Loop, Think, & Generalize Explained: When More Transformer Loops Help or Hurt

Knowing atomic facts is not the same as combining them. This controlled study trains small recurrent-depth transformers from scratch to test systematic composition and extrapolation beyond training depth. It also identifies overthinking: extra recurrence can move predictions past a correct answer. Exact citation: Harsh Kohli, Srinivasan Parthasarathy, Huan Sun, and Yuekun Yao. Loop, Think, & Generalize: Implicit Reasoning in Recurrent-Depth Transformers. arXiv:2604.07822v2, revised 11 August 2026. PDF labeled Published as a conference paper at COLM 2026. https://arxiv.org/abs/2604.07822v2 All 21 PDF pages read, including references and Appendices A-K. Exact versioned public PDF matches the local SHA-256: a1a0e8f0507df84ddc70d438ba465a883c1f0002a7fc04845e471eabcb3d10b8 Task: a head-entity token plus ordered relation tokens must predict the final entity, without intermediate reasoning text. All atomic facts are trained. Training compositions use only the ID atomic subset; systematic tests compose atomic facts seen individually but never composed in training. Depth tests instead require longer ID-fact chains. These are different tests. Architecture: a shared four-layer stack executes R times, effective depth4R; final layer norm and tied output head supervise the final answer position only. No baseline repeated input injection, middle looping, or learned halting gate. Zero attention/FFN output projections initialize residual blocks as identity. Dynamic training samples clipped Poisson recurrence per batch, normally min2/max8; it is not oracle complexity allocation. Systematic setup: 2000 entities,200 relations,40000 atomic facts;95/5 atomic partition;273600 training compositions,3000 ID and nearly2000 OOD queries. Memorization precedes ID grokking, then systematic grokking. Logit lens and activation patching support bridge-mediated composition locally, not universally faithful latent chain of thought. Depth setup:200 entities,10 permutation relations,2000 atomic facts;15000 examples per depth through40;750 held-out per depth. A95% held-out curriculum gate introduces harder data while retaining earlier depths. Main fixedR8 reaches ID16; dynamic reaches ID22. Those22 hops are not all unseen-depth extrapolation. With matched12-hop training, fixedR6 reportedly reaches14 while fixedR8 and dynamic reach19. Consult plotted accuracy profiles; do not silently apply AppendixJ's60% ratio criterion to every reported maximum. We teach ordered relation composition, permutation shortcut control, recurrence/readout, margin and stopping equations one panel at a time. Checked invented examples: red cycles A-B-C-A; blue swaps A/C and fixesB. Query red-red-blue fromA returnsA; red-blue-red returnsC. A separate scalar recurrence0-1-2 decodesA-B-C, so a correctB can be lost at the next step. These are illustrations, not model experiments. Overthinking metric: correct-answer logit minus strongest competitor; average margins peak then decay. Dynamic training slows decay, not eliminates it. Halting requires KL(current||previous) below0.01 AND entropy below3.00. Stable uncertain predictions continue; confidently wrong predictions can still stop. Entropy log base is not specified. Appendix controls and limits: prior apparent train40/test80 success came from a suffix shortcut before permutation control, not the controlled headline. Two fixed seeds and three dynamic seeds are limited evidence; dynamic ID boundaries22/21/19 vary. Larger stacks or recurrence caps do not consistently improve the AppendixJ ratio. No dedicated fact/rule-frequency sweep or detailed input-injection ablation is reported. The symbolic loss shown formalizes described supervision, not a separate quoted source equation. Natural-language variation, distractors and frontier-scale transfer are untested. Independent educational explanation. No experiments independently reproduced; no author endorsement. Source notes document every PDF page, equation provenance, invented toys and public-source ambiguities. #AIResearch #Transformers #ImplicitReasoning #Grokking