# Similarity-Distance-Magnitude Language Models

arXiv: https://arxiv.org/abs/2510.26183 · HTML: https://mlsanity.com/paper/2510.26183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Similarity-Distance-Magnitude Activations](https://mlsanity.com/paper/2509.12760/) (2025)

## Abstract (arXiv)

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.