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:
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.
A Symbolic Model for Recursive Interpretation and Containment in LLMs
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.