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Complementarity-Preserving Generative Theory for Multimodal ECG Synthesis: A Quantum-Inspired Approach

Timothy Oladunni, Farouk Ganiyu-Adewumi, Clyde Baidoo, Kyndal Maclin

Abstract

Multimodal deep learning has substantially improved electrocardiogram (ECG) classification by jointly leveraging time, frequency, and time-frequency representations. However, existing generative models typically synthesize these modalities independently, resulting in synthetic ECG data that are visually plausible yet physiologically inconsistent across domains. This work establishes a Complementarity-Preserving Generative Theory (CPGT), which posits that physiologically valid multimodal signal generation requires explicit preservation of cross-domain complementarity rather than loosely coupled modality synthesis. We instantiate CPGT through Q-CFD-GAN, a quantum-inspired generative framework that models multimodal ECG structure within a complex-valued latent space and enforces complementarity-aware constraints regulating mutual information, redundancy, and morphological coherence. Experimental evaluation demonstrates that Q-CFD-GAN reduces latent embedding variance by 82%, decreases classifier-based plausibility error by 26.6%, and restores tri-domain complementarity from 0.56 to 0.91, while achieving the lowest observed morphology deviation (3.8%). These findings show that preserving multimodal information geometry, rather than optimizing modality-specific fidelity alone, is essential for generating synthetic ECG signals that remain physiologically meaningful and suitable for downstream clinical machine-learning applications.

Complementarity-Preserving Generative Theory for Multimodal ECG Synthesis: A Quantum-Inspired Approach

Abstract

Multimodal deep learning has substantially improved electrocardiogram (ECG) classification by jointly leveraging time, frequency, and time-frequency representations. However, existing generative models typically synthesize these modalities independently, resulting in synthetic ECG data that are visually plausible yet physiologically inconsistent across domains. This work establishes a Complementarity-Preserving Generative Theory (CPGT), which posits that physiologically valid multimodal signal generation requires explicit preservation of cross-domain complementarity rather than loosely coupled modality synthesis. We instantiate CPGT through Q-CFD-GAN, a quantum-inspired generative framework that models multimodal ECG structure within a complex-valued latent space and enforces complementarity-aware constraints regulating mutual information, redundancy, and morphological coherence. Experimental evaluation demonstrates that Q-CFD-GAN reduces latent embedding variance by 82%, decreases classifier-based plausibility error by 26.6%, and restores tri-domain complementarity from 0.56 to 0.91, while achieving the lowest observed morphology deviation (3.8%). These findings show that preserving multimodal information geometry, rather than optimizing modality-specific fidelity alone, is essential for generating synthetic ECG signals that remain physiologically meaningful and suitable for downstream clinical machine-learning applications.

Paper Structure

This paper contains 35 sections, 4 theorems, 25 equations, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. ECG Generative Models
  5. Multimodal ECG Analysis and Complementarity
  6. Complex-Valued and Quantum-Inspired Representation Learning
  7. Q--CFD--GAN Theory
  8. Complementary Feature Domain Structure
  9. Structured Latent Representation for Multimodal Coupling
  10. Interference Operator and Cross-Domain Regulation
  11. Interference collapse.
  12. Complementarity and Morphology Constraints
  13. Proposed Q--CFD--GAN Framework
  14. Multimodal Generator Architecture
  15. Multimodal ECG Preprocessing
  16. ...and 20 more sections

Key Result

Theorem 1

Let $\mathcal{L}_{\mathrm{CFD}} = 0$ iff $(\widehat{C}_{TFS} = C_{TFS},\ \widehat{R}_{ij} = R_{ij})$. If $G^\star = \arg\min_G \mathcal{L}_{\mathrm{CFD}}$, then

Figures (6)

  • Figure 1: Q--CFD--GAN generator architecture. A shared complex-valued latent state is mapped to a common latent core and decoded in parallel to generate synchronized time-, frequency-, and time--frequency ECG representations.
  • Figure 2: Workflow for ECG synthesis evaluation using Q--CFD--GAN. Synthetic time, frequency, and time--frequency ECG modalities and real test data are processed through a pretrained multimodal encoder; CFD and morphology metrics jointly quantify multimodal coherence and physiological fidelity.
  • Figure 3: Peak-to-peak (P2P) amplitude distribution.
  • Figure 4: RMS energy distribution.
  • Figure 5: Spectral entropy distribution.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 1: CFD Preservation
  • Theorem 2: Minimal Complex Latent Structure
  • Theorem 3: Interference Stability
  • Theorem 4: Sufficient Conditions for Coherent Generation