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2020 年度 実施状況報告書

Structured Tensor Approximation under Kronecker Graph and Its Application on Hydrological Data

研究課題

研究課題/領域番号 20K19875
研究機関国立研究開発法人理化学研究所

研究代表者

李 超  国立研究開発法人理化学研究所, 革新知能統合研究センター, 特別研究員 (10869837)

研究期間 (年度) 2020-04-01 – 2022-03-31
キーワードtensor network / time series forecasting
研究実績の概要

In the past year, we had the progress on the project from the follow aspects. We first focused on the structure search of tensor network decomposition, a challenging combination optimization task appearing in various learning methods. Second, we study the memory mechanism of tensor-power recurrent models, a family of nonlinear dynamics based on tensors. Last, we attempted a practical application task, where we addressed it by novel tensor-based algorithms. The progress we have not only reveals deeper understanding on the structured tensor approximation issue from the theoretical side, yet achieves superior performance on real-world tasks from the practical side.

Theoretically, we solve the topology-search issue for tensor network decomposition by evolutionary algorithm, where we encode the topological structures into binary strings, and develop a simple genetic meta-algorithm to search the optimal topology. In addition, we study the memory mechanism of tensor-power recurrent models, where we prove that a large model degree is an essential condition to achieve the long memory effect, yet it would lead to unstable dynamical behaviors.

Empirically, we propose a tensor-based method termed Time Product Fusion Network (TPFN) for the task of multimodal sentiment analysis. We construct the fused features by the tensor product along adjacent time-steps, such that richer modal and temporal interactions are utilized. Results on CMU-MOSI and CMU-MOSEI datasets show that TPFN can compete with state-of-the art approaches in cases of both random and structured missing values.

現在までの達成度 (区分)
現在までの達成度 (区分)

2: おおむね順調に進展している

理由

We have achieved part of the goals in the past year, especially on the theoretical study of the structure search issue and properties of the dynamical behaviour of tensor methods. These results can be used to partially answer the theoretical questions proposed in the project , i.e., the formulation and properties of the structured-tensor-based learning models. The progress is closed to that we expected in the project proposal.

今後の研究の推進方策

In the next year, we plan to pay more effort on the study of the connection between graph theory and tensor networks. Based on the previous works, we plan to continue the topic on the structure search issue, yet to focus on an unsolved question that how the symmetry of the topological structures impacts difficulty of the structure search issue. The topic will be discussed by the tools from group theory and discrete mathematic. The potential results would be useful to develop more efficient tensor methods for various learning tasks. Furthermore, we also have the plan to improve algorithms proposed in the past year and to evaluate their performance on the hydrological data.

次年度使用額が生じた理由

Due to the COVID-19 issue, the total cost was less than expected in the proposal, especially on the travel expense and personnel expenditure. In the next year, we have the plan to increase the virtual academic networking including on-line talks and seminars. In addition, several national travels are also considered this year yet it depends on the COVID condition. The article and personal cost will be also implemented in this year as planed in the proposal.

備考

The urls for the open-access papers are listed.

  • 研究成果

    (10件)

すべて 2021 2020 その他

すべて 雑誌論文 (4件) (うち国際共著 4件、 査読あり 4件、 オープンアクセス 3件) 学会発表 (3件) (うち国際学会 3件) 備考 (3件)

  • [雑誌論文] On the Memory Mechanism of Tensor-Power Recurrent Models2021

    • 著者名/発表者名
      Qiu, Hejia and Li, Chao and Weng, Ying and Sun, Zhun and He, Xingyu and Zhao, Qibin
    • 雑誌名

      Proceedings of the International Conference on Artificial Intelligence and Statistics

      巻: 1 ページ: 3682--3690

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Evolutionary topology search for tensor network decomposition2020

    • 著者名/発表者名
      Li, Chao and Sun, Zhun
    • 雑誌名

      Proceedings of the International Conference on Machine Learning

      巻: 1 ページ: 5947--5957

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Tpfn: Applying outer product along time to multimodal sentiment analysis fusion on incomplete data2020

    • 著者名/発表者名
      Li, Binghua and Li, Chao and Duan, Feng and Zheng, Ning and Zhao, Qibin
    • 雑誌名

      Computer Vision -- ECCV 2020

      巻: 1 ページ: 431-447

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Low Tensor-Ring Rank Completion by Parallel Matrix Factorization2020

    • 著者名/発表者名
      Yu Jinshi、Zhou Guoxu、Li Chao、Zhao Qibin、Xie Shengli
    • 雑誌名

      IEEE Transactions on Neural Networks and Learning Systems

      巻: 1 ページ: 1~14

    • DOI

      10.1109/TNNLS.2020.3009210

    • 査読あり / 国際共著
  • [学会発表] On the Memory Mechanism of Tensor-Power Recurrent Models2021

    • 著者名/発表者名
      Li, Chao
    • 学会等名
      International Conference on Artificial Intelligence and Statistics
    • 国際学会
  • [学会発表] Evolutionary topology search for tensor network decomposition2020

    • 著者名/発表者名
      Li, Chao
    • 学会等名
      International Conference on Machine Learning
    • 国際学会
  • [学会発表] Tpfn: Applying outer product along time to multimodal sentiment analysis fusion on incomplete data2020

    • 著者名/発表者名
      Li, Chao
    • 学会等名
      European Conference on Computer Vision
    • 国際学会
  • [備考] Paper 1

    • URL

      http://proceedings.mlr.press/v130/qiu21a/qiu21a.pdf

  • [備考] Paper 2

    • URL

      http://proceedings.mlr.press/v119/li20l/li20l.pdf

  • [備考] Paper 3

    • URL

      http://www.ecva.net/papers/eccv_2020/papers_ECCV/papers/123690426.pdf

URL: 

公開日: 2021-12-27  

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