# Feature-Based Lie Group Transformer for Real-World Applications

arXiv: https://arxiv.org/abs/2506.04668 · HTML: https://mlsanity.com/paper/2506.04668/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models](https://mlsanity.com/paper/2301.13721/) (2023)
- [Disentangling Patterns and Transformations from One Sequence of Images with Shape-invariant Lie Group Transformer](https://mlsanity.com/paper/2203.11210/) (2022)
- [Unsupervised categorization of similarity measures](https://mlsanity.com/paper/2502.08098/) (2025)
- [Learning Conditionally Independent Transformations using Normal Subgroups in Group Theory](https://mlsanity.com/paper/2504.04490/) (2025)
- [Ablation Study to Clarify the Mechanism of Object Segmentation in Multi-Object Representation Learning](https://mlsanity.com/paper/2310.03273/) (2023)

## Built on by (most cited first, 2 of 2)

- [Transformation Categorization Based on Group Decomposition Theory Using Parameter Division](https://mlsanity.com/paper/2605.04056/) (2026)
- [Unsupervised Learning of Inter-Object Relationships via Group Homomorphism](https://mlsanity.com/paper/2604.20925/) (2026)

## Abstract (arXiv)

The main goal of representation learning is to acquire meaningful representations from real-world sensory inputs without supervision. Representation learning explains some aspects of human development. Various neural network (NN) models have been proposed that acquire empirically good representations. However, the formulation of a good representation has not been established. We recently proposed a method for categorizing changes between a pair of sensory inputs. A unique feature of this approach is that transformations between two sensory inputs are learned to satisfy algebraic structural constraints. Conventional representation learning often assumes that disentangled independent feature axes is a good representation; however, we found that such a representation cannot account for conditional independence. To overcome this problem, we proposed a new method using group decomposition in Galois algebra theory. Although this method is promising for defining a more general representation, it assumes pixel-to-pixel translation without feature extraction, and can only process low-resolution images with no background, which prevents real-world application. In this study, we provide a simple method to apply our group decomposition theory to a more realistic scenario by combining feature extraction and object segmentation. We replace pixel translation with feature translation and formulate object segmentation as grouping features under the same transformation. We validated the proposed method on a practical dataset containing both real-world object and background. We believe that our model will lead to a better understanding of human development of object recognition in the real world.