Attention in Constant Time: Vashista Sparse Attention for Long-Context Decoding with Exponential Guarantees

• URL: http://arxiv.org/abs/2602.13804v1
• Date: Sat, 14 Feb 2026 14:29:10 GMT
• Title: Attention in Constant Time: Vashista Sparse Attention for Long-Context Decoding with Exponential Guarantees
• Authors: Vashista Nobaub,
• Abstract summary: Large language models spend most of their inference cost on attention over long contexts.<n>We formalize this phenomenon by modeling attention as a projection onto the convex hull of key vectors.<n>We introduce Vashista Sparse Attention, a drop-in mechanism that maintains a small candidate set per query.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large language models spend most of their inference cost on attention over long contexts, yet empirical behavior suggests that only a small subset of tokens meaningfully contributes to each query. We formalize this phenomenon by modeling attention as a projection onto the convex hull of key vectors and analyzing its entropic (softmax-like) relaxation. Our main theoretical contribution is a face-stability theorem showing that, under a strict complementarity margin (a support gap (Δ) certified by KKT multipliers), entropic attention concentrates on a constant-size active face: the total mass assigned to inactive tokens decays exponentially as (\exp(-Ω(Δ/\varepsilon))), while the error on the active face scales linearly in the temperature/regularization parameter (\varepsilon). This yields a practical criterion for when sparse long-context decoding is safe and provides a principled knob to trade accuracy for compute. Building on these guarantees, we introduce Vashista Sparse Attention, a drop-in mechanism that maintains a small candidate set per query through a paging-style context selection strategy compatible with modern inference stacks. Across long-context evaluations, we observe stable constant-size effective support, strong wall-clock speedups, and minimal quality degradation in the regimes predicted by the support-gap diagnostics. Finally, we discuss deployment implications for privacy-sensitive and air-gapped settings, where interchangeable attention modules enable predictable latency and cost without external retrieval dependencies.

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