div>\n      <h2>Submission history</h2><p> From: Vishal Misra [<a target=\"_blank\" href=\"https://arxiv.org/show-email/b5133c63/2402.03175\">view email</a>]      <br />            <strong><a target=\"_blank\" href=\"https://arxiv.org/abs/2402.03175v1\">[v1]</a></strong>\n        Mon, 5 Feb 2024 16:42:10 UTC (305 KB)<br />\n    <strong>[v2]</strong>\n        Tue, 24 Sep 2024 13:30:25 UTC (2,800 KB)<br />\n</p></div>\n  </div>\n<div>    <div>\n      <p><a></a>\n      <span>Full-text links:</span></p><h2>Access Paper:</h2>\n      <ul>\n  <p>\nView a PDF of the paper titled Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference, by Siddhartha Dalal and Vishal Misra</p><li><a target=\"_blank\" href=\"https://arxiv.org/pdf/2402.03175\">View PDF</a></li><li><a target=\"_blank\" href=\"https://arxiv.org/src/2402.03175\">TeX Source</a></li><li><a target=\"_blank\" href=\"https://arxiv.org/format/2402.03175\">Other Formats</a></li></ul>\n    </div>\n        <div><p>\n    Current browse context: </p><p>cs.LG</p>\n    </div>\n<p>\n    <span>export BibTeX citation</span>\n</p>\n<div>\n  <p></p><h3>Bookmark</h3><p></p><p><a target=\"_blank\" href=\"http://www.bibsonomy.org/BibtexHandler?requTask=upload&amp;url=https://arxiv.org/abs/2402.03175&amp;description=Beyond%20the%20Black%20Box:%20A%20Statistical%20Model%20for%20LLM%20Reasoning%20and%20Inference\" title=\"Bookmark on BibSonomy\">\n    <img src=\"https://arxiv.org/static/browse/0.3.4/images/icons/social/bibsonomy.png\" alt=\"BibSonomy logo\" />\n  </a>\n  <a target=\"_blank\" href=\"https://reddit.com/submit?url=https://arxiv.org/abs/2402.03175&amp;title=Beyond%20the%20Black%20Box:%20A%20Statistical%20Model%20for%20LLM%20Reasoning%20and%20Inference\" title=\"Bookmark on Reddit\">\n    <img src=\"https://arxiv.org/static/browse/0.3.4/images/icons/social/reddit.png\" alt=\"Reddit logo\" />\n  </a>\n</p></div>  </div>\n<div><p>\n    <label>Bibliographic Tools</label></p><div>\n      <h2>Bibliographic and Citation Tools</h2>\n      <div>\n          <p><label>\n              <span></span>\n              <span>Bibliographic Explorer Toggle</span>\n            </label>\n          </p>\n        </div>\n    </div>\n    <p>\n    <label>Code, Data, Media</label></p><div>\n      <h2>Code, Data and Media Associated with this Article</h2>\n    </div>\n      <p>\n      <label>Demos</label></p><div>\n        <h2>Demos</h2>\n      </div>\n      <p>\n      <label>Related Papers</label></p><div>\n        <h2>Recommenders and Search Tools</h2>\n        <div>\n            <p><label>\n                <span></span>\n                <span>IArxiv recommender toggle</span>\n              </label>\n            </p>\n          </div>\n      </div>\n      <p>\n      <label>\n        About arXivLabs\n      </label></p><div>\n            <h2>arXivLabs: experimental projects with community collaborators</h2>\n            <p>arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.</p>\n            <p>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.</p>\n            <p>Have an idea for a project that will add value for arXiv's community? <a target=\"_blank\" href=\"https://info.arxiv.org/labs/index.html\"><strong>Learn more about arXivLabs</strong></a>.</p>\n          </div>\n    </div>\n</div>",
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