Quantum-inspired Spectral Geometry Enables Operator Equivalence and Structured Pruning for Resource-Constrained Intelligence

The increasing demand for artificial intelligence on everyday devices presents significant challenges, including managing diverse data types, meeting real-time processing needs, and optimising performance across different hardware. Haijian Shao, Wei Liu, and Xing Deng from Jiangsu University of Science and Technology address these issues by introducing a novel geometric framework inspired by quantum mechanics for understanding and optimising neural operators. Their work establishes a rigorous mathematical link between the spectral properties of these operators and their actual function, proving that similarities in their spectra guarantee functional equivalence, a breakthrough for cross-modal and cross-architecture substitutability. This advancement enables the creation of Metric-Driven Functional Redundancy Graphs, which facilitate efficient, one-shot structured pruning of neural networks, ultimately leading to more streamlined and effective AI systems for resource-constrained devices.

Intelligence on resource-constrained and heterogeneous domestic hardware exposes critical bottlenecks, namely 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, representing each operator by its normalized singular value spectrum on the Bloch hypersphere. Researchers prove a tight spectral-to-functional equivalence theorem, demonstrating that a small distance between operator spectra implies provable functional closeness, establishing the first rigorous foundation for cross-modal and cross-architecture operator substitutability. Based on this metric, the team advances the field by enabling efficient operator design and deployment on diverse hardware platforms.

Spectral Embedding of Neural Operator Layers

This research introduces a novel approach to neural network pruning based on principles from quantum mechanics, specifically focusing on the spectral properties of neural operators. The core idea is to represent each layer using its singular value spectrum, allowing for a mathematically rigorous assessment of functional redundancy and interchangeability. This allows scientists to determine when different layers, even those designed for different data types, can perform similar functions. The innovation lies in representing neural operators as points on a Bloch hypersphere, inspired by quantum mechanics.

The team uses the Fubini-Study distance to measure similarity between these operators, proving that a small distance indicates functional equivalence. This provides a mathematically sound basis for identifying redundant layers, unlike traditional pruning methods. The research establishes a theoretical framework linking spectral properties to functional behavior in neural networks. Simulations on ResNet-18 validate the method, demonstrating superior performance compared to magnitude and random pruning, especially at high sparsity levels.

This framework handles networks with diverse layer types and modalities, adapting to scenarios where network structure needs to change during operation. The metric can be weighted to account for the cost of different operations on specific hardware, such as Huawei Ascend and Cambricon MLU, optimizing for hardware efficiency. Future research will explore applying this framework to compress generative models like Latent Diffusion and Stable Diffusion, and to compress large language models while preserving long-context reasoning capabilities. This paper proposes a fundamentally new way to think about neural network pruning, moving beyond simple heuristics to a mathematically grounded approach inspired by the principles of quantum mechanics, potentially leading to more efficient and robust neural networks.

Geometric Pruning Guarantees Functional Operator Similarity

This work introduces a novel framework for neural operator pruning, grounded in a quantum-inspired geometric approach, delivering substantial improvements in model efficiency without significant accuracy loss. Scientists represent each neural operator by its normalized singular value spectrum on the Bloch hypersphere, establishing a direct link between spectral properties and functional behavior. A key achievement is the proof of a tight spectral-to-functional equivalence theorem, rigorously demonstrating that a small distance between operator spectra guarantees functional closeness, providing the first robust criterion for cross-modal and cross-architecture operator substitutability. Specifically, at 90% sparsity, the method retains 61. 26% accuracy, significantly outperforming magnitude pruning at 52. 50% and random pruning at 48. 00%.

These results confirm that the quantum geometric distance accurately captures functional redundancy, preserving essential operator functionality during pruning. Further experiments focused on domestic heterogeneous hardware adaptation, incorporating instruction-level cost models for devices like Huawei Ascend, Cambricon MLU, and Kunlunxin. By weighting the metric based on hardware operation costs, the framework aligns redundancy identification with hardware constraints. On Kunlunxin XLA edge devices, this approach fuses redundant attention heads into matrix-multiply operations, achieving a 2. 1× speedup compared to unadapted pruned models.

For a 30× reduction in floating-point operations, the framework retains 98. 5% accuracy, exceeding the performance of TensorRT-LLM at 95. 2% and quantum-inspired Tensor Networks at 94. 7%, demonstrating a substantial breakthrough in balancing accuracy, resource cost, and functional consistency.

Bloch Sphere Analysis Reveals Operator Redundancy

This work introduces a novel geometric framework, inspired by quantum mechanics, for modelling neural operators, fundamental components of modern artificial intelligence systems. Researchers successfully represent these operators using their spectral characteristics on a Bloch hypersphere, establishing a rigorous mathematical connection between an operator’s spectrum and its actual function. This allows for a provable criterion to determine when operators, even with different designs or handling different types of data, can be functionally interchanged, a significant step towards more flexible and efficient AI architectures. The resulting framework addresses key challenges in deploying multimodal AI on commonly available domestic hardware, offering both theoretical clarity and practical deployability. The authors acknowledge that the current validation is limited to simulations, and a more comprehensive evaluation with large-scale benchmarks and real hardware measurements is forthcoming. Future research will focus on extending this framework to generative models used in image synthesis and applying it to compress large language models while preserving their reasoning abilities, laying a foundation for developing more efficient and adaptable AI systems.