Large Language Models (LLMs) incur quadratic attention complexity with input length, creating a major time bottleneck in the prefilling stage. Existing acceleration methods largely exploit attention score sparsity by estimating blocks with high attention scores and applying dynamic sparse attention. In this work, we identify another untapped form of sparsity in the prefilling stage, namely decoding-time contribution sparsity, where many attention blocks exhibit nontrivial attention scores during prefilling yet contribute negligibly to subsequent decoding. Building on this observation, we propose TriangleMix, which replaces dense attention with Triangle attention in a subset of layers. Extensive experiments demonstrate that TriangleMix achieves near-lossless performance on both long-context and long-context reasoning benchmarks, while significantly improving efficiency. For 128K inputs, Triangle attention in the subset of layers achieves a 15.3 × speedup in attention kernel computation, significantly exceeding the acceleration of typical dynamic sparse methods ( 1.9 × to 3.4 × ). Furthermore, TriangleMix can be seamlessly combined with dynamic sparsity approaches, delivering an additional 6%–19% reduction in TTFT over using dynamic sparsity alone.

Large language models (LLMs) enable long-context tasks but face efficiency challenges due to the growing key-value (KV) cache. We propose LeanK, a learning-based method that prunes unimportant key (K) cache channels by leveraging static channel sparsity. LeanK reduces GPU memory and accelerates decoding without sacrificing accuracy. Experiments demonstrate up to 70% K cache and 16%–18% V cache memory reduction, and 1.45× decoding speedup. We also provide insights into model channels and attention heads during long-context inference by analyzing the learned importance distribution. Our code is anonymously available at https://anonymous.4open.science/r/LeanK-7A87/README.md.