Inside the Loop: A Mechanistic Study of Weight-Tied Transformers on Depth-Bound Algorithmic Tasks

Key points

• Looped transformers, which reuse one block of layers across many iterations, are poised to address this, since they scale effective depth without adding parameters or tokens.1
• Here, we study directed permutation traversal, in which a model follows $H$ hops from a starting node and reports the node it reaches, so every intermediate hop has a known ground truth.1
• Probing and intervening on the residual stream, we find that the looped model advances through the intermediate nodes gradually, forming a staircase that adapts to its iteration budget, whereas the untied model, at that lower rate, exposes them only in its final layers.1
• Taken together, our results recast looped transformers as iterative program learners, which allocate their iterations to successive steps of the algorithm and solve tasks that identically-trained untied models of the same effective depth do not.1

Sources (1)

• [1]Inside the Loop: A Mechanistic Study of Weight-Tied Transformers on Depth-Bound Algorithmic Tasks
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 16, 07:06 PM

  Solving algorithmic tasks with many sequential steps typically requires scaling up transformer depth or chain-of-thought length, incurring unfavorable parameter and inference-compute costs, respectively.

  Looped transformers, which reuse one block of layers across many iterations, are poised to address this, since they scale effective depth without adding parameters or tokens.

Extractive summary: sentences quoted from the sources.