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Long-chain reasoning is one of the most compute-intensive tasks in modern large language models. When a model like DeepSeek-R1 or Qwen3 works through a complex math problem, it can generate tens of thousands of tokens before arriving at an answer. Every one of those tokens must be stored in what is called the KV cache — a memory structure that holds the Key and Value vectors the model needs to attend back to during generation. The longer the reasoning chain, the larger the KV cache grows, and for many deployment scenarios, especially on consumer hardware, this growth eventually exhausts GPU memory entirely.