LayerNorm Transformers Exhibit Algebraic Dead Directions

This research uncovers a specific algebraic "dead direction" within the parameter space of LayerNorm Transformers. These dead directions signify regions where the Fisher information metric, which measures how much the model's output changes with respect to its parameters, degenerates. This implies that changes along these directions have minimal impact on the loss function, indicating the model is near a singular minimum. Crucially, this dead direction can be identified directly from the inverse-scale parameter of the LayerNorm affine transformation. This means it requires no forward or backward passes through the network and no complex eigendecomposition, making it the most computationally efficient method to date for detecting such singular structures. The diagnostic was validated across 14 pretrained transformers, accurately identifying the dead direction in LayerNorm models and its absence in RMSNorm models. The study also reveals that the smallest singular value of the residual stream is largely preserved across blocks, with exceptions pinpointed by this diagnostic, and that the presence of this kernel direction can classify a transformer's normalization type from its parameters alone.