Similarity-Distance-Magnitude Language Models

Allen Schmaltz

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arXiv · 2510.26183

Similarity-Distance-Magnitude Language Models

Allen Schmaltz

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Abstract

We introduce Similarity-Distance-Magnitude (SDM) language models (LMs), which are sequence prediction models fine-tuned to maximize the proportion of generations in the well-calibrated, high-probability region partitioned by a final-layer SDM activation layer used for binary classification of instruction-following. We demonstrate that existing pre-trained decoder-only Transformer LMs can be readily converted into SDM LMs via supervised fine-tuning, using the final-layer SDM activation layer during training to estimate a change-of-base for a supervised next-token loss over a contrastive input encoding scheme, with additional hard negative examples generated online during training. This results in reduced abstentions (i.e., improved statistical efficiency) compared to strong supervised baselines.

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Allen Schmaltz. 2025-10-30. Similarity-Distance-Magnitude Language Models. https://arxiv.org/abs/2510.26183

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