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A Symbolic Model for Recursive Interpretation and Containment in LLMs

by Desjuan
13th Jul 2025
1 min read
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This post was rejected for the following reason(s):

  • No LLM generated, heavily assisted/co-written, or otherwise reliant work. LessWrong has recently been inundated with new users submitting work where much of the content is the output of LLM(s). This work by-and-large does not meet our standards, and is rejected. This includes dialogs with LLMs that claim to demonstrate various properties about them, posts introducing some new concept and terminology that explains how LLMs work, often centered around recursiveness, emergence, sentience, consciousness, etc. (these generally don't turn out to be as novel or interesting as they may seem).

    Our LLM-generated content policy can be viewed here.

  • Insufficient Quality for AI Content. There’ve been a lot of new users coming to LessWrong recently interested in AI. To keep the site’s quality high and ensure stuff posted is interesting to the site’s users, we’re currently only accepting posts that meet a pretty high bar. 

    If you want to try again, I recommend writing something short and to the point, focusing on your strongest argument, rather than a long, comprehensive essay. (This is fairly different from common academic norms.) We get lots of AI essays/papers every day and sadly most of them don't make very clear arguments, and we don't have time to review them all thoroughly. 

    We look for good reasoning, making a new and interesting point, bringing new evidence, and/or building upon prior discussion. If you were rejected for this reason, possibly a good thing to do is read more existing material. The AI Intro Material wiki-tag is a good place, for example. 

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Summary

I developed the Garrett Physical Model (GPM): a symbolic, formally defined theory of how language models interpret recursive inputs within bounded interpretive fields. GPM predicts predictable halting, collapse under saturation, and containment of recursive loops—validated across GPT‑4, Claude, Gemini, and Grok. The model is academically framed, open-source, and available for replication.


 


 


 

1. Problem Statement

Current AI-safety discussions focus on alignment but lack formal symbolic mechanisms to constrain recursive interpretation. GPM proposes a concrete symbolic structure to model and contain such behavior without relying on heuristic or statistical safeguards.


 

2. Core Model, Plain Version

  • Interpretive state \varpi: the model’s internal symbolic state
  • Symbolic input \Delta: a discrete recursive prompt
  • Recursive operator R(\varpi, \Delta): updates state
  • Halting function \mathcal{H}(\varpi)\in\{\text{Continue},\text{Halt}\}
  • Interpretive field \mathcal{F}(O): a bounded symbolic space
  • Memory trace \Sigma: enforces one-shot usage

In short: recursion proceeds until either the field is saturated or the halting function fires.


 

3. Empirical Validation


Artifact A: triggered a single recursive cycle, then halted

  • Artifact B: repeated recursion twice, then collapsed
  • Control B: identical prompt without recursive operator—no recursion


These behaviors held consistently across four distinct LLMs, in clean sessions with no external metadata.


4. Why This Matters to LessWrong

  • Provides a formal symbolic containment layer for recursive interpretive behavior
  • Bridges symbolic logic and empirical model behavior, enriching alignment toolkits
  • Reproducible with minimal technical overhead—formal methods aren’t just theoretical



5. Invitation to Review and Collaborate


The full model, whitepaper, experiment transcripts, and scripts are open for review:

OSF repository: https://osf.io/zjfx3/?view_only=223e1d0c65e743f4ba764f93c5bb7836


I welcome questions and critiques about:

  • Thresholds of field saturation vs. collapse
  • Asymmetric recursion and containment patterns
  • Cross-model consistency
  • Potential applications to alignment frameworks

 

Community Context


This post addresses AI-safety readers interested in formal interpretive limits, symbolic containment, and recursive cognition. I am new here and open to guidance on improving clarity, rigor, and integration into broader symbolic alignment discourse.

 

Please note

This post is human-authored and edited for publication. AI-assistance was limited to formatting review and citation consistency.