Academic

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

arXiv:2602.23795v1 Announce Type: new 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 withou

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Wenwu Tang, Dong Wang, Lothar Thiele, Olga Saukh · · 1 min read · 12 views
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arXiv:2602.23795v1 Announce Type: new 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 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.

Executive Summary

This article proposes GRAIL, a post-hoc compensation method for compressed neural networks that restores each block's input-output behavior using a small calibration set. GRAIL applies ridge regression to linearly reconstruct the original hidden representation from the reduced one and absorbs the resulting reconstruction map into the downstream projection weights. This approach is selector-agnostic, data-aware, and recovers classic pruning or folding when the Gram matrix is near identity. 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 on GitHub, providing a valuable resource for researchers and practitioners.

Key Points

  • ▸ GRAIL is a post-hoc compensation method for compressed neural networks
  • ▸ GRAIL applies ridge regression to linearly reconstruct the original hidden representation
  • ▸ GRAIL is selector-agnostic, data-aware, and recovers classic pruning or folding
  • ▸ GRAIL consistently improves accuracy or perplexity over baselines in practical compression regimes

Merits

Effective Post-hoc Compensation

GRAIL provides a simple and efficient way to compensate for accuracy degradation caused by aggressive compression, making it a valuable tool for researchers and practitioners.

Flexibility and Scalability

GRAIL is selector-agnostic and can be applied to various compression methods, making it a flexible and scalable solution for different neural network architectures.

Manageable Overhead

GRAIL has manageable overhead and does not require backpropagation, making it a practical solution for large-scale neural network compression.

Demerits

Limited Evaluation

The article primarily evaluates GRAIL on a limited set of neural network architectures, and its effectiveness on more complex or larger networks remains to be seen.

Dependence on Calibration Set

GRAIL's performance relies on the accuracy of the calibration set, which may not always be available or reliable, especially for large-scale neural networks.

Expert Commentary

GRAIL is a valuable contribution to the field of neural network compression, offering a simple and efficient way to compensate for accuracy degradation. Its flexibility, scalability, and manageable overhead make it a practical solution for various neural network architectures. However, the article's limited evaluation and dependence on calibration set are limitations that require further investigation. Nonetheless, GRAIL has the potential to significantly impact the development of more efficient and effective deep learning models in various industries.

Recommendations

  • ✓ Further evaluation of GRAIL on more complex or larger neural networks to assess its scalability and effectiveness.
  • ✓ Investigation of methods to improve the accuracy of the calibration set and reduce its dependence on labeled data.

Sources

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