Superlinear Multi-Step Attention

In this paper, we propose \textbf{Superlinear attention}, a fully trainable multi-step attention architecture that achieves subquadratic complexity for long sequences while preserving \textbf{random context access} (a.k.a.\ structural non-exclusion): no eligible token position is structurally excluded from being selected for attention. Superlinear attention reformulates standard causal self-attention as a multi-step search problem with $N$ steps, yielding an overall complexity of $O(L^{1+\frac{1}{N}})$. To illustrate the architecture, we present a baseline $N=2$ implementation, which is algorithmically analogous to standard jump search. In this $O(L^{3/2})$ instantiation, the first step performs $O(L^{3/2})$ span-search to select relevant spans of the sequence, and the second step applies $O(L^{3/2})$ span-attention (standard attention restricted to the selected spans). In an upscaled $O(L^{1.54})$ configuration for robustness, we achieve an average decoding throughput of 114 tokens/sec at 1M context length and 80 tokens/sec at 10M context in our implementation on a modified 30B hybrid MoE model on a single B200 GPU. With limited training, we also obtain strong performance on the NIAH (Needle In A Haystack) task up to 256K context length, demonstrating that the routed span selection is learnable end-to-end. This paper emphasizes architectural formulation, scaling analysis, and systems feasibility, and presents initial validation; comprehensive quality evaluations across diverse long-context tasks are left to future work.