Similarity-Distance-Magnitude Activations

We introduce a more robust and interpretable formulation of the standard softmax activation function commonly used with neural networks by adding Similarity (i.e., correctly predicted depth-matches into training) awareness and Distance-to-training-distribution awareness to the existing output Magnitude (i.e., decision-boundary) awareness. When used as the final-layer activation with language models, the resulting Similarity-Distance-Magnitude (SDM) activation function is more robust than the softmax function to co-variate shifts and out-of-distribution inputs in high-probability regions, and provides interpretability-by-exemplar via dense matching. Complementing the prediction-conditional estimates, the SDM activation enables a partitioning of the class-wise empirical CDFs to guard against low class-wise recall among selective classifications. These properties make it preferable for selective classification, even when considering post-hoc calibration methods over the softmax.