2018 Fiscal Year Research-status Report
An adjoint functors approach to models of cognition
| Project/Area Number |
16KT0025
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| Research Institution | National Institute of Advanced Industrial Science and Technology |
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Principal Investigator |
Phillips Steven 国立研究開発法人産業技術総合研究所, 情報・人間工学領域, 上級主任研究員 (90344209)
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| Co-Investigator(Kenkyū-buntansha) |
武田 裕司 国立研究開発法人産業技術総合研究所, 情報・人間工学領域, 研究チーム長 (10357410)
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| Project Period (FY) |
2016-07-19 – 2020-03-31
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| Keywords | dual-process / category / functor / adjunction / sheaf / sheafification / cognition |
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| Outline of Annual Research Achievements |
This project proposes a category theory approach to the development of theory and experiments for dual-process cognition, i.e. where multiple cognitive processing paths a deployed for a common cognitive task, which has been characterized as fast versus slow thinking (Kahneman, 2011). The working hypothesis is that adjoint functors underlie dual- process cognition. Experiments based on this formal category theory construction were conducted (Phillips, et al. 2016, 2017). For the purpose of pursuing the theoretically side of this project, the main result for this financial year was the development of a category (sheaf) theory model (Phillips, 2018) that accounts for certain generalization effects observed for a dual-process experiment (Phillips, et al. 2016), where participants where required to learn cue-target mappings that could be realized by associative processes; no generalization case, or relational process: as the product of two cue-target maps; generalization case.
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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
These results were modeled as data attached to an underlying topological space (presheaf/sheaf): first and second letter/feature dimensions constitute the space, and the data are the cues/targets. Sheaving models the generalization observed in the experiment. The data labelled “old” are attached as a result of learning the mappings given by the training set. In the case that the underlying space is the discrete topology, then sheaving results in the data labelled “new”, which correspond to the mappings given by the testing set. This situation corresponds to the relational process path. In the case that the space is the indiscrete topology sheaving is trivial: the presheaf is also a sheaf, so no new data are attached, hence no generalization. This situation corresponds to the associative process.
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| Strategy for Future Research Activity |
The plan for future work is to continue developing the sheaf theoretic account. In particular the current model only models two aspects of generalization, but not the transition from no generalization to generalization. Since generalization depends on the underlying topology, we need to consider how that topology is obtained from the data. Further use of sheaf theory and related constructions should be applicable here.
The budget for the new financial year is intended to cover the cost of:
- employing a technical assistant to manage administrative aspects of the project, and
- expenses associated with presenting results for conferences and journal publications.
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| Causes of Carryover |
The budget for the new financial year is intended to cover the cost of:
- employing a technical assistant to manage administrative aspects of the project, and
- expenses associated with presenting results for conferences and journal publications.
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