# Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

arXiv: https://arxiv.org/abs/2104.07060 · HTML: https://mlsanity.com/paper/2104.07060/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 9 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [Differentially Private Transferrable Deep Learning with Membership-Mappings](https://mlsanity.com/paper/2105.04615/) (2021)
- [On Mitigating the Utility-Loss in Differentially Private Learning: A new Perspective by a Geometrically Inspired Kernel Approach](https://mlsanity.com/paper/2304.01300/) (2023)
- [Membership-Mappings for Practical Secure Distributed Deep Learning](https://mlsanity.com/paper/2204.05765/) (2022)
- [Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent](https://mlsanity.com/paper/2407.04335/) (2024)
- [Information Theoretic Evaluation of Privacy-Leakage, Interpretability, and Transferability for Trustworthy AI](https://mlsanity.com/paper/2106.06046/) (2021)

## Abstract (arXiv)

A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy theoretic analytical deep models is still not available. This paper introduces using measure theoretic basis the notion of membership-mapping for representing data points through attribute values (motivated by fuzzy theory). A property of the membership-mapping, that can be exploited for data representation learning, is of providing an interpolation on the given data points in the data space. An analytical approach to the variational learning of a membership-mappings based data representation model is considered.