arXiv subjects

Lorenzo Buffa

Publications and source records attributed to Lorenzo Buffa.

3 recordsLinked to original sources

arXiv2026

An exact and fast solution of the inverse Regularized Optimal Transport problem

Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.

cond-mat.stat-mech↗

arXiv2026

Statistical Mechanics of the Sub-Optimal Transport

Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit, where systems collapse onto optimal configurations, a.k.a. the ground states. Real-world systems often occupy intermediate regimes where entropy and cost minimization genuinely compete, producing configurations that are structured yet sub-optimal. The Sub-Optimal Transport (SOT) model captures this competition through an ensemble of weighted bipartite graphs: a coupling parameter interpolates between entropy-dominated dense configurations and cost-dominated sparse structures. This crossover has been observed numerically but lacked analytical understanding. Here we develop a mean-field theory that characterizes this transition. We show that local fluctuations in Lagrange multipliers become sub-extensive in the thermodynamic limit, reducing the full model with strength constraints to an effective single-constraint problem admitting an exact solution in some intermediate regime. The resulting free energy is analytic in the coupling parameter, confirming a smooth crossover rather than a phase transition. We derive closed-form expressions for thermodynamic observables and weight distributions, validated against numerical simulations. These results establish the first analytical description of the SOT model, extending statistical mechanics methods beyond the zero-temperature regime.

cond-mat.stat-mech↗

arXiv2025

Maximum entropy modeling of Optimal Transport: the sub-optimality regime and the transition from dense to sparse networks

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply or receive, while an external cost field favors a minimal set of links, driving the system toward a sparse, tree-like structure. By tuning the control parameter, one transitions from uniformly distributed weights to an optimal transport regime in which weights condense onto cost-favorable edges. We quantify this dense-to-sparse transition, showing with numerical analyses that the process does not hinge on specific assumptions about the node-strength or cost distributions. Finite-size analysis confirms that the results persist in the thermodynamic limit. Because the model offers explicit control over the degree of sub-optimality, this approach lends to practical applications in link prediction, network reconstruction, and statistical validation, particularly in systems where partial optimization coexists with other noise-like factors.

cond-mat.stat-mech↗