Model Compression with Exact Budget Constraints via Riemannian Manifolds

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, arising in mixed-precision quantization, non-uniform pruning, and expert selection. The objective (model loss) depends on all assignments jointly and does not decompose across groups, so combinatorial solvers can only optimize proxy objectives. Evolutionary search evaluates the actual loss but lacks gradients, while penalty-based methods enforce the budget only approximately and often require heavy hyperparameter tuning. We show that under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually clean geometry: the normal vect...

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