Long chain-of-thought (CoT) reasoning models such as DeepSeek-R1 keep lengthening their inference chains under test-time scaling, yet standard self-attention incurs quadratic cost in context length, making long-CoT deployment costly in production. We therefore introduce LISA (Linear-Indexed Sparse Attention), a plug-and-play replacement for self-attention that requires no full pretraining. LISA combines a linear-attention branch for long-range memory with a Lightning Indexer that dynamically selects the most relevant tokens for a sparse self-attention branch. The two branches are fused through a learned gate, so the model retains broad context while focusing computation on informative tokens. We train LISA in two stages. In Stage 1, a linear-attention branch is integrated with sliding-window attention and distilled from a frozen teacher's full-attention distribution. In Stage 2, the Lightning Indexer replaces the static window and is trained with a per-head KL-divergence objective to mimic teacher attention patterns. The resulting model reduces eager-mode self-attention computation from quadratic in sequence length to linear in the number of generated tokens and the selected context budget. Experiments on DeepSeek-distilled Qwen models show that LISA cuts measured eager-mode mean sample latency by 23.9% at 16K context without degrading long-context reasoning quality. Across nine mathematical and code reasoning benchmarks, the gated LISA-1.5B model improves the equal-weight benchmark average by 4.2 percentage points relative to the full-attention baseline.

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