What Survives KV-Cache Compression for Reasoning? A Dual-Channel View of Structural and Associative Memory

Long reasoning traces make Transformer key–value (KV) caches grow linearly with generation length. Existing compression methods adopt different memory topologies, but it is unclear how those choices affect the information that survives eviction. We observe a task–fidelity mismatch: dense summaries achieve low KV reconstruction error yet lose information required for structured reasoning. We explain this through a dual-channel model of compressed memory consisting of a temporally organized scaffold and sparse associative bindings, suggesting that structure and association should be stored separately. We instantiate this idea as TT–Delta, which combines a Tensor-Train structural state with a Delta-rule associative state. On a frozen Qwen2.5-0.5B task model, TT–Delta compresses an evicted prefix by 25.3× (46,680 persistent scalars) and improves exact-answer generation on sequential linear-system reasoning from 0.302±0.113 to 0.839±0.171. In contrast, multi-head Delta is strongest on associative recall and branching graph search. These results suggest that no single compressed-memory topology is universally optimal; the appropriate topology depends on the structure of the reasoning state.