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Limitation of Threshold Circuits designed for Machine Learning

Research Project

Project/Area Number 16K00006
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionYamagata University

Principal Investigator

Uchizawa Kei  山形大学, 大学院理工学研究科, 准教授 (90510248)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsニューラルネットワーク / しきい値回路 / 段数 / マージン / 機械学習 / エネルギー計算量 / 離散力学系 / ホップフィールドネットワーク / 計算複雑さ / 深層学習 / 計算量理論 / 特徴写像
Outline of Final Research Achievements

In this research, we theoretically investigate a question why neural networks of large depth obtained by a machine learning method show significant performance for various tasks. We consider a particular type of neural networks, called threshold circuits, and then provide mathematical proofs which suggest that large depth contributes to the performance of threshold circuits that carry out (somewhat artificial) information processing. As part of the proofs, we also show detailed constructions (that is, placement of neural computational elements and their connections) of threshold circuits that are guaranteed to be achieve good performance for the information processing.

Academic Significance and Societal Importance of the Research Achievements

ニューラルネットワークによって実現できる情報処理の性質を理解することは,脳型の計算機,あるいはニューラルネットワークを用いた機械学習の基礎研究として重要である.特に本研究の結果は,ニューラルネットワークを用いて情報処理を行う場合,どのようなタスクに対してニューラルネットワークの性能が発揮されるのか,あるいは性能が発揮できる場合どのような設計が有効であるのかを明らかにすることにつながる.

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (10 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (3 results)

  • [Int'l Joint Research] University of Miami(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Miami(米国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Generalized predecessor existence problems for Boolean finite dynamical systems on directed graphs2019

    • Author(s)
      Kawachi Akinori、Ogihara Mitsunori、Uchizawa Kei
    • Journal Title

      Theoretical Computer Science

      Volume: 762 Pages: 25-40

    • DOI

      10.1016/j.tcs.2018.08.026

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Computational Power of Threshold Circuits of Energy at most Two2018

    • Author(s)
      MANIWA Hiroki、OKI Takayuki、SUZUKI Akira、UCHIZAWA Kei、ZHOU Xiao
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E101.A Issue: 9 Pages: 1431-1439

    • DOI

      10.1587/transfun.E101.A.1431

    • NAID

      130007479449

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2018-09-01
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Computational complexity studies of synchronous Boolean finite dynamical systems on directed graphs2017

    • Author(s)
      Mitsunori Ogihara, Kei Uchizawa
    • Journal Title

      Information and Computation

      Volume: 256 Pages: 226-236

    • DOI

      10.1016/j.ic.2017.07.008

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems2017

    • Author(s)
      Akinori Kawachi, Mitsunori Ogihara, Kei Uchizawa
    • Journal Title

      Proceedings of the 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

      Volume: 83

    • DOI

      10.4230/LIPIcs.MFCS.2017.8

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Threshold Circuits Detecting Global Patterns in Two-dimensional Maps2016

    • Author(s)
      Kei Uchizawa, Daiki Yashima, Xiao Zhou
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 20 Issue: 1 Pages: 115-131

    • DOI

      10.7155/jgaa.00387

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] パリティ関数を計算するしきい値回路のエネルギー計算量と段数2019

    • Author(s)
      内澤 啓
    • Organizer
      京都大学数理解析研究所RIMS共同研究(公開型)「アルゴリズムと計算理論の新潮流」
    • Related Report
      2018 Annual Research Report
  • [Presentation] 一般化対称関数を計算するエネルギー効率の良いしきい値回路に関する研究2017

    • Author(s)
      間庭 宏貴, 大木 貴之, 鈴木 顕, 内澤 啓, 周 暁
    • Organizer
      冬のLAシンポジウム
    • Place of Presentation
      京都大学,数理解析研究所
    • Year and Date
      2017-02-01
    • Related Report
      2016 Research-status Report
  • [Presentation] 正規化マージンを用いたしきい値回路の性能評価2017

    • Author(s)
      坂口慶介,内澤 啓,瀧本英二
    • Organizer
      電子情報通信学会総合大会,COMP-ELC学生シンポジウム
    • Place of Presentation
      名城大学,天白キャンパス
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2022-02-21  

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