Language models that reason step by step must remember everything they have written. That memory, called a key-value cache, grows with each new word and becomes a bottleneck, slowing long answers and using lots of memory.
FAD-KV compresses this cache with a dictionary, a fixed set of vector building blocks. Instead of scanning the whole dictionary for every new word, it first picks a shortlist of likely blocks, then refines the choice. It also replaces unused blocks with newly relevant ones, so the dictionary never grows.
On reasoning and long-context benchmarks, FAD-KV keeps quality high while cutting compression overhead and unbounded memory growth. That makes long reasoning cheaper and faster.