AI RESEARCH
On the Approximation Complexity of Matrix Product Operator Born Machines
arXiv CS.LG
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ArXi:2605.11471v1 Announce Type: new Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive perspectives. First, we prove that KL approximation is NP-hard for MPO-BMs in the continuous setting, ruling out universal efficient approximation in the worst case.