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RIE-SenseNet: Riemannian Manifold Embedding of Multi-Source Industrial Sensor Signals for Robust Pattern Recognition

Xu Wang, Puyu Han, Jiaju Kang, Weichao Pan, Luqi Gong

TL;DR

This work addresses the dual challenges of nonlinear structure and distribution shifts in industrial sensor signals by introducing RIE-SenseNet, a geometry-aware Transformer that operates on a hyperbolic Riemannian manifold with a learnable curvature parameter $c$. It combines Möbius-based hyperbolic mapping, a curvature-aware Transformer backbone, and a manifold-based data augmentation pipeline to preserve data geometry and generate faithful synthetic samples. The approach yields state-of-the-art performance, achieving over $>90 ext{%}$ F1-score and substantial robustness improvements over Euclidean CNNs and standard Transformers. The findings demonstrate the practical value of non-Euclidean feature representations and geometry-consistent augmentation for reliable pattern recognition in industrial sensing, with potential for broader IIoT applications. Key contributions include the geometry-aware embedding, hyperbolic attention mechanism, and a principled augmentation strategy that respects manifold structure.

Abstract

Industrial sensor networks produce complex signals with nonlinear structure and shifting distributions. We propose RIE-SenseNet, a novel geometry-aware Transformer model that embeds sensor data in a Riemannian manifold to tackle these challenges. By leveraging hyperbolic geometry for sequence modeling and introducing a manifold-based augmentation technique, RIE-SenseNet preserves sensor signal structure and generates realistic synthetic samples. Experiments show RIE-SenseNet achieves >90% F1-score, far surpassing CNN and Transformer baselines. These results illustrate the benefit of combining non-Euclidean feature representations with geometry-consistent data augmentation for robust pattern recognition in industrial sensing.

RIE-SenseNet: Riemannian Manifold Embedding of Multi-Source Industrial Sensor Signals for Robust Pattern Recognition

TL;DR

This work addresses the dual challenges of nonlinear structure and distribution shifts in industrial sensor signals by introducing RIE-SenseNet, a geometry-aware Transformer that operates on a hyperbolic Riemannian manifold with a learnable curvature parameter . It combines Möbius-based hyperbolic mapping, a curvature-aware Transformer backbone, and a manifold-based data augmentation pipeline to preserve data geometry and generate faithful synthetic samples. The approach yields state-of-the-art performance, achieving over F1-score and substantial robustness improvements over Euclidean CNNs and standard Transformers. The findings demonstrate the practical value of non-Euclidean feature representations and geometry-consistent augmentation for reliable pattern recognition in industrial sensing, with potential for broader IIoT applications. Key contributions include the geometry-aware embedding, hyperbolic attention mechanism, and a principled augmentation strategy that respects manifold structure.

Abstract

Industrial sensor networks produce complex signals with nonlinear structure and shifting distributions. We propose RIE-SenseNet, a novel geometry-aware Transformer model that embeds sensor data in a Riemannian manifold to tackle these challenges. By leveraging hyperbolic geometry for sequence modeling and introducing a manifold-based augmentation technique, RIE-SenseNet preserves sensor signal structure and generates realistic synthetic samples. Experiments show RIE-SenseNet achieves >90% F1-score, far surpassing CNN and Transformer baselines. These results illustrate the benefit of combining non-Euclidean feature representations with geometry-consistent data augmentation for robust pattern recognition in industrial sensing.

Paper Structure

This paper contains 13 sections, 6 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Problem Context and Approach
  4. Riemannian Manifold Data Augmentation
  5. Hyperbolic Mapping and Model Architecture
  6. Hyperbolic Attention Mechanism
  7. Experiments
  8. Datasets and Preprocessing
  9. Experimental Setup
  10. Baselines
  11. Quantitative Results
  12. Analysis and Discussion
  13. Conclusion

Figures (2)

  • Figure 1: Comparison of Möbius and Euclidean operations in the Poincaré disk model. The left subplot illustrates Möbius addition (blue) and Euclidean addition (magenta), showing that Möbius addition preserves hyperbolic geometry while Euclidean addition may lead to distortions outside the disk. The right subplot highlights the same behavior for Möbius matrix-vector multiplication versus Euclidean multiplication, with Möbius operations maintaining the integrity of the hyperbolic space.
  • Figure 2: Manifold-based data augmentation pipeline for Sensor Data signals.