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

Haijian Shao, Wei Liu, Xing Deng

TL;DR

Addresses cross-modal and hardware-heterogeneous deployment by introducing a quantum-inspired spectral geometry for neural operators. Represents each operator by its normalized singular-value spectrum on the Bloch hypersphere and establishes a tight spectral-to-functional equivalence via the Fubini-Study distance and Wasserstein bounds. Proposes QM-FRG to identify functionally redundant subnetworks and enable one-shot structured pruning with controllable quantum kernel approximations, including hardware-aware extensions. Controlled simulations on ResNet-18 demonstrate superior pruning robustness over magnitude and random baselines and lay the groundwork for large-scale multimodal and domestic hardware deployments in future work.

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.

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

TL;DR

Addresses cross-modal and hardware-heterogeneous deployment by introducing a quantum-inspired spectral geometry for neural operators. Represents each operator by its normalized singular-value spectrum on the Bloch hypersphere and establishes a tight spectral-to-functional equivalence via the Fubini-Study distance and Wasserstein bounds. Proposes QM-FRG to identify functionally redundant subnetworks and enable one-shot structured pruning with controllable quantum kernel approximations, including hardware-aware extensions. Controlled simulations on ResNet-18 demonstrate superior pruning robustness over magnitude and random baselines and lay the groundwork for large-scale multimodal and domestic hardware deployments in future work.

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.

Paper Structure

This paper contains 21 sections, 1 theorem, 15 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Quantum-Inspired Geometric Foundation of Operator Equivalence
  3. Quantum-Inspired Spectral Representation of Neural Operators
  4. Cross-Modal Alignment via Spectral Embedding
  5. Fubini--Study Metric as Functional Distance
  6. Quantum Metric-Driven Functional Redundancy Graph and One-Shot Structured Pruning
  7. Functional Redundancy Graph (QM-FRG)
  8. Controllable Quantum Kernel Approximation
  9. Time-Varying Redundancy Evolution
  10. One-Shot Structured Pruning via Quantum Geometric Clustering
  11. Quantum Policy Gating and Resource-Accuracy Unified Optimization
  12. Towards Domestic Heterogeneous Hardware Adaptation
  13. Experiments
  14. Experimental Setup
  15. Model and Operators.
  16. ...and 6 more sections

Key Result

Theorem 2.1

Let $\Phi_i(x)=\sigma(W_i x + b_i)$ with $L$-Lipschitz activation ($|\sigma(0)|\le M$). Define the normalized cumulative singular-value distribution (majorization profile) and the quantum-inspired state $|\psi_i\rangle = s_i / \|s_i\|_2$ as before. Then, for any $\|x\|_2\le R$, where $\mathcal{W}_2$ is the 2-Wasserstein distance between the two cumulative distributions. Furthermore, if $\|\wideh

Figures (1)

  • Figure 1: Top-1 Accuracy vs. Sparsity on ResNet18 (Simulation). QM-FRG demonstrates significantly better robustness under high sparsity.

Theorems & Definitions (4)

  • Theorem 2.1: Tight Spectral-to-Functional Equivalence
  • Remark 1
  • proof
  • Remark 2