# MoSAR: Mixture of Semantic Attention Regimes for Learning Adaptive and Approximable Attention Geometries

arXiv: https://arxiv.org/abs/2609.31261 · HTML: https://mlsanity.com/paper/2609.31261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 39 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [MoBA: Mixture of Block Attention for Long-Context LLMs](https://mlsanity.com/paper/2502.13189/) (2025)
- [Adaptive Attention Span in Transformers](https://mlsanity.com/paper/1905.07799/) (2019)

## Abstract (arXiv)

The quadratic complexity of dense self-attention remains a central bottleneck for long-context language modeling. Many efficient alternatives address this cost by deciding in advance where attention should be sparse or local. We argue that attention approximation should instead be approached as a geometric problem, with the relevant interaction geometry learned from data: natural-language dependencies are input-dependent and difficult to prescribe in advance, so the model should learn where positional relevance can decay and where broader interactions must be preserved. We introduce Mixture of Semantic Attention Regimes (MoSAR), which learns such an adaptive, controlled-decay geometry over query--key interactions. Input-conditioned query and key routers, applied after positional encoding, select mixtures over short, medium, and global regimes, inducing a continuous distance-dependent attention field rather than a fixed sparsity pattern. This geometry is learned during training and can subsequently be discretized through top-1 routing. In controlled pre-training experiments with matched 500M-parameter models, MoSAR learns a substantially lower-reach attention geometry without degrading language-modeling quality, improving perplexity over dense RoPE at the training context length. Under length extrapolation, MoSAR achieves the best perplexity among all evaluated variants, including strong baselines such as ALiBi. Moreover, the learned geometry remains stable under deterministic top-1 discretization, suggesting that it is not only adaptive, but also amenable to low-cost approximation at inference time.