Limitations. While SECToR demonstrates the possibility of self-learning in addition with language
models, it is far from showing that models can self-learn in general. A natural question is whether
methods like SECToR can generalize to more complex tasks, such as multiplication or perhaps
even general mathematics or programming. Secondly, models trained with SECToR do not improve
forever. We speculate that a larger model, or a stronger consistency check, might allow for the
models to continue improving beyond 29 digits. Finally, while SECToR is data efficient, it is highly
compute inefficient, requiring a large amount of compute to generate the next iteration’s training
data. We leave the development of more efficient methods for SECToR to future work.
Safety. While SECToR is merely a proof-of-concept demonstration of the possibility of self-learning
in language models, this line of research brings both tremendous opportunities as well as potential
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