A topological model for partial equivariance in deep learning and data analysis

• 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)

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