Phase Transition of Logic: Experimental Observation of Logical Collapse in Transformer Hidden Spaces
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2025
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| _version_ | 1866901105510711296 |
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| author | Wang, Zhongren |
| author_facet | Wang, Zhongren |
| contents | <p>This paper reports a reproducible experimental observation in large language models (LLMs): <strong>Logical Collapse</strong>. Using the Qwen3-4B model, we show that logically contradictory statements—such as “I like apples” and “I hate apples”—exhibit extremely high cosine similarity (>0.93) in their final hidden states, yet can be perfectly separated by projecting onto a <em>Logical Differential Vector</em> (LDV) constructed via simple vector subtraction. The LDV isolates the direction of logical polarity from entangled semantic representations. Critically, this separation is only observable at the <strong>last token</strong> of the sequence, revealing that logical judgment undergoes a phase transition at sequence termination. Our method requires no retraining and uses only standard hidden state extraction.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18052338 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Phase Transition of Logic: Experimental Observation of Logical Collapse in Transformer Hidden Spaces Wang, Zhongren large language models transformer interpretability hidden space geometry logical reasoning semantic representations cosine similarity vector arithmeti final token representation logical polarity differential probing <p>This paper reports a reproducible experimental observation in large language models (LLMs): <strong>Logical Collapse</strong>. Using the Qwen3-4B model, we show that logically contradictory statements—such as “I like apples” and “I hate apples”—exhibit extremely high cosine similarity (>0.93) in their final hidden states, yet can be perfectly separated by projecting onto a <em>Logical Differential Vector</em> (LDV) constructed via simple vector subtraction. The LDV isolates the direction of logical polarity from entangled semantic representations. Critically, this separation is only observable at the <strong>last token</strong> of the sequence, revealing that logical judgment undergoes a phase transition at sequence termination. Our method requires no retraining and uses only standard hidden state extraction.</p> |
| title | Phase Transition of Logic: Experimental Observation of Logical Collapse in Transformer Hidden Spaces |
| topic | large language models transformer interpretability hidden space geometry logical reasoning semantic representations cosine similarity vector arithmeti final token representation logical polarity differential probing |
| url | https://doi.org/10.5281/zenodo.18052338 |