Canonical-basis realignment for Transformer LLMs: every hidden axis becomes independently measurable and controllable

A new method has been developed that enables the rotation of a Transformer's internal coordinate system into a "canonical basis" that aligns with its own weight matrices. This process is lossless, meaning the model's outputs and perplexity scores remain unchanged. By utilizing orthogonal matrices constructed from the singular vectors of the model, researchers can transform architectures such as Qwen or Pythia without affecting their performance.

The transformation reveals the hidden geometric structures operating within the network, previously obscured and unobservable. Researchers have identified intriguing patterns, including a bipolar oscillator where certain axes act as inhibitory pairs, firing against each other in perfect opposition. Additionally, they have observed a rhythmic respiration across layers, where the model alternates between absorbing knowledge and filtering it.

Furthermore, the approach uncovers a homeostatic defense mechanism capable of rapidly eradicating localized perturbations within just a few layers. This newfound insight provides researchers with a powerful tool for mapping out how language models perform reasoning. For instance, it was discovered that the effective rank of the correlation matrix in a half-billion parameter model may be as low as eleven independent patterns.

By reframing the study of language models' internal activations, this method offers a standardized approach to understanding their underlying architecture. This development promises to significantly advance our comprehension of these complex systems and their reasoning capabilities.