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Loop as a Bridge: Can Looped Transformers Truly Link Representation Space and Natural Language Outputs?

Guanxu Chen, Dongrui Liu, Jing Shao

TL;DR

The paper probes whether Looped Transformers (LTs) can bridge the gap between internal representations and linguistic outputs by using iterative looping as introspection. Through a formal framework and experiments on safety and math tasks with Ouro and baselines, it finds that loop depth can narrow the gap, but largely due to representational degradation rather than improved representation readout, and that introspective awareness remains confined to the final loop. Injection-based tests reveal limited continuous introspection; concept signals are detected mainly when injected late in the loop. While LTs remain a promising direction for deeper computation, the study suggests current architectures do not yet realize truly coupled representation-language introspection, pointing to future work in training objectives and architecture refinements.

Abstract

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational depth by iterating shared layers--can bridge this gap by utilizing their iterative nature as a form of introspection. Our experiments reveal that while increasing loop iterations narrows the gap, it is partly driven by a degradation of their internal knowledge carried by representations. Moreover, another empirical analysis suggests that current LTs' ability to perceive representations does not improve across loops; it is only present in the final loop. These results suggest that while LTs offer a promising direction for scaling computational depth, they have yet to achieve the introspection required to truly link representation space and natural language.

Loop as a Bridge: Can Looped Transformers Truly Link Representation Space and Natural Language Outputs?

TL;DR

The paper probes whether Looped Transformers (LTs) can bridge the gap between internal representations and linguistic outputs by using iterative looping as introspection. Through a formal framework and experiments on safety and math tasks with Ouro and baselines, it finds that loop depth can narrow the gap, but largely due to representational degradation rather than improved representation readout, and that introspective awareness remains confined to the final loop. Injection-based tests reveal limited continuous introspection; concept signals are detected mainly when injected late in the loop. While LTs remain a promising direction for deeper computation, the study suggests current architectures do not yet realize truly coupled representation-language introspection, pointing to future work in training objectives and architecture refinements.

Abstract

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational depth by iterating shared layers--can bridge this gap by utilizing their iterative nature as a form of introspection. Our experiments reveal that while increasing loop iterations narrows the gap, it is partly driven by a degradation of their internal knowledge carried by representations. Moreover, another empirical analysis suggests that current LTs' ability to perceive representations does not improve across loops; it is only present in the final loop. These results suggest that while LTs offer a promising direction for scaling computational depth, they have yet to achieve the introspection required to truly link representation space and natural language.
Paper Structure (16 sections, 9 equations, 6 figures)

This paper contains 16 sections, 9 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Looped Transformers
  4. AI Monitors
  5. Introspective Awareness of LLMs
  6. Formulation
  7. Formulation of Hierarchical Performance.
  8. Formulation of Performance Gaps.
  9. Claim 2: $\sup_{\pi,A,s} \textcolor{ETHGreen}{P_{SV}}(\pi,A,s)\le\sup_{\pi,A,l,g} \textcolor{ETHPurpleDark}{P_{RR}}(\pi,A,l,g)$.
  10. Can LTs align linguistic output with representation?
  11. Setups.
  12. Results.
  13. Can LTs enhance their introspective awareness on representations?
  14. Setups.
  15. Results.
  16. ...and 1 more sections

Figures (6)

  • Figure 1: A gap often exists among the three levels of capabilities in practice.
  • Figure 2: Accuracy/F1 of language-based self-verification.
  • Figure 3: Accuracy/F1 of linear probes trained on internal representations.
  • Figure 4: Gap between representation readout and language-based self-verification.
  • Figure 5: Injection awareness across the extract loop and inject loop.
  • ...and 1 more figures