We focus on "shortest path in maze" planning problems. We solve 50K instances of mazes from Wilson distribution with A* search, and train transformers with <problem, A* derivational trace, solution> 2/

Starting with a transformer trained on Wilson mazes, we have it "solve" 1K test instances each group drawn from a different distribution, and examine the correlation between "trace validity" and "solution accuracy". The confusion matrices show at best a loose correlation between

Note that unlike the free form intermediate tokens generated by DeepSeek R1, the training traces all come from formal derivational traces of A* search. We can thus verify the correctness of intermediate tokens output during the test/inference stage. 4/

Given the lack of strong correlation between trace validity and solution accuracy, we ask the question "are correct traces really needed at the training stage?". To check, we take the same 50K training mazes, but now do a pair-wise swap of their traces--thus ensuring that every

When we test a transformer trained on this incorrect trace data, we find that not only does it provide the same accuracy in distribution but actually gives significantly higher accuracy out of distribution! 6/

These results thus question the prevailing wisdom that the reason for the improved performance of LRMs like DeepSeek is having access to reasoing/thinking traces. In short, not only is there no strong correlation between trace and solution validity when trained on correct traces,

In other words, while intermediate tokens may be helping the LLMs in improving solution accuracy, they don't provide any dependable signal to the end user--and can even engender false trust in potentially wrong solutions. 8/ https://x.com/rao2z/status/189...

Intermediate tokens should perhaps be seen as dynamically generated "reason-less" prompt augmentations that just increase solution accuracy. If so, we may as well directly optimize for that without looking for non-existent trace semantics.. 9/ https://x.com/rao2z/status/186...

Here is the arXiv preprint 9/ https://arxiv.org/abs/2505.137...