  Large Language Models (LLMs) can justify or critique their predictions
through discussions with other models or humans, thereby enriching their
intrinsic understanding of instances. While proactive discussions in the
inference phase have been shown to boost performance, such interactions have
not been extensively explored during the training phase. We hypothesize that
incorporating interactive discussions into the training process can enhance the
models' understanding and improve their reasoning and verbal expression
abilities during inference. This work introduces the SAIE framework, which
facilitates supportive and adversarial discussions between learner and partner
models. The learner model receives responses from the partner, and its
parameters are then updated based on this discussion. This dynamic adjustment
process continues throughout the training phase, responding to the evolving
outputs of the learner model. Our empirical evaluation across various tasks,
including math problems, commonsense reasoning, and multi-domain knowledge,
demonstrates that models fine-tuned with the SAIE framework outperform those
trained with conventional fine-tuning approaches. Furthermore, our method
enhances the models' reasoning capabilities, improving both individual and
multi-agent inference performance.
