HOST: So if I'm building math-focused language models specifically, why should I care about this? EXPERT: It suggests a possible training approach when you've got both an improved model and the version it started from. The authors tested that on competition math problems. HOST: So why keep the older version around at all? EXPERT: It gives the authors a before-and-after comparison. They measure how the model's internal signals change when the teacher was trained with rewards for desired responses. HOST: Right, so where does the student come in? EXPERT: The student starts from that older version and generates part of an answer. Both saved models process the same partial answer. RIDE then trains the student toward an internal target farther along the measured change. HOST: Does moving farther mean the final answer improves? EXPERT: Not by itself. That is the training target. In the authors' math evaluations, RIDE's average score was above the teacher's fixed score on each of four model pairs, though three of those margins were within one across-run standard deviation. HOST: So what would I need to remember before tying it? EXPERT: Yeah, you need the earlier checkpoint and comparable internal states. The authors tested one reward training recipe on math, and they say safety and calibration need separate checks. The official repository does not yet provide runnable training code.