LAG-XAI: A Lie-Inspired Affine Geometric Framework for Interpretable Paraphrasing in Transformer Latent Spaces

Transformer models contain interpretable geometric structure: Rather than being completely opaque "black boxes," the paper demonstrates that language model embeddings follow predictable geometric patterns. Specifically, paraphrasing operations can be decomposed into measurable components (rotation, deformation, and translation), suggesting that semantic transformations follow consistent mathematical rules that humans can understand.

There's a trade-off between interpretability and accuracy worth considering: The LAG-XAI framework achieves 77% accuracy (AUC 0.7713) compared to 84% for a non-interpretable baseline model. The authors argue this 7-point gap is acceptable because it captures 80% of the baseline's performance while providing explicit, human-understandable explanations—a key principle in responsible AI where transparency can be more valuable than marginal accuracy gains.

Interpretable AI methods can work across different datasets: The model was validated on two independent datasets (PIT-2015 Twitter corpus and TURL dataset), demonstrating that the geometric patterns discovered aren't just artifacts of one specific dataset. This cross-domain validation is important for responsible AI because it suggests the interpretability insights are robust and generalizable.

Geometric invariants reveal how language models actually work: The discovery of a stable reconfiguration angle (~27.84°) and near-zero deformation suggests that paraphrasing operations follow consistent geometric principles. This kind of fundamental insight helps demystify how these powerful systems process language, supporting more trustworthy AI development.