# Lossless Compression of Structured Convolutional Models via Lifting

arXiv: https://arxiv.org/abs/2007.06567 · HTML: https://mlsanity.com/paper/2007.06567/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

## Built on by (most cited first, 11 of 11)

- [The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks](https://mlsanity.com/paper/2203.04466/) (2022)
- [Symmetry in Neural Network Parameter Spaces](https://mlsanity.com/paper/2506.13018/) (2025)
- [Scaling Up Exact Neural Network Compression by ReLU Stability](https://mlsanity.com/paper/2102.07804/) (2021)
- [Recall Distortion in Neural Network Pruning and the Undecayed Pruning Algorithm](https://mlsanity.com/paper/2206.02976/) (2022)
- [Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions](https://mlsanity.com/paper/2301.07966/) (2023)
- [Universal approximation and model compression for radial neural networks](https://mlsanity.com/paper/2107.02550/) (2021)
- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)
- [The Minimum Edit Arborescence Problem and Its Use in Compressing Graph Collections [Extended Version]](https://mlsanity.com/paper/2107.14525/) (2021)
- [Towards Global Neural Network Abstractions with Locally-Exact Reconstruction](https://mlsanity.com/paper/2210.12054/) (2022)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [Discovering Symmetries in Neural Network Parameter Spaces](https://mlsanity.com/paper/2609.33527/) (2026)

## Abstract (arXiv)

Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured representations, such as various attributed graphs and relational databases. To address the irregular structure of the data, the models typically extrapolate on the idea of convolution, effectively introducing parameter sharing in their, dynamically unfolded, computation graphs. The computation graphs themselves then reflect the symmetries of the underlying data, similarly to the lifted graphical models. Inspired by lifting, we introduce a simple and efficient technique to detect the symmetries and compress the neural models without loss of any information. We demonstrate through experiments that such compression can lead to significant speedups of structured convolutional models, such as various Graph Neural Networks, across various tasks, such as molecule classification and knowledge-base completion.