Interpretation as Linear Transformation: A Cognitive-Geometric Model of Concepts and Meaning
arXiv:2512.09831v2 Announce Type: replace Abstract: This paper develops a geometric framework for modeling concepts, motivation, and influence across cognitively heterogeneous agents. Each agent is represented by a personalized value space, a vector space encoding the internal dimensions through which the agent interprets and evaluates meaning. Evaluative concepts are formalized as structured vectors, abstract beings, whose transmission is mediated by linear interpretation maps. An abstract being survives communication only if it avoids the null spaces of these maps, yielding a structural crit
This paper represents a significant theoretical advancement in understanding AI cognition and inter-agent communication, published at a time of rapid AI expansion and increasing complexity.
A strategic reader should care because a unified cognitive-geometric model could unlock more sophisticated AI agent design and foster better human-AI and AI-AI collaboration by formalizing interpretation.
This research provides a novel mathematical framework for modeling how AI agents understand and influence each other, moving beyond current black-box approaches to agent interaction.
- · AI researchers
- · Developers of multi-agent systems
- · Cognitive scientists
- · AI models lacking sophisticated interpretive layers
- · Simple rule-based AI systems
It will directly influence the theoretical underpinnings of future AI agent architectures and communication protocols.
This refined understanding of interpretation could lead to more robust, ethical, and collaborative multi-agent AI systems across various domains.
Such systems might then enable the collapse of complex white-collar workflows requiring inter-agent negotiation and interpretation, driving further societal restructuring.
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Read at arXiv cs.AI