---
title: "Best-of-Depth: Learning Exploratory Dynamics in Looped Transformers"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.04663v1"
permalink: "https://feed.astralor.com/items/itm_ff7f07bfbcd1b65e377d1879"
published: "2026-11-03T10:50:34.000Z"
score: 57
channel: "tech"
tags: ["推理效率","RAG","多模态","Best-of-Depth","Learning Exploratory Dynamics","Looped Transformers Looped","Transformers","BoD"]
---

# Best-of-Depth: Learning Exploratory Dynamics in Looped Transformers

## At a glance

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…

## Key points

- 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.

## Full text

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 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.

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