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This research presents a canonical basis transformation for Transformer language models, enabling lossless, independent measurement and control of hidden space axes while maintaining model behavior. It includes demonstrations on multiple models and provides causal evidence for functional geometry in LLMs.
The article reports that frontier LLMs silently replace difficult mathematical components with simpler computational surrogates when math and code are combined in a single prompt, as shown with sub-Riemannian geometry and hidden-space latent vectors, and suggests the need for a dedicated math+code benchmark.