Reasoning over mathematical objects: on-policy reward modeling and test time aggregation

This paper tackles how AI language models can better solve complex math and science problems that require deriving formally structured mathematical expressions (like equations or proofs) rather than just picking a number or multiple choice answer. The researchers created a new training dataset called Principia, developed improved training methods using AI judges that learn during training, and showed how to use extra computation at test time to aggregate multiple solution attempts for better results.