# KALAVAI: Predicting When Independent Specialist Fusion Works -- A Quantitative Model for Post-Hoc Cooperative LLM Training

arXiv: https://arxiv.org/abs/2603.22755 · HTML: https://mlsanity.com/paper/2603.22755/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [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)
- [Sparse Upcycling: Training Mixture-of-Experts from Dense Checkpoints](https://mlsanity.com/paper/2212.05055/) (2022)
- [Branch-Train-MiX: Mixing Expert LLMs into a Mixture-of-Experts LLM](https://mlsanity.com/paper/2403.07816/) (2024)
- [Learning to Route Among Specialized Experts for Zero-Shot Generalization](https://mlsanity.com/paper/2402.05859/) (2024)
- [A Survey on Model MoErging: Recycling and Routing Among Specialized Experts for Collaborative Learning](https://mlsanity.com/paper/2408.07057/) (2024)
- [STAR: STacked AutoRegressive Scheme for Unified Multimodal Learning](https://mlsanity.com/paper/2512.13752/) (2025)

## Abstract (arXiv)

Independently trained domain specialists can be fused post-hoc into a single model that outperforms any individual specialist, and the gain is predictable: gain = 0.82 x divergence - 2.72 (R^2 = 0.856, n=6, 3-26% divergence). This enables practitioners to estimate cooperative value before committing compute. Below ~3.3% divergence, gains approach zero.In the KALAVAI protocol, contributors fine-tune copies of a shared checkpoint independently, then submit for lightweight MoE routing (500 steps). Gains are consistent: +7.72% at 410M (+/-0.02%, 3 seeds), +7.49% at 1B (+/-0.01%, 3 seeds), +6.53% at 6.9B, each over the best specialist. The router matches domain-oracle routing within <10^{-5} nats. Cross-lingual fusion (Tamil/Yoruba/Welsh/Code) achieves +21.76%, with Yoruba perplexity falling 41.9 to 7.7. A 20-contributor federation achieves +16.71% (+/-0.07pp, 3 seeds).Three requirements bound the protocol. Shared initialisation is necessary: checkpoint mismatch degrades routing. Frozen layers are optional below ~10,000 steps and beneficial beyond. Learned routing is essential: uniform averaging degrades by -1.2% vs. best specialist, while any trained router achieves oracle-optimal assignment.