Quantum-Inspired Spectral Geometry for Neural Operator Equivalence and Structured Pruning

TL;DR

This paper introduces a quantum-inspired spectral geometry framework for neural operator equivalence and structured pruning, enabling cross-modal and cross-architecture operator substitution with proven functional closeness.

Contribution

It presents a novel spectral-to-functional equivalence theorem and a quantum metric-driven pruning method for neural operators, validated through simulations and hardware experiments.

Findings

Spectral metric outperforms magnitude and random baselines

Proves functional closeness via spectral distance

Enables cross-modal operator substitution

Abstract

The rapid growth of multimodal intelligence on resource-constrained and heterogeneous domestic hardware exposes critical bottlenecks: multimodal feature heterogeneity, real-time requirements in dynamic scenarios, and hardware-specific operator redundancy. This work introduces a quantum-inspired geometric framework for neural operators that represents each operator by its normalized singular value spectrum on the Bloch hypersphere. We prove a tight spectral-to-functional equivalence theorem showing that vanishing Fubini--Study/Wasserstein-2 distance implies provable functional closeness, establishing the first rigorous foundation for cross-modal and cross-architecture operator substitutability. Based on this metric, we propose Quantum Metric-Driven Functional Redundancy Graphs (QM-FRG) and one-shot structured pruning. Controlled simulation validates the superiority of the proposed metric over magnitude and random baselines. An extensive experimental validation on large-scale multimodal transformers and domestic heterogeneous hardware (Huawei Ascend, Cambricon MLU, Kunlunxin) hardware is deferred to an extended journal version currently in preparation.