Long-context LLMs are constrained by the linear growth of key–value (KV) caches during autoregressive decoding, which incurs pronounced latency and memory overhead. KV eviction mitigates this issue, with existing efforts fall into offline policies with fixed eviction patterns and online policies that adaptively discard cache based on attention scores. While online eviction typically preserves accuracy under standard benchmarks, its performance can collapse in practical multi-turn dialogue scenarios where the query positions vary, and integration with pre-fill acceleration remains challenging. In contrast, offline eviction is infrastructure-friendly and generalizable but commonly sacrifices more accuracy. In this paper, we explore Supervised Fine-Tuning (SFT) for offline KV eviction and demonstrate its efficacy as a simple and powerful alternative to the design of complex online eviction metrics. We further propose Hybrid Sparse Supervised Fine-Tuning (HS-SFT) to explore the optimal offline design of KV eviction within SFT. In particular, HS-SFT employs a straight-through estimator to learn discrete local-window allocations of streaming heads across layers with budget-aware balancing loss, such that under high compression ratios—where dense-head capacity is constrained—the budget can be more effectively skewed to capture critical information. Across extensive evaluations on a wide array of LLMs and long-context tasks, HS-SFT delivers substantial performance gains over state-of-the-art eviction baselines. For example, with fewer than 4 hours of SFT of LLaMA-3-8B-1048K using a single 8-GPU node, HS-SFT achieves 5.86% and 38.3% higher average accuracy than Duo-attn on Longbench and Ruler-16K at 10% KV budget, respectively. These results position training-aware offline eviction—achieved with simple SFT—as an effective and practical path to scalable long-context inference.

While long-context large language models (LLMs) exhibit remarkable document processing capabilities, their prohibitively high training costs often hinder customized applications. To mitigate this issue, we propose Sequential Chunk-wise Optimization (SeCO), a memory-efficient training paradigm that partitions lengthy inputs into manageable chunks. Each chunk independently constructs its computational graph and performs localized backpropagation, ensuring that only one chunk’s forward activations are stored in memory. Building on SeCO, we further introduce Sparse Chunk-wise Optimization (SpaCO), which reduces computational overhead by selectively propagating gradients to specific chunks and incorporates a carefully designed compensation factor to ensure unbiased gradient estimation. SpaCO decouples the computational cost of backpropagation from the context length, enabling training time to gradually converge to inference time as sequences become longer. Implemented as lightweight training wrappers, both SeCO and SpaCO offer substantial practical benefits. For example, when fine-tuning an 8B model with LoRA on a single RTX 3090 GPU, SeCO expands maximum sequence length from 1K to 16K tokens, while SpaCO demonstrates accelerated training speed—achieving up to 3× faster than SeCO under the same experimental setup. These innovations provide new insights into optimizing long-context models, making them more accessible for practical applications. We have open-sourced the code at https://anonymous.4open.science/r/seco-CCBD.