← 研踪 PaperTrailarXiv:2609.39164 · v2
Quantum-Inspired Score-Based Variational Inference
首次提交 2026-09-30 15:25
版本更新 2026-11-09 21:28
雷达观测 2026-11-10 15:22
摘要
Score-based variational inference (SBVI) provides an alternative to classical Kullback--Leibler (KL)-based variational inference by learning a distribution using only score queries of the target. EigenVI~\cite{cai2024eigenvi} formulates SBVI as an eigenvalue problem, but faces two limitations: the number of variational parameters grows exponentially with the data dimension, and the single-eigenvector formulation cannot represent the full minimum-eigenvalue eigenspace. We propose QuanVI, a quantum-inspired SBVI algorithm that addresses both limitations. Rather than selecting a single eigenvector, QuanVI captures a learned subspace through a density-operator formulation. To enable scalable computation, \model{} employs a matrix-product-operator (MPO) structure parameterized by a quantum tensor network (QTN) with unitary-constrained local tensors and auxiliary ancilla wires. Numerical experiments demonstrate the scalability of QuanVI beyond EigenVI and competitive performance on synthetic distributions and Bayesian posterior-approximation benchmarks, including challenging non-Gaussian targets. The code is available at https://github.com/ChaoLiAtRIKEN/quanvi.
作者备注：Accepted to NeurIPS 2026
观测到的版本
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v2 · 2026-11-09 21:28 · 最新观测版本
Quantum-Inspired Score-Based Variational Inference
Score-based variational inference (SBVI) provides an alternative to classical Kullback--Leibler (KL)-based variational inference by learning a distribution using only score queries of the target. EigenVI~\cite{cai2024eigenvi} formulates SBVI as an eigenvalue problem, but faces two limitations: the number of variational parameters grows exponentially with the data dimension, and the single-eigenvector formulation cannot represent the full minimum-eigenvalue eigenspace. We propose QuanVI, a quantum-inspired SBVI algorithm that addresses both limitations. Rather than selecting a single eigenvector, QuanVI captures a learned subspace through a density-operator formulation. To enable scalable computation, \model{} employs a matrix-product-operator (MPO) structure parameterized by a quantum tensor network (QTN) with unitary-constrained local tensors and auxiliary ancilla wires. Numerical experiments demonstrate the scalability of QuanVI beyond EigenVI and competitive performance on synthetic distributions and Bayesian posterior-approximation benchmarks, including challenging non-Gaussian targets. The code is available at https://github.com/ChaoLiAtRIKEN/quanvi.
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