Additive decomposition of one-dimensional signals using Transformers

2025-06-06

AI Summary

This work addresses the interpretable additive decomposition of one-dimensional signals. We propose the first Transformer-based end-to-end deep learning method that automatically disentangles an input signal into four physically meaningful components: piecewise-constant, smooth (low-frequency), texture (high-frequency), and noise. Unlike conventional approaches relying on hand-crafted mathematical priors (e.g., total variation or sinusoidal models), our method employs a sequence-to-sequence architecture with a multi-branch output head to jointly predict all components, trained exclusively on synthetically generated data. Experiments on in-distribution synthetic signals demonstrate significantly lower reconstruction errors for each component compared to classical methods—including TV-L1 regularization and synchrosqueezing transform—validating the Transformer’s capacity to learn effective signal priors from data. The results establish a new data-driven paradigm for interpretable signal decomposition, highlighting both modeling efficacy and generalization potential.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often rely on mathematical models, recent research suggests that applying the latest deep learning models to this problem presents an exciting, unexplored area with promising potential. This work presents a novel method for the additive decomposition of one-dimensional signals. We leverage the Transformer architecture to decompose signals into their constituent components: piece-wise constant, smooth (low-frequency oscillatory), textured (high-frequency oscillatory), and a noise component. Our model, trained on synthetic data, achieves excellent accuracy in modeling and decomposing input signals from the same distribution, as demonstrated by the experimental results.

Problem

• Decompose 1D signals into components using Transformers
• Replace traditional math models with deep learning
• Achieve accurate decomposition of synthetic signal data

Innovation

• Uses Transformer architecture for signal decomposition
• Decomposes signals into four distinct components
• Trained on synthetic data for high accuracy