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Quantum-Inspired Relational Distillation

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Relational distillation, a technique for transferring knowledge from a source to a target model based on their relational structures, has demonstrated promise in various domains. However, its effectiveness is often limited by the exponential growth of parameters when dealing with high-dimensional and complex relational data. This paper introduces a novel approach, Quantum-Inspired Relational Distillation (QIRD), that addresses this challenge by incorporating quantum-inspired concepts such as Tensor Networks and superposition. The core idea is to represent relational structures using quantum states, enabling a compressed representation of multiple relationships simultaneously. This is achieved through a distillation process guided by quantum measurement principles, effectively learning from the correlations inherent in the relational data. The proposed method aims to provide a scalable solution for complex relational knowledge transfer, potentially overcoming the limitations of traditional relational distillation techniques. The key formula used throughout is (Rs, Rt), where Rs represents the relational structure of the source data, and Rt represents the relational structure of the target data. We introduce a new loss function, L, defined as: L = Σi |⟨ψi| Rt |ψi⟩ - ⟨ψi| Rs |ψi⟩| , where ψi represents a quantum state and ⟨...| ... |...⟩ denotes a quantum expectation value. This loss function quantifies the difference between the expected relational values in the source and target models. The efficiency of QIRD is also partially dependent on the entanglement entropy, S, of the quantum state representation: S = -kb Σi ln(pi), where kb is Boltzmann's constant and pi is the probability of a specific state. Furthermore, the compression ratio, C, achieved by QIRD is defined as C = (Size of Rt) / (Size of Rs). ---

DOI: 10.5281/zenodo.22314946

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