Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2
Abstract:Do large language models internally encode ontological relations in a formally verifiable algebraic structure? We introduce Algebraic Ontology Projection (AOP), which projects LLM hidden states into the Galois Field F2 under Liskov Substitution Principle constraints, using only 42 relational pairs as algebraic keys. AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone.
This algebraic structure is strongly layer-dependent. We introduce Semantic Crystallisation (SC), a metric that quantifies F2 constraint satisfaction relative to a random baseline and predicts zero-shot accuracy without held-out data. System prompts act as algebraic boundary conditions: only their combination with instruction tuning prevents Late-layer Collapse -- a systematic degradation of logical consistency in the final layers, observed in 7 of 10 conditions. These findings reframe forward computation as an iterative process of algebraic organisation, and open a path toward LLMs whose logical structure is not merely approximated, but formally accessible.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2605.12968 [cs.LG] |
| (or arXiv:2605.12968v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.12968
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
Current browse context:
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Learning When to Act: Communication-Efficient Reinforcement Learning via Run-Time Assurance
May 14
-
CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks
May 14
-
Towards Robust Federated Multimodal Graph Learning under Modality Heterogeneity
May 14
-
OceanCBM: A Concept Bottleneck Model for Mechanistic Interpretability in Ocean Forecasting
May 14
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.