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Curvature-Aware Deep Learning for Vector Boson Fusion: Differential Geometry, Physics-Inspired Features, and Quantum Method Limitations

Alibordi Muhammad

TL;DR

The paper argues that collider data occupy curved statistical manifolds and that curvature-aware learning can better capture nonlinear feature correlations than flat Euclidean models. It introduces a Vector Boson Fusion Higgs classification framework that combines Euclidean, hyperbolic, and spherical representations with physics-inspired, quantum-inspired features, and a quantum feature map mapped to a 5-qubit embedding. Empirically, curvature-aware product-manifold networks yield modest but meaningful improvements over a classical Euclidean baseline (best ROC-AUC of 0.9477), while quantum kernels underperform due to current hardware and sample-size constraints. The study shows that classical differential geometry provides practical benefits for high-energy physics classification, clarifies the limited immediate viability of quantum approaches, and outlines a pathway toward robust curvature-informed learning with domain-specific observables. It emphasizes that quantum-inspired features contribute mainly when embedded in appropriate geometric scaffolding rather than via direct quantum computation, and it lays out a framework for future research in curvature-aware, physics-guided machine learning for particle physics.

Abstract

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired observables with product manifold neural networks. The method unifies Euclidean, hyperbolic, and spherical representations to capture nonlinear correlations among kinematic features. Geometric embedding yields measurable improvements over flat baselines, demonstrating that curvature-aware architectures recover information lost in standard approaches. The study highlights how incorporating geometric structure enhances discrimination power in high-energy collision data.

Curvature-Aware Deep Learning for Vector Boson Fusion: Differential Geometry, Physics-Inspired Features, and Quantum Method Limitations

TL;DR

The paper argues that collider data occupy curved statistical manifolds and that curvature-aware learning can better capture nonlinear feature correlations than flat Euclidean models. It introduces a Vector Boson Fusion Higgs classification framework that combines Euclidean, hyperbolic, and spherical representations with physics-inspired, quantum-inspired features, and a quantum feature map mapped to a 5-qubit embedding. Empirically, curvature-aware product-manifold networks yield modest but meaningful improvements over a classical Euclidean baseline (best ROC-AUC of 0.9477), while quantum kernels underperform due to current hardware and sample-size constraints. The study shows that classical differential geometry provides practical benefits for high-energy physics classification, clarifies the limited immediate viability of quantum approaches, and outlines a pathway toward robust curvature-informed learning with domain-specific observables. It emphasizes that quantum-inspired features contribute mainly when embedded in appropriate geometric scaffolding rather than via direct quantum computation, and it lays out a framework for future research in curvature-aware, physics-guided machine learning for particle physics.

Abstract

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired observables with product manifold neural networks. The method unifies Euclidean, hyperbolic, and spherical representations to capture nonlinear correlations among kinematic features. Geometric embedding yields measurable improvements over flat baselines, demonstrating that curvature-aware architectures recover information lost in standard approaches. The study highlights how incorporating geometric structure enhances discrimination power in high-energy collision data.

Paper Structure

This paper contains 32 sections, 59 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Vector Boson Fusion Reaction
  3. Event Representation
  4. Quantum-Inspired Feature Engineering
  5. Enhanced Momentum Entanglement ($\mathcal{E}_p$)
  6. Enhanced Angular Coherence ($\mathcal{C}_\Omega$)
  7. Multi-Resonance Mass Superposition ($\mathcal{S}_m$)
  8. Redesigned VBF Coherence ($\mathcal{C}_{\mathrm{VBF}}$)
  9. Enhanced Hierarchy Measure ($\mathcal{H}$)
  10. Statistical properties of quantum-inspired features
  11. Quantum Feature Mapping
  12. Quantum Embedding Architecture
  13. Feature-to-Parameter Encoding
  14. Single-Qubit Encoding Layer
  15. Multi-Qubit Entanglement Structure
  16. ...and 17 more sections

Figures (12)

  • Figure 1: Classical correlation among the kinematic observables related to the Vector Boson Fusion decay process.
  • Figure 2: Representative kinematic distributions from the Drell–Yan sample. The panels illustrate, respectively, the Z$_1$ mass spectrum, the four-lepton invariant mass around the Higgs resonance, and the canonical VBF discriminating variables $m_{jj}$ and $\Delta\eta_{jj}$.
  • Figure 3: Cumulative distribution comparison for key observables highlighting tail behaviors between signal and background.
  • Figure 4: Contour representation of the variable-wise separation power between signal and background samples.
  • Figure 5: Enhanced corner plot showing pairwise correlations among principal kinematic observables.
  • ...and 7 more figures