Sakana AI has a new paper out, Sheaf-ADMM, headed to ICML 2026. The idea: instead of one model chewing on a whole problem, split the input into overlapping pieces, hand each piece to an agent that sees nothing else, and make the agents haggle their way to a global answer. Jeffrey Seely, Bartlomiej Cupial, and Llion Jones wrote it. The write-up went live in July.
The negotiation, roughly
Each agent gets a private slice of the input and solves a small convex problem over it. Then it checks its answer against neighbors wherever their slices overlap, and the disagreements get smoothed out over repeated rounds. The clever bit is memory: a term the paper calls the dual variable accumulates every round, so an agent that keeps drifting from consensus gets shoved harder each time until it falls in line.
Two math traditions are bolted together here. ADMM, from distributed optimization, handles the propose-and-reconcile loop. Cellular sheaves, out of applied topology, define what "agree" even means, because agents don't sync their whole state, only a learned linear projection of it. That last point is what keeps communication cheap.
Does it actually work?
They tested on a version of Sudoku rigged to be a coordination problem. Each agent sees only one row, column, or 3x3 box, and can talk only to agents it shares cells with. Sheaf-ADMM solved 92.6% of full puzzles. The strongest message-passing baseline they threw at it, one with four times the parameters, managed 34.7%.
Worth flagging: some numbers floating around describe this as 93% versus an 11% baseline. The published table doesn't support that gap. The 11% figure matches only their smallest param-matched baseline on the puzzle-solve metric, not the best comparison they ran. On per-cell accuracy the baselines actually do fine, in the high 80s to low 90s, which the headline solve-rate number quietly buries.
The maze results are the interesting ones anyway. Sheaf-ADMM hits near-perfect exact-solve on in-distribution mazes using a 5-dimensional communication channel between agents, and holds up on mazes twice the training size where the baselines start slipping. Because each agent carries its own local memory, it doesn't have to cram everything into the message it sends. That trade, more local state for a skinnier channel, is the whole pitch.
Why anyone should care
The selling point isn't accuracy. It's that you can watch the thing think. Every agent keeps three inspectable numbers, and all the negotiation happens in the open rather than getting smeared across hidden states. Because the communication is linear, you can even bring topological tools to bear on the whole network. Seely and company are upfront that these are toy tasks a single monolithic model could solve without breaking a sweat.
The bet is that the coordination lessons carry over to problems where no single agent could ever see the whole board. Sensor networks, that kind of thing. The JAX code is up, with maze, MNIST, and Sudoku builders included. ICML 2026 runs this year, and that's where the full results get their airing.
