QuanVI: Score-based Variational Inference via Quantum Maximally Mixed States
QuanVI scales score-based variational inference using mixed-state density operators and matrix product operators.
QuanVI is a quantum-inspired score-based variational inference method that minimizes Fisher divergence instead of KL divergence. It replaces a non-unique low-energy eigenvector with a mixed-state density operator and parameterizes that operator with a matrix product operator to avoid exponential parameter growth. Experiments match exact solutions in low dimensions and scale to high-dimensional synthetic targets and Bayesian posterior approximation, including non-Gaussian distributions.
- Minimizes Fisher divergence rather than KL divergence for variational inference.
- Represents degenerate low-energy subspaces by their maximally mixed state.
- Matrix product operators compress the density operator and limit parameter growth.
- Matches exact low-dimensional solutions and scales to non-Gaussian posteriors.
From the original article
1 min read at arxiv.orgScore-based variational inference (VI) provides an alternative to Kullback--Leibler (KL)-based VI by minimizing the Fisher divergence between the variational distribution and the target. A prior score-VI approach formulates this optimization as an eigenvalue problem, with the variational distribution constructed from low-energy eigenstates.
By Yuchen Cong · arxiv.org
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