# SLIM: Simplex-Lattice Interpolation Merging

arXiv: https://arxiv.org/abs/2610.01037 · HTML: https://mlsanity.com/paper/2610.01037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [MetaGPT: Merging Large Language Models Using Model Exclusive Task Arithmetic](https://mlsanity.com/paper/2406.11385/) (2024)
- [MergeBench: A Benchmark for Merging Domain-Specialized LLMs](https://mlsanity.com/paper/2505.10833/) (2025)
- [MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation](https://mlsanity.com/paper/2406.07529/) (2024)
- [It's Morphing Time: Unleashing the Potential of Multiple LLMs via Multi-objective Optimization](https://mlsanity.com/paper/2407.00487/) (2024)
- [MERGE3: Efficient Evolutionary Merging on Consumer-grade GPUs](https://mlsanity.com/paper/2502.10436/) (2025)
- [Model Merging in the Era of Large Language Models: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2603.09938/) (2026)
- [Fine, I'll Merge It Myself: A Multi-Fidelity Framework for Automated Model Merging](https://mlsanity.com/paper/2502.04030/) (2025)
- [Data Mixing as Mixture Experiment: Response Surface Methodology and Optimal Design for Large Language Model Pretraining](https://mlsanity.com/paper/2608.23922/) (2026)

## Abstract (arXiv)

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.