[2602.23795] GRAIL: Post-hoc Compensation by Linear Reconstruction for Compressed Networks

Computer Science > Machine Learning arXiv:2602.23795 (cs) [Submitted on 27 Feb 2026] Title:GRAIL: Post-hoc Compensation by Linear Reconstruction for Compressed Networks Authors:Wenwu Tang, Dong Wang, Lothar Thiele, Olga Saukh View a PDF of the paper titled GRAIL: Post-hoc Compensation by Linear Reconstruction for Compressed Networks, by Wenwu Tang and 3 other authors View PDF HTML (experimental) Abstract: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 corre...