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A topological model...
A topological model for partial equivariance in deep learning and data analysis
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- Ferrari, Lucia (författare)
- Department of Mathematics, University of Bologna, Bologna, Italy
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- Frosini, Patrizio (författare)
- Department of Mathematics, University of Bologna, Bologna, Italy
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- Quercioli, Nicola (författare)
- Department of Electrical, Electronic, and Information Engineering (DEI), WiLab-National Laboratory for Wireless Communications, National Inter-University Consortium for Telecommunications (CNIT), University of Bologna, Bologna, Italy
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- Tombari, Francesca (författare)
- KTH,Matematik (Inst.)
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(creator_code:org_t)
- Frontiers Media SA, 2023
- 2023
- Engelska.
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Ingår i: Frontiers in Artificial Intelligence. - : Frontiers Media SA. - 2624-8212. ; 6
- Relaterad länk:
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https://doi.org/10.3...
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https://urn.kb.se/re...
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https://doi.org/10.3...
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Abstract
Ämnesord
Stäng
- In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of transformations, in a non-expansive way. If the set of transformations acting is a group, we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subjected to the action of certain self-maps and the space of P-GENEOs between these spaces. We define pseudo-metrics on them and show some properties of the resulting spaces. In particular, we show how such spaces have convenient approximation and convexity properties.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
Nyckelord
- compactness
- convexity
- P-GENEO
- partial-equivariant neural network
- pseudo-metric space
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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