# SDG-MoE: Signed Debate Graph Mixture-of-Experts

arXiv: https://arxiv.org/abs/2605.08322 · HTML: https://mlsanity.com/paper/2605.08322/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 13 of its 16 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 13 of 13)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [HyperMoE: Towards Better Mixture of Experts via Transferring Among Experts](https://mlsanity.com/paper/2402.12656/) (2024)
- [MoDE: A Mixture-of-Experts Model with Mutual Distillation among the Experts](https://mlsanity.com/paper/2402.00893/) (2024)
- [Chain-of-Experts: Unlocking the Communication Power of Mixture-of-Experts Models](https://mlsanity.com/paper/2506.18945/) (2025)
- [GRAPHMOE: Amplifying Cognitive Depth of Mixture-of-Experts Network via Introducing Self-Rethinking Mechanism](https://mlsanity.com/paper/2501.07890/) (2025)
- [Modeling Expert Interactions in Sparse Mixture of Experts via Graph Structures](https://mlsanity.com/paper/2510.16411/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond Routing: Decoupling Expert Dispatch and Aggregation in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2608.08853/) (2026)

## Abstract (arXiv)

Sparse MoE models achieve a good balance between capacity and compute by routing each token to a small subset of experts. However, in most MoE architectures, once a token is routed, the selected experts process it independently and their outputs are combined via a weighted sum. This leaves open whether enabling communication among them could improve performance. While prior work has raised this question, direct interaction among the active routed experts remains underexplored. In this paper, we propose SDG-MoE (Signed Debate Graph Mixture-of-Experts), a novel architecture that adds a lightweight, iterative deliberation step before final aggregation. SDG-MoE introduces three components: (i) two learned interaction matrices over the active experts, a support graph A^+ and a critique graph A^-, capturing reinforcing and corrective influences; (ii) a signed message-passing step that updates expert representations before aggregation; and (iii) a disagreement-gated Friedkin-Johnsen-style anchoring that controls deliberation strength while preventing expert drift. Together, these enable a structured deliberation process where interaction strength scales with disagreement and specialization is preserved. We also provide a theoretical analysis establishing stability conditions on expert states and showing that deliberation adds only low-order overhead over the active set. In controlled three-seed pretraining experiments, SDG-MoE improves validation perplexity over both an unsigned graph communication baseline and vanilla MoE, outperforming the strongest baseline by 19.8%, and gives the best external perplexity on WikiText-103, C4, and Paloma among the compared systems.