What question did this study set out to answer?

To address semantic instability in large language models by stabilizing inference through geometric methods.

April 3, 2026Open Access

ACE Semantic Gateway: Geometric Stabilization of Language Model Inference

Key Points

To address semantic instability in large language models by stabilizing inference through geometric methods.
Introduced the ACE Semantic Gateway architecture for language model inference stabilization.
Constructed a Context Matrix using domain anchors, semantic invariants, and constraint rules.
Evaluated candidate responses geometrically with the Origin Cost criterion.
Developed theoretical components including the Semantic Stability Principle and ACE Theorem.
Responses minimizing Origin Cost align better with contextual domain structure.
Reduced semantic exploration leads to decreased token usage and lower energy consumption.
Hallucinations linked to geometric instability in semantic representation space.

Abstract

Large Language Models (LLMs) generate responses by exploring high-dimensional semantic spaces learned from training data. While this probabilistic approach enables powerful language generation, it also introduces semantic instability, which can produce hallucinations, ambiguous reasoning paths, and excessive token usage. This work introduces the ACE Semantic Gateway, a semantic middleware architecture designed to stabilize language model inference before generation occurs. The ACE framework constructs a contextual reference field using a Context Matrix composed of domain anchors, semantic invariants, and constraint rules. Within this framework, candidate responses are evaluated geometrically using the Origin Cost criterion: O (z) = || z − PS (z) ||² where z represents a candidate semantic representation and PS (z) is its projection onto a contextual semantic subspace S defined by domain invariants. This formulation transforms semantic coherence from a probabilistic property of language generation into a geometric alignment problem. Responses that minimize the Origin Cost remain aligned with the invariant structure of the contextual domain, while large deviations correspond to semantic drift. The framework also introduces several theoretical components: • Context Matrix Specification • Semantic Stability Principle • Semantic Origin Hypothesis • Low-Dimensional Context Hypothesis • ACE Theorem on contextual alignment and stable inference Within this perspective, hallucinations can be interpreted as geometric instability in semantic representation space. By constraining inference to contextual semantic subspaces, the ACE architecture reduces semantic exploration, token usage, and computational energy consumption. The ACE Semantic Gateway proposes a new architectural layer for AI systems that separates semantic stabilization from language generation, providing a framework for improving reliability, efficiency, and interpretability in large language model systems. Repositoryhttps: //github. com/rosatisoft/ace-semantic-gateway This work proposes a geometric interpretation of semantic stability and invites the research community to explore its implications.

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