As LLMs process increasingly long contexts, the KV cache has become a major source of memory and bandwidth overhead during inference. Existing methods compress the KV cache by preserving attention sinks, recent tokens, or layer-local important tokens, but they rarely exploit how token importance is shared and specialized across layers. In this paper, we introduce ConsistKV, an adaptive KV cache compression method that exploits consensus in token importance across layers. For each layer, ConsistKV aggregates importance scores from neighboring layers to identify shared contextual anchors, while using residual local importance to preserve tokens that are salient to the current layer. It further estimates the cache demand of each layer from disagreement between layers and importance dispersion, enabling adaptive budget allocation under a fixed global cache budget. Experiments on LongBench show that ConsistKV achieves the highest average performance among evaluated KV cache compression baselines under the same cache budget.

Through systematic experiments on long-context generation, we observe a damaging failure mode in which decoding can collapse into persistent repetition loops. We find that this degeneration is driven by collapsed attention patterns, where a subset of heads locks onto a narrow suffix of the history, and is further stabilized by inference-time KV cache reuse. Crucially, since many existing KV cache policies rely on attention-based importance, this collapse can produce spuriously high scores for repetitive tokens, causing cache management to inadvertently amplify repetition. To study this phenomenon in a controlled and reproducible manner, we introduce LoopBench, a benchmark with explicit loop-inducing conditions and loop-oriented metrics that quantify repetition severity and generation instability beyond downstream task scores. Building on these insights, we propose LoopGuard, a lightweight, plug-in KV cache guard that detects loop onset online and disrupts the feedback cycle by pruning repetitive tail spans under a fixed cache budget. Experiments on LoopBench show that LoopGuard reduces loop incidence by over 90 percentage points, while restoring output diversity and reducing token waste.

SQL query rewriting reformulates queries into more efficient forms while preserving equivalence. Most existing methods rely on predefined rules that struggle to generalize beyond fixed query patterns and cannot express complex rewriting strategies. Large language models (LLMs) can reason over complex structures and generalize to diverse patterns, but their limited execution awareness and semantic grounding often result in non-equivalent or inefficient rewrites. To this end, we propose E3-Rewrite, an LLM-based framework that generates executable, equivalent, and efficient SQL rewrites. It features two key designs: (1) an execution-aware context construction that integrates query plans and retrieved examples to expose structural bottlenecks; and (2) a reinforcement learning optimization with executability, equivalence, and efficiency rewards, trained under a correctness-to-efficiency curriculum for stable convergence. Experiments on multiple benchmarks show that E3-Rewrite-Rewrite reduces execution time by up to 25.6% over leading baselines and delivers 7.3% more equivalent rewrites, extending SQL rewriting to query patterns previously beyond rule-based methods.