LLM-powered multi-agent systems (MAS) have demonstrated strong performance on complex tasks. However, most existing approaches still rely on hand-crafted communication protocols or automatically designed communication topologies, which generalize poorly across tasks. We introduce NeuralFSM, a state-driven framework that formulates multi-agent problem solving as a finite-state execution process. NeuralFSM learns both the state transition distribution and inter-agent communication weights from interaction traces using a Temporal Coordination Controller. Rather than prioritizing explicit structure generation, the proposed framework uses task context to modulate transition and routing decisions, enabling flexible coordination without manual protocol design. To improve robustness against noisy or adversarial agents, we incorporate graph regularization during training and apply trust-aware message attenuation at runtime. Experiments on diverse benchmarks show that NeuralFSM consistently outperforms prior baselines by an average margin of 6.74%–19.39%, while substantially reducing token consumption. Moreover, NeuralFSM exhibits strong inherent robustness, which is further enhanced by the protection layer, resulting in only a 1.82% performance drop under attack.