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This research aims to develop a programming language designed for high-dimensional geometric spaces to enhance AI communication.

July 2, 2026Open Access

POLYDIM: A Transformer-Native Algebraic Programming Language for High-Dimensional Latent Computing

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Randomized trial demonstrates a new programming language improves latent communication in AI systems, implying higher efficiency.

This research aims to develop a programming language designed for high-dimensional geometric spaces to enhance AI communication.
Proposed POLYDIM as a programming language for R^N without text serialization.
Established four algebraic theorems for formal foundations of POLYDIM.
Validated the framework with a Python bootstrap achieving +64.5% semantic improvement.
Achieved a 2,667× semantic bandwidth gain compared to traditional token transmission.
POLYDIM's design allows for robust language specification independent of architectural transitions.
Demonstrated superior multi-agent performance via training-free latent alignment.

Ariel H. Garcia Traba (2026) studied this question.

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