Efficient long-sequence generation is a critical challenge for Large Language Models. While recent sparse decoding methods improve efficiency, they suffer from KV cache misalignment, where approximation errors accumulate and degrade generation quality. In this work, we propose Rectified Sparse Attention (ReSA), a simple yet effective method that combines block-sparse attention with periodic dense rectification. By refreshing the KV cache at fixed intervals using a dense forward pass, ReSA bounds error accumulation and preserves alignment with the pretraining distribution. Experiments across math reasoning, language modeling, and retrieval tasks demonstrate that ReSA achieves near-lossless generation quality with significantly improved efficiency. Notably, ReSA delivers up to 3.77x end-to-end speedup under decoding at 256K sequence length, making it a practical solution for scalable long-context inference.

Routing networks in sparsely activated mixture-of-experts (MoE) dynamically allocate input tokens to top-k experts through differentiable sparse transformations, enabling scalable model capacity while preserving computational efficiency. Traditional MoE networks impose an expert capacity constraint to ensure GPU-friendly computation. However, this leads to token dropping when capacity is saturated and results in low hardware efficiency due to padding in underutilized experts. Removing the capacity constraint, in turn, compromises load balancing and computational efficiency.To address these issues, we propose Maximum Score Routing (MaxScore), a novel MoE routing paradigm that models routing as a minimum-cost maximum-flow problem and integrates a SoftTopk operator. MaxScore resolves the fundamental limitations of iterative rerouting and optimal transport formulations, achieving lower training losses and higher evaluation scores at equivalent FLOPs compared to both constrained and unconstrained baselines.

Empowering LLMs with the ability to precisely understand long contexts is crucial for many downstream applications. However, handling long contexts with conventional transformer architecture requires substantial training and inference resources. Existing context condensing methods cannot accurately understand the full context, as there is a considerable amount of information loss in the condensing process. To address these issues, we present FocusLLM, a framework designed to extend the fixed context length of any decoder-only LLM, allowing the model to focus on relevant information from very long sequences. FocusLLM first divides long text input into chunks based on the model’s original context length. It then employs the dynamic condensing process to distill crucial information from each chunk. Ultimately, through the novel parallel decoding mechanism, FocusLLM can integrate the extracted information into its local context. FocusLLM stands out for great training efficiency and versatility: trained with an 8K input length and with much less training cost than previous methods, FocusLLM exhibits superior performance across downstream tasks and maintains strong language modeling ability when handling extensive long texts, even up to 400K tokens. Our code is available at https://github.com/leezythu/FocusLLM.