Feature-Based Lie Group Transformer for Real-World Applications

2025-06-05

AI Summary

Existing unsupervised representation learning methods struggle with high-resolution, background-rich real-world images due to reliance on pixel-level translation modeling and insufficient semantic feature extraction. Method: We propose a semantics-structured group decomposition representation framework. Its core innovation lies in the first integration of Galois-theoretic group decomposition with feature-level Lie group transformations—extending group actions from pixel translations to semantic feature translations—and introducing an object-segmentation-guided, transformation-driven feature grouping mechanism. Contribution/Results: Our approach relaxes the strong conditional independence assumptions inherent in conventional disentangled representation learning. Evaluated on background-contaminated real-object datasets, it demonstrates preserved transformation structure and consistent object recognition performance. It significantly enhances interpretability and generalization capability of unsupervised representations in complex scenes, advancing semantic-aware, geometry-grounded representation learning.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Develop unsupervised representation learning for real-world sensory inputs
• Overcome limitations of disentangled feature axes in representation learning
• Apply group decomposition theory to realistic scenarios with feature extraction

Innovation

• Combines feature extraction with group decomposition
• Replaces pixel translation with feature translation
• Formulates object segmentation via transformation grouping