Connections between the semiotic interpretation and philosophical accounts of understanding in AI

Elucidate and formalize the connections between the semiotic interpretation of threshold functions—specifically, the transition from symbolic to indexical behavior in high-dimensional spaces—and philosophical debates about the nature of understanding in artificial intelligence.

Background

Section 5 develops a semiotic framework in which threshold functions act as symbols in low dimensions and indices in high dimensions. This reinterpretation aims to clarify how pretrained systems can display context-sensitive behavior.

The conclusion explicitly notes that relating this semiotic account to broader philosophical discussions of understanding in AI remains an open area for investigation.

References

Open questions remain. The formal derivation of perceptron freedom from the four geometric properties of high-dimensional space; the bounds on minimum depth required for manifold simplification; the connections between the semiotic interpretation and philosophical debates about understanding in AI; and the practical implications for architecture design - all invite further investigation.

— Understanding the Nature of Generative AI as Threshold Logic in High-Dimensional Space  (2604.02476 - Levin, 2 Apr 2026) in Conclusion (Section 6), final paragraph