Quantum-Inspired Complex Transformers: Resolving the Fundamental Algebraic Ambiguity for Enhanced Neural Representations

Bhargav Patel

Keywords: Quantum-Inspired Computing, Complex Neural Networks, Algebraic and Geometric Deep Learning, Parameter Efficiency, Transformers

TL;DR: QIC Transformers learn imaginary numbers via "quantum superposition," reducing parameters by ~21% & improving accuracy in sequence tasks. Training is ~2x slower, but the efficiency suits constrained deployments.

Abstract: We present Quantum-Inspired Complex (QIC) Transformers, a novel architecture that enhances neural network expressiveness through learnable algebraic structures. Our key insight is that the fundamental equation $x^2 = -1$ has two solutions, traditionally resolved by arbitrary selection. We propose treating the imaginary unit as a learnable quantum superposition: $J(\theta) = \cos(\theta)J_+ + \sin(\theta)J_-$, where $\theta$ is trainable. This yields $J^2 = -1 + \sin(2\theta)$, creating an adaptive algebra that interpolates between mathematical regimes. We validate our approach on real-world text classification tasks (IMDB sentiment analysis and AG News categorization) with $\sim$2M parameter models. QIC Transformers achieve 47.2\% parameter reduction while maintaining or improving accuracy: on IMDB, both models achieve 100\% accuracy; on AG News, QIC attains 78.0\% versus 73.3\% for standard Transformers (+4.7\%). We provide rigorous algebraic formulation, architectural specifications, comprehensive ablation studies, and comparisons to complex-valued baselines, demonstrating that learnable algebraic structures fundamentally enhance neural network capabilities for parameter-efficient deployments.

Submission Number: 1