# SimCert: Probabilistic Certification for Behavioral Similarity in Deep Neural Network Compression

arXiv: https://arxiv.org/abs/2603.14818 · HTML: https://mlsanity.com/paper/2603.14818/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [Quantitative Verification of Neural Networks And its Security Applications](https://mlsanity.com/paper/1906.10395/) (2019)
- [A Statistical Approach to Assessing Neural Network Robustness](https://mlsanity.com/paper/1811.07209/) (2018)
- [Robustness of Neural Networks: A Probabilistic and Practical Approach](https://mlsanity.com/paper/1902.05983/) (2019)
- [ReluDiff: Differential Verification of Deep Neural Networks](https://mlsanity.com/paper/2001.03662/) (2020)
- [SDQ: Stochastic Differentiable Quantization with Mixed Precision](https://mlsanity.com/paper/2206.04459/) (2022)
- [NeuroDiff: Scalable Differential Verification of Neural Networks using Fine-Grained Approximation](https://mlsanity.com/paper/2009.09943/) (2020)
- [The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks](https://mlsanity.com/paper/2301.07068/) (2023)
- [PDP: Parameter-free Differentiable Pruning is All You Need](https://mlsanity.com/paper/2305.11203/) (2023)
- [PROVEN: Certifying Robustness of Neural Networks with a Probabilistic Approach](https://mlsanity.com/paper/1812.08329/) (2018)
- [QEBVerif: Quantization Error Bound Verification of Neural Networks](https://mlsanity.com/paper/2212.02781/) (2022)
- [NestQuant: Post-Training Integer-Nesting Quantization for On-Device DNN](https://mlsanity.com/paper/2506.17870/) (2025)
- [Expediting Neural Network Verification via Network Reduction](https://mlsanity.com/paper/2308.03330/) (2023)

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

- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)

## Abstract (arXiv)

Deploying Deep Neural Networks (DNNs) on resource-constrained embedded systems requires aggressive model compression techniques like quantization and pruning. However, ensuring that the compressed model preserves the behavioral fidelity of the original design is a critical challenge in the safety-critical system design flow. Existing verification methods often lack scalability or fail to handle the architectural heterogeneity introduced by pruning. In this work, we propose SimCert, a probabilistic certification framework for verifying the behavioral similarity of compressed neural networks. Unlike worst-case analysis, SimCert provides quantitative safety guarantees with adjustable confidence levels. Our framework features: (1) A dual-network symbolic propagation method supporting both quantization and pruning; (2) A variance-aware bounding technique using Bernstein's inequality to tighten safety certificates; and (3) An automated verification toolchain. Experimental results on ACAS Xu and computer vision benchmarks demonstrate that SimCert outperforms state-of-the-art baselines.