Capacity Arc Routing Problem (CARP) is a classic combinatorial optimization problem in transportation and logistics. Neural solvers based on the attention mechanism for routing problems have gained attention because they require little expert knowledge. However, existing neural solvers are typically trained on tasks with fixed distributions, leading to poor performance when solving problems with different distributions. To address this issue, we propose an Expert Multi-Head Attention (EMHA) neural solver for cross-distribution generalization in CARP. The EMHA module combines a top- \(\mathcal {K}\) router with multiple independent parameter query vectors. This allows the model to dynamically adjust attention mechanisms based on input distribution features, generating more suitable feature representations. In addition, our model employs an encoder–decoder architecture trained via the REINFORCE algorithm augmented with an auxiliary loss to encourage balanced utilization of the different query vectors. Extensive experimental results demonstrate that the proposed method improves both cross-distribution performance and solution quality.