# On the relation between Loss Functions and T-Norms

## TL;DR

This paper explores the connection between loss functions and t-norms, providing a new interpretation that leads to the development of novel loss functions potentially improving convergence in supervised learning.

## Contribution

It introduces a general relation between loss functions and t-norms, offering a new perspective and a novel class of loss functions for supervised learning.

## Key findings

- Derived a relation between loss functions and t-norms.
- Proposed a new class of loss functions based on t-norms.
- Potential for faster convergence than cross-entropy loss.

## Abstract

Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures. While the cross-entropy loss is usually justified from a probabilistic perspective, this paper shows an alternative and more direct interpretation of this loss in terms of t-norms and their associated generator functions, and derives a general relation between loss functions and t-norms. In particular, the presented work shows intriguing results leading to the development of a novel class of loss functions. These losses can be exploited in any supervised learning task and which could lead to faster convergence rates that the commonly employed cross-entropy loss.