Self-training Language Models for Arithmetic Reasoning

Recent language models achieve impressive results in tasks involving complex multistep reasoning, but scaling these capabilities further traditionally requires expensive collection of more annotated data. In this work, we explore the potential of improving models' reasoning capabilities without new data, merely using automated feedback to the validity of their predictions in arithmetic reasoning (self-training). In systematic experimentation across six different arithmetic reasoning datasets, we find that models can substantially improve in both single-round (offline) and online self-training, reaching a correct result in +13.9% and +25.9% more cases, respectively, underlining the importance of actuality of self-training feedback. We further find that in the single-round, offline self-training, traditional supervised training can deliver gains comparable to preference optimization, but in online self-training, preference optimization methods largely outperform supervised training thanks to their superior stability and robustness on unseen types of problems.