# A Unified View of Polarity for Functions

arXiv: https://arxiv.org/abs/2410.16773 · HTML: https://mlsanity.com/paper/2410.16773/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [Comparing Corrupted Constrained Learning Problems](https://mlsanity.com/paper/2608.25745/) (2026)

## Abstract (arXiv)

We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices. Also, we explore three possible notions of polar subdifferential associated with a nonnegative function, and we make the connection with the notion of alignement of vectors.