In large language models performing long-form reasoning, the KV cache grows rapidly with decode length, creating bottlenecks in memory and inference stability. Existing reasoning-oriented KV compression has mostly followed an eviction-centered view: estimate token importance more accurately, then discard lower-ranked entries. Our analysis suggests that scorer refinement alone often fails to substantially reorganize the actual keep-set and may therefore not be the main lever for preserving reasoning behavior. We instead frame reasoning KV compression as a behavior-preserving structured consolidation problem. CASK partitions the decode-time reasoning trace into a protected core that anchors answer formation and intermediate state, and mergeable scratch with high redundancy. The core is preserved, while selective consolidation is applied only to the scratch. To address prompt-heavy regimes where the prefix can exhaust the budget before decode-stage compression becomes active, CASK further uses a two-stage design: prefix eviction followed by decode-stage consolidation. On the H100 reasoning gate, CASK shows higher full-KV continuation fidelity than TriAttention at matched budgets on both AIME24 and AIME25, with recurring cask@384 > triattention@512 crossings. In prompt-heavy replay, multi_news and vcsum act as decode-active witnesses, while qmsum and gov_report expose the prefix_budget_exhausted boundary. The overall evidence supports a simple conclusion: effective reasoning KV compression depends less on more elaborate scorer engineering than on combining core preservation with selective scratch consolidation to lower the usable budget frontier.
Figures & tables
Figure 1: Method overview. CASK separates prefix-stage eviction from decode-stage selective consolidation, while enforcing protected core preservation inside the decode trace.
Figure 2: H100 reasoning replay gate. CASK improves replay fidelity at matched budgets on both AIME24 and AIME25, and repeatedly crosses higher-budget TriAttention points.
Slice
Method
Budget
Top-1
Top-5
Mean NLL
First Mismatch
Saved Ratio
AIME24 ref6
TriAttention
256
86.1%
98.0%
0.463
8.7
65.3%
AIME24 ref6
CASK
256
88.4%
99.2%
0.359
8.7
65.3%
AIME24 ref6
TriAttention
384
88.2%
98.9%
0.383
8.7
61.6%
AIME24 ref6
CASK
384
90.7%
99.7%
0.268
8.7
61.6%
AIME24 ref6
TriAttention
512
89.4%
99.1%
0.333
8.7
43.6%
AIME24 ref6
CASK
512
91.7%
99.9%
0.233
8.7
43.5%
Table 1: Table 1. H100 reasoning fidelity gate
Figure 3: Prompt-heavy weighted aggregate. Across the package-level replay summary, CASK improves weighted top-1, weighted top-5, and weighted mean NLL at both budgets.
Figure 4: Prompt-heavy witness map. The tasks do not all play the same role: some are decode-active witnesses, some are prefix-dominant crossings, and some are retained boundaries.
Figure 5: Actual-output bridge. Replay-level gains are not purely diagnostic: they connect to lexical, semantic, and task-level output behavior on selected witnesses.
Task
Variant
Budget
Sequence Ratio
Prefix Ratio
Output Ratio
Task Metric
Terminal Saved
Compression Events
qasper
TriAttention
512
17.3%
3.7%
100.0%
11.94
-
-
qasper
CASK
256
23.8%
5.5%
100.0%
12.77
90.9%
1.0
multi_news
TriAttention
384
0.0%
0.0%
100.0%
0.00
-
-
multi_news
CASK
384
16.9%
8.1%
100.0%
15.16
84.1%
3.0
hotpotqa
TriAttention
256
100.0%
100.0%
100.0%
27.27
-
-
hotpotqa
CASK
256
100.0%
100.0%
100.0%
27.27
97.6%
0.0
Table 9
Figure 6: Mass recovery on the hexagon witness. Directly protected core mass is insufficient on its own; representative reconstruction recovers a large share of oracle-relevant mass.
Figure 7: Healthy representative preservation versus boundary collapse. Collapse is structural: when available slots collapse, unrecovered oracle-relevant mass grows sharply.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 8: Prompt-heavy per-task mean NLL view. This appendix-level figure preserves the per-task NLL readout underlying the package-level prompt-heavy interpretation.