Sinkhorn-Optimized Capacity-Constrained Temporal Heterogeneous Graph Model for Startup–Investor Matching

Investment capacity couples startup–investor recommendations, but independent scoring and ranking ignores this coupling, repeatedly recommending a few investors. We formulate quarterly matching as capacity-constrained entropic optimal transport and propose CapTHG. A relation-specific heterogeneous attention encoder processes causal quarterly snapshots of a temporal heterogeneous graph, and a differentiable Sinkhorn layer converts its scores into a capacity-feasible transport plan. A dustbin handles upper-bound capacities, training is end-to-end with a plan likelihood loss, and an activity-based proxy from a recent window estimates capacity. We characterize the capacity-feasible set with the dustbin score as a retention threshold, derive the linear programming limit and error bound as regularization vanishes, and prove linear convergence and a gradient equal to the plan. In a quarterly rolling evaluation on real financing rounds from a public Crunchbase snapshot, CapTHG attains the highest round-level recall and normalized discounted cumulative gain among all baselines. For every encoder, capacity-constrained Sinkhorn ranking lowers capacity overload and raises investor coverage versus score ranking. Accuracy also improves only under joint training with the plan. Capacity and plan likelihood loss contribute most in the ablation study; results are stable across capacity definitions and candidate sets. Controlled numerical experiments agree with the theory, supporting transport-based capacity-constrained matching.