# Semiring Activation in Neural Networks

arXiv: https://arxiv.org/abs/2405.18805 · HTML: https://mlsanity.com/paper/2405.18805/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [A survey on modern trainable activation functions](https://mlsanity.com/paper/2005.00817/) (2020)
- [NVIDIA Tensor Core Programmability, Performance & Precision](https://mlsanity.com/paper/1803.04014/) (2018)
- [PDE-based Group Equivariant Convolutional Neural Networks](https://mlsanity.com/paper/2001.09046/) (2020)
- [Adaptive Blending Units: Trainable Activation Functions for Deep Neural Networks](https://mlsanity.com/paper/1806.10064/) (2018)
- [Deep Morphological Neural Networks](https://mlsanity.com/paper/1909.01532/) (2019)

## Abstract (arXiv)

We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators generalize the traditional alternation of linear operators with activation functions in neural networks. Semirings are algebraic structures that describe a generalised notation of linearity, greatly expanding the range of trainable operators that can be included in neural networks. In fact, max- or min-pooling operations are convolutions in the tropical semiring with a fixed kernel. We perform experiments where we replace the activation functions for trainable semiring-based operators to show that these are viable operations to include in fully connected as well as convolutional neural networks (ConvNeXt). We discuss some of the challenges of replacing traditional activation functions with trainable semiring activations and the trade-offs of doing so.