A note on the impossibility of conditional PAC-efficient reasoning in large language models
This is a foundational theoretical limitation for researchers working on efficient reasoning in AI systems.
The paper proves that conditional PAC-efficient reasoning in large language models is impossible in distribution-free settings, showing any algorithm must defer to expert models with probability at least 1-α for almost every input.
We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch between expensive expert models and cheaper fast models, we show that conditional (pointwise) guarantees are impossible in the distribution-free setting. Specifically, for non-atomic input spaces, any algorithm achieving conditional PAC efficiency must be trivial in the sense that it defers to the expert model with probability at least $1-α$ for almost every input.