Test-Time Collaborative Classification over Multi-Agent Networks

Multi-agent systems (MAS) can outperform individual language-model agents by combining specialized roles, diverse reasoning processes, and collaborative decision-making. However, collaborative MAS training is typically centralized, requiring a common trainer to aggregate role-local trajectories and learning signals and maintain model and optimization states. This motivates a distributed multi-agent learning paradigm in which agents improve system-level capabilities through role-local learning and decentralized communication, paving the way toward scalable, resilient, and self-organizing MAS. To this end, we introduce, to the best of our knowledge, the first optimization-grounded framework for distributed MAS training based on consensus alternating direction method of multipliers (ADMM). We formulate collaborative MAS learning as a consensus-constrained finite-sum optimization problem, naturally lending itself to distributed optimization via ADMM. The proposed approach alternates role-local learning with inter-agent consensus using distributed communication protocols such as ring all-reduce, enabling joint optimization while keeping each agent's data and training state local. We evaluate our framework on distributed safety alignment and general reasoning tasks. Under compromised-agent settings, ADMM can reduce HarmBench attack success rate (ASR) by up to 26.4%, while achieving reasoning gains comparable to centralized training. These results show that distributed MAS training retains the benefits of centralized joint optimization without requiring a centralized trainer.

Multilayer Artificial Neural Networks trained via backpropagation are the basic blocks of many, more complex, classification algorithms. Their strength lies in the possibility of realizing, with arbitrary precision, any function. This result comes at the cost of the large number of involved parameters to be optimized. In this work, we propose a mechanism for cooperation, i.e., information exchange among several artificial neural networks, with the goal of reducing model complexity while maintaining performance. More precisely, we consider several "small" agents, i.e., containing fewer parameters than a reference "large" one, that during training share their predictions by incorporating this information into the loss function and thus directly influence weight updates. We consider several strategies for implementing cooperation, e.g., the voter model, majority model, and weighted average model based on an agent's confidence in its prediction. We numerically compare the accuracy of those strategies on several standard benchmarks. Our results support the claim that several small agents can outperform a single large model on a given classification task; the shared signals affect each agent's optimization algorithm by modulating both the descent direction and the step size, converging toward a global consensus. The proposed proof-of-concept significantly reduces the number of parameters to be trained while preserving comparable performance, thereby limiting computational resource usage.

Science advances not in isolation but through collaboration, yet existing agentic systems capture little of this. Whether communicating agents help remains an open question with mixed prior results. We show that test-time communication can substantially outperform independent parallel attempts on challenging tasks, where sharing a breakthrough can push the whole group forward. We first study the effect of scaling multi-agent test-time communication, where agents have no predefined roles and communicate via a shared directory, on ARC-AGI-3, a benchmark requiring novel problem solving. We find that a team of $k$ communicating agents, team@$k$, matches the success rate of $4k$ independent agents, and this advantage grows with $k$, suggesting gains compound with scale. The effect is not merely efficiency: a task that no single agent can solve, a team of agents can solve reliably. Furthermore, these gains transfer to research-oriented tasks, given sufficient compute. On polyomino packing, communicating agents outperform best@$k$ and exceed the prior best-known score. On MNIST classifier compression, communication surpasses the best-known human solution. A team of four agents produced a 1,957-byte classifier submission achieving 99.4% test accuracy, smaller than both the best-known human solution and the best single-agent result. These gains are not unconditional. Independent agents may outperform communication when compute is limited or when a clear measure of progress is absent. However, under sufficient compute and clear feedback, multi-agent communication consistently yields stronger results.