Behnam Tajfar

Mechanistic interpretability often rests safety claims on thresholded numbers that can flip under small changes to weights, training seed or threshold. Working on toy models and synthetic dictionaries with known ground-truth features, this work characterizes exactly where feature dimensionality is discontinuous and replaces it with a ridge-regularized version whose stability constant grows with feature scale and whose coefficient is optimal. On 12 trained toy models, the regularized sum rule gave the same verdict at all 21 pre-set values of its smoothing parameter, while the version that ignores short feature vectors gave the opposite verdict for two of the models.

Mechanistic interpretability often rests safety claims on thresholded numbers that can flip under small changes to weights, training seed or threshold. Working on toy models and synthetic dictionaries with known ground-truth features, this work characterizes exactly where feature dimensionality is discontinuous and replaces it with a ridge-regularized version whose stability constant grows with feature scale and whose coefficient is optimal. On 12 trained toy models, the regularized sum rule gave the same verdict at all 21 pre-set values of its smoothing parameter, while the version that ignores short feature vectors gave the opposite verdict for two of the models.