# GRAIL: Post-hoc Compensation by Linear Reconstruction for Compressed Networks

arXiv: https://arxiv.org/abs/2602.23795 · HTML: https://mlsanity.com/paper/2602.23795/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [REPAIR: REnormalizing Permuted Activations for Interpolation Repair](https://mlsanity.com/paper/2211.08403/) (2022)
- [Fluctuation-based Adaptive Structured Pruning for Large Language Models](https://mlsanity.com/paper/2312.11983/) (2023)
- [A Modern Look at the Relationship between Sharpness and Generalization](https://mlsanity.com/paper/2302.07011/) (2023)
- [SlimGPT: Layer-wise Structured Pruning for Large Language Models](https://mlsanity.com/paper/2412.18110/) (2024)
- [Wanda++: Pruning Large Language Models via Regional Gradients](https://mlsanity.com/paper/2503.04992/) (2025)
- [Numerical Pruning for Efficient Autoregressive Models](https://mlsanity.com/paper/2412.12441/) (2024)
- [Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theory](https://mlsanity.com/paper/2310.06756/) (2023)
- [HRel: Filter Pruning based on High Relevance between Activation Maps and Class Labels](https://mlsanity.com/paper/2202.10716/) (2022)
- [Forget the Data and Fine-Tuning! Just Fold the Network to Compress](https://mlsanity.com/paper/2502.10216/) (2025)
- [Cut Less, Fold More: Model Compression through the Lens of Projection Geometry](https://mlsanity.com/paper/2602.18116/) (2026)
- [Restoring Pruned Large Language Models via Lost Component Compensation](https://mlsanity.com/paper/2510.21834/) (2025)

## Built on by (most cited first, 1 of 1)

- [Retraining-Free Depth Pruning of Vision Transformers: A Cross Domain Study of Layer Redundancy](https://mlsanity.com/paper/2610.15005/) (2026)

## Abstract (arXiv)

Structured deep model compression methods are hardware-friendly and substantially reduce memory and inference costs. However, under aggressive compression, the resulting accuracy degradation often necessitates post-compression finetuning, which can be impractical due to missing labeled data or high training cost. We propose post-hoc blockwise compensation, called GRAIL, a simple zero-finetuning step applied after model compression that restores each block's input-output behavior using a small calibration set. The method summarizes hidden activations via a Gram matrix and applies ridge regression to linearly reconstruct the original hidden representation from the reduced one. The resulting reconstruction map is absorbed into the downstream projection weights, while the upstream layer is compressed. The approach is selector-agnostic (Magnitude, Wanda, Gram-based selection, or folding), data-aware (requiring only a few forward passes without gradients or labels), and recovers classic pruning or folding when the Gram matrix is near identity, indicating weak inter-channel correlations. Across ResNets, ViTs, and decoder-only LLMs, GRAIL consistently improves accuracy or perplexity over data-free and data-aware pruning or folding baselines in practical compression regimes, with manageable overhead and no backpropagation. The code is available at https://github.com/TWWinde/GRAIL_Compensation.