Large Language Models (LLMs) exhibit enhanced capabilities by Chain-of-Thought reasoning. However, the extended reasoning sequences introduce significant GPU memory overhead due to increased key-value (KV) cache. Existing KV cache compression methods mitigate memory bottlenecks but struggle in long reasoning tasks. In this paper, we analyze attention patterns in reasoning tasks and reveal a **Token Importance Recurrence** phenomenon: a large proportion of tokens regain high attention after multiple decoding steps, which is failed to capture by existing works and may lead to unpredictable eviction on such periodically critical tokens. To address this, we propose **LazyEviction**, an observation window-based lagged eviction framework retaining latent recurring tokens by prioritized eviction based on tokens’ recurrence patterns. Extensive experiments demonstrate that LazyEviction reduces KV cache by 50% 70% while maintaining comparable accuracy, outperforming existing KV cache baselines. Our implementation code can be found at https://github.com/Halo-949/LazyEviction.

Recent Large Reasoning Models (LRMs) excel at complex reasoning tasks but often suffer from overthinking, generating overly long and redundant reasoning trajectories. To explore its essence, our empirical analysis reveals that LRMs are primarily limited to recognizing task properties (i.e., difficulty levels) like humans before solving the problem, leading to a one-size-fits-all reasoning strategy. This observation motivates a fundamental question: Can we explicitly bootstrap such ability to alleviate overthinking in LRMs? To this end, we propose Think-How-to-Think (TH2T), a novel two-stage fine-tuning strategy that progressively inspires LRMs’ difficulty cognition and redundancy cognition of LRMs. Specifically, we first inject Difficulty Dypnosis into output prefixes as cues for global, prospective reasoning strategy selection, stimulating the model’s sharper sensitivity to task complexity and adaptive control of reasoning depth. Then, we incorporate Redundancy Hypnosis into in-progress reasoning steps, which serve as local, retrospective signals for behavior correction by identifying and eliminating superfluous reasoning detours. Experiments across 7B/14B/32B models demonstrate that TH2T significantly reduces inference costs by over 70% on easy tasks and 40% on complex ones without compromising performance. The resultant models exhibit a nascent ability for difficulty-aware reasoning, effectively mitigating behaviors like excessive reflection and looping, thereby paving the way for more cognitively efficient LRMs.