# Capsule Networks with Max-Min Normalization

arXiv: https://arxiv.org/abs/1903.09662 · HTML: https://mlsanity.com/paper/1903.09662/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 6 of 6)

- [Recurrent Attention Models with Object-centric Capsule Representation for Multi-object Recognition](https://mlsanity.com/paper/2110.04954/) (2021)
- [Enhancing Classification Performance via Reinforcement Learning for Feature Selection](https://mlsanity.com/paper/2403.05979/) (2024)
- [WideCaps: A Wide Attention based Capsule Network for Image Classification](https://mlsanity.com/paper/2108.03627/) (2021)
- [Capsule networks with non-iterative cluster routing](https://mlsanity.com/paper/2109.09213/) (2021)
- [Reconstruction-guided attention improves the robustness and shape processing of neural networks](https://mlsanity.com/paper/2209.13620/) (2022)
- [Bhargava Cube--Inspired Quadratic Regularization for Structured Neural Embeddings](https://mlsanity.com/paper/2512.11392/) (2025)

## Abstract (arXiv)

Capsule Networks (CapsNet) use the Softmax function to convert the logits of the routing coefficients into a set of normalized values that signify the assignment probabilities between capsules in adjacent layers. We show that the use of Softmax prevents capsule layers from forming optimal couplings between lower and higher-level capsules. Softmax constrains the dynamic range of the routing coefficients and leads to probabilities that remain mostly uniform after several routing iterations. Instead, we propose the use of Max-Min normalization. Max-Min performs a scale-invariant normalization of the logits that allows each lower-level capsule to take on an independent value, constrained only by the bounds of normalization. Max-Min provides consistent improvement in test accuracy across five datasets and allows more routing iterations without a decrease in network performance. A single CapsNet trained using Max-Min achieves an improved test error of 0.20% on the MNIST dataset. With a simple 3-model majority vote, we achieve a test error of 0.17% on MNIST.