Looped Transformers extend inference-time computation through repeated latent-state updates, but final-depth training does not directly encourage useful intermediate alternatives.
We introduce Best-of-Depth (BoD), which trains a recurrent trajectory as a candidate set by minimizing prediction loss across depths. Different valid targets can be matched at different depths without architectural changes or depth-specific labels.
An exact-match analysis connects this objective to solution coverage.
On N-Queens completion and graph coloring, BoD improves coverage over final-depth and intermediate-supervision objectives.
- N-Queens completion
- graph coloring
N-Queens coverage reaches 91.03%, versus 45.75% for final-depth training.
Further experiments show discovery beyond the training depth and recovery of solutions withheld from teacher pools on familiar inputs.
Fine-tuning a pretrained looped language model with BoD yields higher pooled code-generation success than final-depth training when programs are generated separately at evaluated fixed depths.
These results support training recurrent computation for solution discovery along its trajectory.