# Counterexamples to Local Reconstruction Gain as a Proxy for Final Fidelity in Residual Completion

arXiv: https://arxiv.org/abs/2609.34063 · HTML: https://mlsanity.com/paper/2609.34063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 22 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [A Discourse-Aware Attention Model for Abstractive Summarization of Long Documents](https://mlsanity.com/paper/1804.05685/) (2018)
- [InfiniGen: Efficient Generative Inference of Large Language Models with Dynamic KV Cache Management](https://mlsanity.com/paper/2406.19707/) (2024)
- [BIGPATENT: A Large-Scale Dataset for Abstractive and Coherent Summarization](https://mlsanity.com/paper/1906.03741/) (2019)
- [SparQ Attention: Bandwidth-Efficient LLM Inference](https://mlsanity.com/paper/2312.04985/) (2023)
- [MagicPIG: LSH Sampling for Efficient LLM Generation](https://mlsanity.com/paper/2410.16179/) (2024)
- [Get More with LESS: Synthesizing Recurrence with KV Cache Compression for Efficient LLM Inference](https://mlsanity.com/paper/2402.09398/) (2024)
- [Multi-LexSum: Real-World Summaries of Civil Rights Lawsuits at Multiple Granularities](https://mlsanity.com/paper/2206.10883/) (2022)
- [PISA: Piecewise Sparse Attention Is Wiser for Efficient Diffusion Transformers](https://mlsanity.com/paper/2602.01077/) (2026)
- [ReST-KV: Robust KV Cache Eviction with Layer-wise Output Reconstruction and Spatial-Temporal Smoothing](https://mlsanity.com/paper/2605.08840/) (2026)
- [Delta Attention: Fast and Accurate Sparse Attention Inference by Delta Correction](https://mlsanity.com/paper/2505.11254/) (2025)
- [ResKV: Reconstructing Omitted Attention Contributions for Fixed-Budget KV Cache Compression](https://mlsanity.com/paper/2607.29591/) (2026)
- [Residual-Mass Accounting for Partial-KV Decoding](https://mlsanity.com/paper/2604.05438/) (2026)
- [Understanding Sparse Attention Selectivity in Long-Context Foundation Models via Counterfactual Evaluation](https://mlsanity.com/paper/2608.01676/) (2026)
- [RippleKV: Cross-Layer KV Cache Allocation via Perturbation Propagation](https://mlsanity.com/paper/2608.08684/) (2026)
- [KVDiagnosis: A Diagnostic Benchmark for KV-Cache Compression in Long-Context Language Models](https://mlsanity.com/paper/2608.09412/) (2026)

## Abstract (arXiv)

Residual completion augments query-aware sparse attention by estimating the contribution of tokens omitted from the exact sparse computation. We ask whether improving a layer's attention-output reconstruction on the same incoming Q/K/V and selected support necessarily improves the fidelity of the final model output. We study training-free RESA and learned Top-K+φ with frozen backbone language models. A prespecified single-layer screen yields two Qwen3-0.6B/Multi-LexSum interventions for which direct-runtime measurements show positive prespecified request-aggregate local reconstruction gain but worse final KL fidelity than the corresponding all-abstain Exact Top-K baseline on both discovery and prompt-token-disjoint holdout requests. Exact restoration at the same layer instead improves final fidelity, showing that the reversal is specific to approximate completion in these cases. In complementary multi-layer experiments, a task-independent local diagnostic often repairs the tested completion estimators, although the repaired models do not consistently outperform Exact Top-K. Together, these results show that better local reconstruction need not translate into better final-model fidelity.