• Computer Science > Machine Learning [Submitted on 12 Feb 2026] Title:Tensor Network Generator-Enhanced Optimization for Traveling Salesman Problem View PDF HTML (experimental)Abstract:We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. • Our approach employs a tensor network Born machine based on automatically differentiable matrix product states (MPS) as the generative model, using the Born rule to define probability distributions over candidate solutions. • Unlike approaches based on binary encoding, which require $N^2$ variables and penalty terms to enforce valid tour constraints, we adopt a permutation-based formulation with integer variables and use autoregressive sampling with masking to guarantee that every generated sample is a valid tour by construction. • We also introduce a $k$-site MPS variant that learns distributions over $k$-grams (consecutive city subsequences) using a sliding window approach, enabling parameter-efficient modeling for larger instances. • Experimental validation on TSPLIB benchmark instances with up to 52 cities demonstrates that TN-GEO can outperform classical heuristics including swap and 2-opt hill-climbing. • The $k$-site variants, which put more focus on local correlations, show better results compared to the full-MPS case.

Article Summaries:

  • Computer Science > Machine Learning [Submitted on 12 Feb 2026] Title:Tensor Network Generator-Enhanced Optimization for Traveling Salesman Problem View PDF HTML (experimental)Abstract:We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. Our approach employs a tensor network Born machine based on automatically differentiable matrix product states (MPS) as the generative model, using the Born rule to define probability distributions over candidate sol

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