Excited to share our paper, “Learning Multi-Agent Coordination via Sheaf-ADMM” to be presented at #ICML2026
Blog: https://t.co/F5CVepgivO
Most AI models process information as one giant, monolithic block. But in nature, intelligence often comes from a group of individuals working together, where each individual only has a limited view of the world.
We built a framework called Sheaf-ADMM to study how this kind of collective problem-solving works. We divide a complex task into smaller overlapping pieces, and assign one agent to each piece.
To solve the global puzzle, the agents negotiate in three simple steps:
1. Local Guesses: Every agent looks at its limited view and proposes a solution.
2. Finding Common Ground: Agents communicate with their direct neighbors to smooth out conflicts. They do not need to agree on everything, but they must agree on the boundaries where their tasks overlap.
3. Remembering Disagreements: If neighbors cannot agree, they keep a memory of that conflict. This memory forces them to try harder to compromise in the next round.
We tested this on problems where no single agent has enough information to succeed alone:
• Multi-Agent Sudoku: Each agent sees only a single row, column, or 3x3 box. The framework achieved a 93% solve rate, while a parameter-matched message-passing baseline scored 11%.
• Image Classification: When we tested canvas-size domain shifts, a standard CNN dropped to 11% accuracy on MNIST, while our method retained 86%.
• Maze Pathfinding: Sheaf-ADMM matches a message-passing baseline’s accuracy while agents communicate over a 5-dimensional channel, 8x smaller than that required of the baseline (42).
Traditional message-passing networks hide their reasoning inside opaque hidden states. Our framework makes coordination completely transparent. You can watch exactly how local agents debate, compromise, and eventually reach a global consensus.
Sheaf-ADMM draws inspiration from two fields with long histories in distributed consensus: ADMM from distributed optimization, and sheaves from applied topology. We think these perspectives may offer insights for the distributed, multi-agent AI systems increasingly being built today.
Read our full paper: https://t.co/RoOHfekjQE
Code: https://t.co/KDKZRcbuQH
「LLMは層が深くなるほど、表面的な単語の一致から離れ、より抽象的な意味を捉えるようになる」本論文は、この素朴な前提に疑問を投げかける研究です。
ここでいう「語彙の重なり」とは、意味が同じということではなく、文同士に同じ単語や表現が多く含まれていることを指します。著者らは、意味は同じだが語彙が異なる文と、意味は異なるが語彙がよく重なる文を比較し、LLMの各層の内部表現がどちらに引き寄せられるのかを調���ました。
その結果、語彙の重なりに引きずられるバイアスは浅い層だけでなく深い層まで残り、指示チューニングや埋め込み学習によって改善されても完全には消えないことが示されました。
さらに、中間層付近では、元の単語を線形に復元しにくくなる一方で、意味的な性能も十分に高まらない「谷」のような領域が観察されます。この現象は、情報の圧縮・再拡張のような層ごとの変化と対応している可能性がありますが、論文はそれを直接の因果機構として断定しているわけではありません。
こうした語彙バイアスは、内部表現上の現象にとどまりません。要約評価では、語彙が似ているだけの不適切な要約候補が高く評価される場合があり、モデル編集では、編集対象と表面的に似た無関係な入力まで影響を受けるリスクが示されました。
LLMの埋め込み、評価指標、モデル介入を実務で使う際には、意味の一致だけでなく、語彙重複に惑わされていないかを検証するストレステストが重要であることを示す論文です。
On the Persistent Effects of Lexicality in Large Language Models. Hammad Rizwan, Muhammad Umair Haider, Nishant Subramani, Mona T. Diab, A.B. Siddique, Hassan Sajjad. Arxiv:2606.02750
> “LLMs generate the consensus response to hard questions,” he said. “You are the best physicist when you give the not consensus answer, which is what AI is incapable of doing.”