To support the big-data processing needs of large-scale deployments of smart devices, there is significant interest in moving from cloud-computing to multi-agent (fog-computing) models, given these algorithms scalability and self-healing properties with respect to nodes and link failures. However, these algorithms are often based on the average consensus primitive, which is, unfortunately, vulnerable to data injection attacks. Recognizing this challenge, this work proposes three novel methods for detecting and localizing adversarial nodes using neural network (NN) models. The methods proposed are based on fully distributed algorithms, wherein each node locally updates its local states by exchanging information with its neighbors without supervision. Compared to the state-of-the-art, the proposed approach leverages the automatic learning characteristics of NN to reduce the dependence on pre-designed models and human expertise in complex internal attack scenarios. Simulation results show that the NN-based methods can significantly improve the attacker detection and localization performance. INDEX TERMS Gossip algorithm, average consensus, neural network (NN), insider attack, detection and localization.