# Towards Global Neural Network Abstractions with Locally-Exact Reconstruction

arXiv: https://arxiv.org/abs/2210.12054 · HTML: https://mlsanity.com/paper/2210.12054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 60 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Knowledge Distillation and Student-Teacher Learning for Visual Intelligence: A Review and New Outlooks](https://mlsanity.com/paper/2004.05937/) (2020)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Stochastic Activation Pruning for Robust Adversarial Defense](https://mlsanity.com/paper/1803.01442/) (2018)
- [A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks](https://mlsanity.com/paper/1902.08722/) (2019)
- [MLPerf Tiny Benchmark](https://mlsanity.com/paper/2106.07597/) (2021)
- [Adversarial Robustness vs Model Compression, or Both?](https://mlsanity.com/paper/1903.12561/) (2019)
- [Defensive Quantization: When Efficiency Meets Robustness](https://mlsanity.com/paper/1904.08444/) (2019)
- [Representation Benefits of Deep Feedforward Networks](https://mlsanity.com/paper/1509.08101/) (2015)
- [ResNet with one-neuron hidden layers is a Universal Approximator](https://mlsanity.com/paper/1806.10909/) (2018)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [An Abstraction-Based Framework for Neural Network Verification](https://mlsanity.com/paper/1910.14574/) (2019)
- [Neural Network with Unbounded Activation Functions is Universal Approximator](https://mlsanity.com/paper/1505.03654/) (2015)
- [Privacy-Preserving Machine Learning with Fully Homomorphic Encryption for Deep Neural Network](https://mlsanity.com/paper/2106.07229/) (2021)
- [Mad Max: Affine Spline Insights into Deep Learning](https://mlsanity.com/paper/1805.06576/) (2018)
- [POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems](https://mlsanity.com/paper/2106.13867/) (2021)
- [Lossless Compression of Deep Neural Networks](https://mlsanity.com/paper/2001.00218/) (2020)
- [Abstraction based Output Range Analysis for Neural Networks](https://mlsanity.com/paper/2007.09527/) (2020)
- [ReachNN: Reachability Analysis of Neural-Network Controlled Systems](https://mlsanity.com/paper/1906.10654/) (2019)
- [On the Effect of Pruning on Adversarial Robustness](https://mlsanity.com/paper/2108.04890/) (2021)
- [Scaling Up Exact Neural Network Compression by ReLU Stability](https://mlsanity.com/paper/2102.07804/) (2021)
- [Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis](https://mlsanity.com/paper/1901.01780/) (2019)

## Abstract (arXiv)

Neural networks are a powerful class of non-linear functions. However, their black-box nature makes it difficult to explain their behaviour and certify their safety. Abstraction techniques address this challenge by transforming the neural network into a simpler, over-approximated function. Unfortunately, existing abstraction techniques are slack, which limits their applicability to small local regions of the input domain. In this paper, we propose Global Interval Neural Network Abstractions with Center-Exact Reconstruction (GINNACER). Our novel abstraction technique produces sound over-approximation bounds over the whole input domain while guaranteeing exact reconstructions for any given local input. Our experiments show that GINNACER is several orders of magnitude tighter than state-of-the-art global abstraction techniques, while being competitive with local ones.