Long-context inference in Large Language Models (LLMs) is bottlenecked by the linear growth of Key-Value (KV) cache memory. Existing KV cache compression paradigms are fundamentally limited by heuristics: heuristic budgeting relies on statistical priors rather than task objectives, causing resource misallocation, while heuristic selection relies on coupled query-key interactions or static inductive biases (e.g., attention sinks). To address this limitation, we introduce LKV (Learned KV Eviction), which formulates KV compression as an end-to-end differentiable optimization problem. LKV integrates LKV-H to learn task-optimized global budgets, and LKV-T to derive intrinsic KV importance without materializing attention matrices. This design bypasses heuristic proxies, strictly aligning compression with task objectives. Extensive evaluations demonstrate that LKV achieves state-of-the-art performance on both LongBench and RULER benchmarks at high compression rates. In particular, on LongBench, LKV achieves near-lossless performance with only 15% KV cache retention, and delivers up to 3.19x decoding throughput gains with negligible (~0.7%) overhead. Crucially, our analysis identifies learned budgeting as the dominant driver of fidelity, demonstrating that data-driven allocation is essential to overcome the limitations of hand-crafted heuristics.

Intelligent education systems often collect exam sheets as in-the-wild photos. These photos often suffer from distortions and noise caused by handwriting and occlusions, collectively referred to as Real-World Degraded Exam Images (RDEI). Structure-preserving reconstruction is key to converting RDEI into structured assets for downstream educational applications. Existing Multimodal Large Language Models (MLLMs) often fail under RDEI, leading to disrupted structure and evidence-unsupported hallucinations. To tackle these challenges, we propose MessToClean, a backbone-agnostic, evidence-driven pipeline that treats off-the-shelf MLLMs as interchangeable components. By grounding extraction in pixel-aligned evidence and enforcing post-hoc consistency auditing on recovered structures, MessToClean mitigates unsupported hallucinations and enhances both controllability and structural fidelity in question-level reconstruction. We curate RDEI-Exam from our educational platforms and evaluate across 12 state-of-the-art MLLM backbones. Across these, MessToClean improves stem consistency by 1.01-3.18%, figure consistency by 0.50-49.16%, and refusal F1 by 1.06-10.88% across question types.