| 研究課題/領域番号 |
23K16855
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| 研究種目 |
若手研究
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| 配分区分 | 基金 |
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| 審査区分 |
小区分60030:統計科学関連
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| 研究機関 | 株式会社アラヤ(研究開発部) |
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研究代表者 |
モラレス パブロ 株式会社アラヤ(研究開発部), 研究開発部, チーフリサーチャー (60903804)
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| 研究期間 (年度) |
2023-04-01 – 2026-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
4,680千円 (直接経費: 3,600千円、間接経費: 1,080千円)
2025年度: 1,560千円 (直接経費: 1,200千円、間接経費: 360千円)
2024年度: 1,950千円 (直接経費: 1,500千円、間接経費: 450千円)
2023年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
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| キーワード | Information Theory / Generalized Entropies / Information Geometry / Complex Systems |
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| 研究開始時の研究の概要 |
The Maximum Entropy Principle (MEP) is effective for producing unbiased statistical models, yet its standard formulation leaves out many systems of interest. As these setups gain interest, a principled extension of the MEP is necessary. This project uses information-geometry to extend the MEP.
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| 研究実績の概要 |
This project aims at a generalization of the maximum entropy principle (MEP) which has successfully served at a large range of scenarios as a guiding principle for the production of unbiased statistical models. In particular, its geometrization in statistical manifolds has revealed an extended MEP via Renyi entropies. In this first term, it was shown that this Renyi-extended MEP may be understood via deformations of the Legendre transform which mediates between the primal and dual variables that characterize an statistical manifold. Consequences of this deformation were studied via symplectic geometry and complex manifolds. Furthermore, implications of this deformation were studied within the stochastic thermodynamics, being deeply connected to Kolmogorov-Nagumo averages.
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| 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
For this first term the project has been progressing according to research proposal, in the expected time frame.
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| 今後の研究の推進方策 |
A better understanding of higher order multivariate interactions (HOIs) in dynamical systems may be crucial to describe neural activity and artificial networks. The simultaneous silence of neurons as a ubiquitous feature may result from HOIs that constrain neural activity patterns influencing information processing in the brain. Currently, to deal with higher order couplings in neuron systems, one often has to resort to adhoc semi-analytical methods to deal with the large order of parameters. However, an immediate consequences of the Renyi-extended MEP is the induction of HOIs modulated by the statistical manifold's curvature. For the next term of this project, implications of these HOIs will be studied for Hopfield networks and neuron systems within the context of statistical mechanics.
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