# The Functional Structure of Post-Compression Recovery in Low-Rank LLMs

arXiv: https://arxiv.org/abs/2610.05504 · HTML: https://mlsanity.com/paper/2610.05504/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 28 of 28)

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- [AA-SVD : Anchored and Adaptive SVD for Large Language Model Compression](https://mlsanity.com/paper/2604.02119/) (2026)
- [Restoring Pruned Large Language Models via Lost Component Compensation](https://mlsanity.com/paper/2510.21834/) (2025)
- [Low-Rank Prehab: Preparing Neural Networks for SVD Compression](https://mlsanity.com/paper/2512.01980/) (2025)
- [TraceNAS: Zero-shot LLM Pruning via Gradient Trace Correlation](https://mlsanity.com/paper/2602.02891/) (2026)
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## Abstract (arXiv)

Different low-rank compression methods can produce compressed LLMs that respond differently to the same post-compression recovery procedure, and relative advantages observed between methods at the compression endpoint may shrink, grow, or even reverse after recovery. We ask whether this recovery heterogeneity reflects functional structure beyond scalar loss evolution, and how that structure evolves throughout recovery. Our results establish that this heterogeneity reflects a reproducible compression-induced functional structure, which we formalize as recovery pressure. To characterize this structure consistently throughout recovery, we develop a standardized functional characterization within each backbone that is applicable across heterogeneous low-rank methods. The primary backward characterization reveals reproducible module-wise structure across independent probes, while a complementary forward-only characterization recovers related structure without loss or backpropagation. We further find that recovery pressure measured at the endpoint is associated with subsequent recovery response; during recovery, its module-wise structure is reorganized non-uniformly, and localized updates induce distributed responses beyond directly updated modules. Further evidence indicates that tracking this evolving structure provides a complementary functional view of recovery progress alongside scalar loss.