Provably Bounding Neural Network Preimages
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911799801020416 |
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| author | Kotha, Suhas Brix, Christopher Kolter, Zico Dvijotham, Krishnamurthy Zhang, Huan |
| author_facet | Kotha, Suhas Brix, Christopher Kolter, Zico Dvijotham, Krishnamurthy Zhang, Huan |
| contents | Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs. We present the INVPROP algorithm for verifying properties over the preimage of a linearly constrained output set, which can be combined with branch-and-bound to increase precision. Contrary to other approaches, our efficient algorithm is GPU-accelerated and does not require a linear programming solver. We demonstrate our algorithm for identifying safe control regions for a dynamical system via backward reachability analysis, verifying adversarial robustness, and detecting out-of-distribution inputs to a neural network. Our results show that in certain settings, we find over-approximations over 2500x tighter than prior work while being 2.5x faster. By strengthening robustness verification with output constraints, we consistently verify more properties than the previous state-of-the-art on multiple benchmarks, including a large model with 167k neurons in VNN-COMP 2023. Our algorithm has been incorporated into the $α,\!β$-CROWN verifier, available at https://abcrown.org. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01404 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Provably Bounding Neural Network Preimages Kotha, Suhas Brix, Christopher Kolter, Zico Dvijotham, Krishnamurthy Zhang, Huan Machine Learning Artificial Intelligence Systems and Control Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs. We present the INVPROP algorithm for verifying properties over the preimage of a linearly constrained output set, which can be combined with branch-and-bound to increase precision. Contrary to other approaches, our efficient algorithm is GPU-accelerated and does not require a linear programming solver. We demonstrate our algorithm for identifying safe control regions for a dynamical system via backward reachability analysis, verifying adversarial robustness, and detecting out-of-distribution inputs to a neural network. Our results show that in certain settings, we find over-approximations over 2500x tighter than prior work while being 2.5x faster. By strengthening robustness verification with output constraints, we consistently verify more properties than the previous state-of-the-art on multiple benchmarks, including a large model with 167k neurons in VNN-COMP 2023. Our algorithm has been incorporated into the $α,\!β$-CROWN verifier, available at https://abcrown.org. |
| title | Provably Bounding Neural Network Preimages |
| topic | Machine Learning Artificial Intelligence Systems and Control |
| url | https://arxiv.org/abs/2302.01404 |