SLIM: Simplex-Lattice Interpolation Merging

Optimizing merging coefficients for large language models can require many costly benchmark evaluations. We propose Simplex-Lattice Interpolation Merging (SLIM), which constructs a quadratic surrogate of aggregate performance on the coefficient simplex using a classical mixture design. Evaluations of individual experts and equal-weight pairs determine the surrogate with the minimum number of measurements needed to identify a general quadratic on this domain. SLIM then optimizes the surrogate without further target-metric evaluations. Experiments on two model architectures demonstrate accurate prediction of unseen multi-expert mixtures and competitive merge performance under limited evaluation budgets. Matched-budget comparisons show that structured evaluation points improve prediction fidelity over random designs, including those using regularized fitting.