Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
The Geometric Price of Discrete Logic: Context-driven Manifold Dynamics of Number Representations
Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric proj…
Logical ReasoningProbing Ethical Framework Representations in Large Language Models: Structure, Entanglement, and Methodological Challenges
When large language models make ethical judgments, do their internal representations distinguish between normative frameworks, or collapse ethics into a single acceptability dimension? We probe hidden representations acr…
$\mathbfλ$-VAE: Variance Equalization for Posterior Collapse
Variational Autoencoders (VAEs) frequently suffer from posterior collapse, a failure mode in which the approximate posterior converges to the prior, rendering the latent code uninformative. Despite extensive research, a …
The Mercurial Top-Level Ontology of Large Language Models
In our work, we systematize and analyze implicit ontological commitments in the responses generated by large language models (LLMs), focusing on ChatGPT 3.5 as a case study. We investigate how LLMs, despite having no exp…
FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning
Current multimodal benchmarks for scientific reasoning primarily evaluate local information extraction -- models recognize symbols and values and then perform textual inference. They do not assess whether models can reas…
Information ExtractionMultimodal Reasoning