A principled generalization of the maximum entropy principle for non-Shannon systems
| Project/Area Number |
23K16855
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Araya Inc. (Research & Development Department) |
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Principal Investigator |
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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| Project Period (FY) |
2023-04-01 – 2026-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2025: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2024: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Information Theory / Generalized Entropies / Information Geometry / Complex Systems |
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| Outline of Research at the Start |
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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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
For this first term the project has been progressing according to research proposal, in the expected time frame.
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| Strategy for Future Research Activity |
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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Report
(1 results)
Research Products
(3 results)
