Multi-agent interactions, such as communication, teaching, and bluffing, often rely on higher-order social inference, i.e., understanding how others infer oneself. Such intricate rea- soning can be effectively modeled through nested multi-agent reasoning. Nonetheless, the computational complexity es- calates exponentially with each level of reasoning, posing a significant challenge. However, humans effortlessly per- form complex social inferences as part of their daily lives. To bridge the gap between human-like inference capabilities and computational limitations, we propose a novel approach: leveraging neural networks to amortize high-order social in- ference, thereby expediting nested multi-agent reasoning. We evaluate our method in two challenging multi-agent interac- tion domains. The experimental results demonstrate that our method is computationally efficient while exhibiting minimal degradation in accuracy.