The expanding long-context capabilities of large language models are constrained by a significant memory bottleneck: the key-value (KV) cache required for autoregressive generation. This bottleneck is substantial; for instance, a Llama-3.1-8B model processing a 32K-token prompt at a batch size of 4 requires approximately 16 GB for its KV cache, exceeding the model’s weights. While KV-cache compression via low-rank projection is promising, existing methods rely on a static, offline-learned subspace that performs poorly under distribution shifts. To overcome these limitations, we introduce OjaKV, a novel framework integrating a hybrid storage policy with online subspace adaptation. OjaKV preserves crucial tokens in full rank as high-fidelity anchors, while applying low-rank compression to intermediate tokens by adapting the projection basis using Oja’s algorithm for online PCA. This adaptation involves a comprehensive update during prefilling and lightweight periodic updates during decoding, ensuring the subspace remains aligned with evolving context. Our framework is fully compatible with FlashAttention. Experiments demonstrate that OjaKV maintains or improves zero-shot accuracy at high compression ratios, achieving the strongest gains on long-context benchmarks requiring complex reasoning. Furthermore, our approach combines with token-selection methods for compounded memory savings, establishing a practical, plug-and-play solution for memory-efficient long-context inference without fine-tuning.

Large language models (LLMs) have shown great performance on complex reasoning tasks but often require generating long intermediate thoughts before reaching a final answer. During generation, LLMs rely on a key-value (KV) cache for autoregressive decoding. However, the memory footprint of the KV cache grows with output length. Prior work on KV cache optimization mostly focus on compressing the long input context, while retaining the full KV cache for decoding. For tasks requiring long output generation, this leads to increased computational and memory costs. In this paper, we introduce ZoomR, a novel approach that enables LLMs to adaptively compress verbose reasoning thoughts into summaries and uses a dynamic KV cache selection policy that leverages these summaries while also strategically "zooming in" on fine-grained details. By using summary keys as a coarse-grained index during decoding, ZoomR uses the query to retrieve details for only the most important thoughts. This hierarchical strategy significantly reduces memory usage by avoiding full-cache attention at each step. Experiments across math and reasoning tasks show that our approach achieves competitive performance compared to baselines, while reducing inference memory requirements by more than 4 ×. These results demonstrate that a multi-granularity KV selection enables more memory efficient decoding, especially for long output generation.