AI 中文总结
研究深度循环Transformer中每个令牌的计算，发现其循环状态会收敛到逐令牌定点，且收敛不均。展示了逐令牌变化可读，读出优于学习预测，无训练规则可降低平均深度，完整研究在单个RTX 4090上约100 GPU小时完成。
AI 中文摘要
深度循环Transformer多次应用权重绑定核心，先前工作表明随机递归计数训练可产生一个适用于一系列推理深度的检查点。本文研究该模型每个令牌实际计算的内容并直接测量。在FineWeb-Edu上训练的135M级模型中，循环状态收敛到逐令牌定点：平均连续输出KL散度从第二个循环的3.9e-1降至第十六循环的8.5e-6，且逐令牌状态变化逐步衰减。关键的是，这种收敛在令牌间并不均匀。中位数令牌在第六个循环收敛，约10%的令牌在训练平均深度为八时仍继续更新，平均收敛深度按令牌类型排序。本文展示了这种逐令牌变化是可读的，且读出优于学习预测：一个在输出稳定时停止每个令牌的无训练规则在4.94个平均循环时达到均匀深度8的质量（平均深度降低38%）并在平均深度范围内匹配均匀深度，而在相同模型收集的收敛标签上训练的线性路由器需要几乎完整深度且无深度降低。使这成为可能的弹性在此作为背景重现（验证损失从一个循环的3.80单调降至八个循环的3.20并保持稳定至32个循环）。我们报告平均深度作为FLOP代理，带有三点挂钟括号而非实际加速，不做FLOP匹配的对等声明，并指出分配结果是在单一规模和种子下建立的。完整研究在单个RTX 4090上运行约100 GPU小时。
英文摘要
A depth-recurrent transformer applies a weight-tied core a variable number of times, and prior work has shown that training with a randomized recursion count yields one checkpoint usable across a range of inference depths. We ask what such a model actually computes per token, and measure it directly. On a 135M-class model trained on FineWeb-Edu, the recurrent state converges to a per-token fixed point: mean successive-output KL divergence falls from 3.9e-1 at the second loop to 8.5e-6 by the sixteenth, and per-token state change decays in step. Crucially, this convergence is not uniform across tokens. The median token converges by loop six, while approximately 10 percent of tokens continue to update at the training-mean depth of eight, and mean convergence depth is ordered by token type (whitespace shallowest, content words deepest). This per-token variation is the central object of the paper. We show it is directly readable and that reading it outperforms learning to predict it: a training-free rule that halts each token once its output stabilizes attains uniform depth-8 quality at 4.94 average loops (a 38 percent reduction in average depth) and matches uniform depth across the average-depth range, whereas a linear router trained on convergence labels harvested from the same model requires nearly full depth and yields no reduction. The elasticity that makes this possible reproduces here as background (validation loss decreases monotonically from 3.80 at one loop to 3.20 at eight and remains stable to 32 loops). We report average depth as a FLOP proxy with a three-point wall-clock bracket rather than a realized speedup, make no FLOP-matched parity claim, and note that the allocation results are established at a single scale and seed. The complete study runs on a single RTX 4090 in approximately 100 GPU-hours.
Comments15 pages, 4 figures. Code, configs, experiment log, and checkpoint at https://github.com/jlognn/depth-recurrent-convergence
