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

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.