Set-Based Training for Neural Network Verification

Authors: Lukas Koller, Tobias Ladner, Matthias Althoff

TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Our extensive evaluation demonstrates that set-based training produces robust neural networks with competitive performance, which can be verified using fast (polynomial-time) verification algorithms due to the reduced output set. An extensive empirical evaluation in which we demonstrate the competitive performance of our set-based training and compare it with state-of-the-art robust training approaches. Moreover, we include large-scale ablation studies to justify our design choices.
Researcher Affiliation Academia Lukas Koller EMAIL Technical University of Munich; Tobias Ladner EMAIL Technical University of Munich; Matthias Althoff EMAIL Professorship for Cyber-Physical Systems Technical University of Munich
Pseudocode Yes Algorithm 1: Image Enclosure of a Nonlinear Layer. Algorithm 2: Set-based Training Iteration.
Open Source Code No We use the MATLAB toolbox CORA (Althoff, 2015) to implement set-based training. This statement indicates the use of a third-party toolbox, not the release of the authors' own implementation code for their methodology. No explicit statement of code release or repository link is found.
Open Datasets Yes We train a 6-layer convolutional neural network on Mnist (Le Cun et al., 2010), Svhn (Netzer et al., 2011), Cifar-10 (Krizhevsky, 2009), and Tiny Image Net (Le & Yang, 2015).
Dataset Splits Yes We use the canonical split of training and test data for each dataset and the entire test data for evaluation; because test labels are not available for Tiny Image Net, we follow (Müller et al., 2023) and use the validation set for testing.
Hardware Specification Yes Our experiments were run on a server with 2 AMD EPYC 7763 (64 cores/128 threads), 2TB RAM, and a NVIDIA A100 40GB GPU.
Software Dependencies No The paper mentions using the 'MATLAB toolbox CORA (Althoff, 2015)' and 'Adam optimizer (Kingma & Ba, 2015)' but does not specify version numbers for these or any other software components.
Experiment Setup Yes Table 6: Training hyperparameters. #Epochs Dataset η ϵ τ Batch Size (warm-up / ramp-up) Decay ...; The weights and biases are initialized as in (Shi et al., 2021).; We use Adam optimizer (Kingma & Ba, 2015) with the recommended hyperparameters.; For any PGD during training (...) we used the settings from (Müller et al., 2023): 8 iterations with an initial step size 0.5, which is decayed twice by 0.1 at iterations 4 and 7. All PGD attacks for testing are computed with 40 iterations of step size 0.01.