Faithful reasoning architecture
A few months after publishing the selection-inference prompting technique, the authors extended the technique in a follow-up paper, with ideas for:

figuring out when the selection-inference cycle should stop or continue
adding a value function to help search over multiple reasoning paths
reducing hallucination of fake facts by fine-tuning a model to reason about sentence labels (e.g., sen1) rather than writing out the sentences themselves
Method
In the original selection-inference technique, specialized 'selection' and 'inference' prompts are alternated to select facts and make inferences from those facts, combining to generate a sequence of reasoning steps.