{
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  "authors": [
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "University of Texas Rio Grande Valley, School of Mathematical and Statistical Sciences, , , One West University Blvd., Brownsville, TX 78520, , , USA"
        }
      ], 
      "surname": "Z\u00fa\u00f1iga-Galindo", 
      "email": "wilson.zunigagalindo@utrgv.edu", 
      "full_name": "Z\u00fa\u00f1iga-Galindo, W A", 
      "given_names": "W A"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Oklahoma State University, Department of Mathematics, , , MSCS 425, Stillwater, OK, , , USA"
        }
      ], 
      "surname": "He", 
      "given_names": "C", 
      "full_name": "He, C"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "University of Texas Rio Grande Valley, School of Mathematical and Statistical Sciences, , , One West University Blvd., Brownsville, TX 78520, , , USA"
        }
      ], 
      "surname": "Zambrano-Luna", 
      "given_names": "B A", 
      "full_name": "Zambrano-Luna, B A"
    }
  ], 
  "titles": [
    {
      "source": "OUP", 
      "title": "-Adic statistical field theory and convolutional deep Boltzmann machines An introduction to restricted Boltzmann machines"
    }
  ], 
  "dois": [
    {
      "value": "10.1093/ptep/ptad061"
    }
  ], 
  "publication_info": [
    {
      "journal_title": "Progress of Theoretical and Experimental Physics", 
      "material": "article", 
      "journal_volume": "2023", 
      "artid": "063A01", 
      "year": 2023, 
      "journal_issue": "6"
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    "submission_number": "7d98f3dc0b9111ee8e62c23b20d38f61"
  }, 
  "page_nr": [
    17
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses/by/4.0/", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "statement": "\u00a9 The Author(s) 2023. Published by Oxford University Press on behalf of the Physical Society of Japan.", 
      "year": "2023"
    }
  ], 
  "control_number": "78326", 
  "record_creation_date": "2023-06-15T15:30:22.752001", 
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      "primary": "Progress of Theoretical and Experimental Physics"
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  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "cond-mat.dis-nn"
      ], 
      "value": "2302.03817"
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  "abstracts": [
    {
      "source": "OUP", 
      "value": "Abstract Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories has been proposed. This work investigates this correspondence in the framework of p-adic statistical field theories (SFTs) and neural networks. In this case, the fields are real-valued functions defined on an infinite regular rooted tree with valence p, a fixed prime number. This infinite tree provides the topology for a continuous deep Boltzmann machine (DBM), which is identified with a statistical field theory on this infinite tree. In the p-adic framework, there is a natural method to discretize SFTs. Each discrete SFT corresponds to a Boltzmann machine with a tree-like topology. This method allows us to recover the standard DBMs and gives new convolutional DBMs. The new networks use O(N) parameters while the classical ones use O(N$^{2}$) parameters."
    }
  ], 
  "imprints": [
    {
      "date": "2023-05-10", 
      "publisher": "OUP"
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}