Similarity-Distance-Magnitude Activations

• URL: http://arxiv.org/abs/2509.12760v2
• Date: Thu, 30 Oct 2025 06:08:58 GMT
• Title: Similarity-Distance-Magnitude Activations
• Authors: Allen Schmaltz,
• Abstract summary: We introduce the Similarity-Distance-Magnitude activation function, a more robust and interpretable formulation of the standard softmax activation function.<n>We also introduce the SDM estimator, based on a data-driven partitioning of the class-wise empirical CDFs via the SDM activation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Similarity-Distance-Magnitude (SDM) activation function, a more robust and interpretable formulation of the standard softmax activation function, 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, and enabling interpretability-by-exemplar via dense matching. We further introduce the SDM estimator, based on a data-driven partitioning of the class-wise empirical CDFs via the SDM activation, to control the class- and prediction-conditional accuracy among selective classifications. When used as the final-layer activation over pre-trained language models for selective classification, the SDM estimator is more robust to co-variate shifts and out-of-distribution inputs than existing calibration methods using softmax activations, while remaining informative over in-distribution data.

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