This is very interesting:

"Empirical Validation. While we cannot verify these theoretically, we evaluate each empirically. We use the Qwen-2.5-7B-Instruct model (Hui et al., 2024) as the base policy and the ToolAlpaca dataset (Tang et al., 2023). In this benchmark, the model receives a tool-API specification and a user request, and must identify the correct tool call. Without demonstrations, the base model solves only 42% of examples. When provided with the appropriate demonstration c for each prompt x , the teacher achieves a 100% success rate. To further test reward proximity, we manually inspected 50 teacher reasoning traces. In all cases, not only were the final tool calls correct, but the intermediate chain-of-thought was valid and semantically grounded. This suggests that the teacher is reconstructing a correct reasoning process rather than merely copying the expert output. These observations provide evidence for the first requirement, that the demonstration-conditioned model behaves as an optimal policy."

I find the choice of the words "enable" in the title and "establishing" at the end of the abstract to be particularly jarring.

Gemini tells me it's the probability of the next token for an LLM. Okay then.