Bort: Towards Explainable Neural Networks with Bounded Orthogonal Constraint
Not on the map. Why?
Abstract (arXiv)
Deep learning has revolutionized human society, yet the black-box nature of deep neural networks hinders further application to reliability-demanded industries. In the attempt to unpack them, many works observe or impact internal variables to improve the comprehensibility and invertibility of the black-box models. However, existing methods rely on intuitive assumptions and lack mathematical guarantees. To bridge this gap, we introduce Bort, an optimizer for improving model explainability with boundedness and orthogonality constraints on model parameters, derived from the sufficient conditions of model comprehensibility and invertibility. We perform reconstruction and backtracking on the model representations optimized by Bort and observe a clear improvement in model explainability. Based on Bort, we are able to synthesize explainable adversarial samples without additional parameters and training. Surprisingly, we find Bort constantly improves the classification accuracy of various architectures including ResNet and DeiT on MNIST, CIFAR-10, and ImageNet. Code: https://github.com/zbr17/Bort.
Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 46 of its 59 references that are in the map. First posted on arXiv 18 Dec 2022.
Builds on
46 of 59 references.
References · 46
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
- 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,139
- 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,733
- 2017A Unified Approach to Interpreting Model Predictionscited by 6,555
- 2017mixup: Beyond Empirical Risk Minimizationcited by 5,183
- 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,070
- 2020Training data-efficient image transformers & distillation through attentioncited by 4,586
- 2017Axiomatic Attribution for Deep Networkscited by 3,384
- 2019CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Featurescited by 2,884
34 more
- 2015Learning Deep Features for Discriminative Localizationcited by 2,436
- 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,371
- 2013Visualizing and Understanding Convolutional Networkscited by 2,290
- 2019RandAugment: Practical automated data augmentation with a reduced search spacecited by 2,269
- 2017Learning Important Features Through Propagating Activation Differencescited by 1,458
- 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
- 2017SmoothGrad: removing noise by adding noisecited by 1,109
- 2014Striving for Simplicity: The All Convolutional Netcited by 990
- 2017Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networkscited by 939
- 2018RISE: Randomized Input Sampling for Explanation of Black-box Modelscited by 838
- 2018This Looks Like That: Deep Learning for Interpretable Image Recognitioncited by 737
- 2019Large Batch Optimization for Deep Learning: Training BERT in 76 minutescited by 674
- 2017Interpretable Explanations of Black Boxes by Meaningful Perturbationcited by 612
- 2018Explaining Explanations: An Overview of Interpretability of Machine Learningcited by 508
- 2017Methods for Interpreting and Understanding Deep Neural Networkscited by 345
- 2017The Expressive Power of Neural Networks: A View from the Widthcited by 320
- 2020Neural Additive Models: Interpretable Machine Learning with Neural Netscited by 319
- 2017Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictionscited by 234
- 2020Concept Whitening for Interpretable Image Recognitioncited by 225
- 2018Universality of Deep Convolutional Neural Networkscited by 176
- 2017Visualizing Deep Neural Network Decisions: Prediction Difference Analysiscited by 166
- 2017Interpretable Convolutional Neural Networkscited by 162
- 2018Visual Interpretability for Deep Learning: a Surveycited by 155
- 2021Benchmarking and Survey of Explanation Methods for Black Box Modelscited by 136
- 2019XRAI: Better Attributions Through Regionscited by 116
- 2022GlanceNets: Interpretabile, Leak-proof Concept-based Modelscited by 73
- 2021Entropy-based Logic Explanations of Neural Networkscited by 51
- 2020NBDT: Neural-Backed Decision Treescited by 46
- 2017Stochastic Configuration Networks: Fundamentals and Algorithmscited by 34
- 2020Training Interpretable Convolutional Neural Networks by Differentiating Class-specific Filterscited by 26
- 2022Enhance the Visual Representation via Discrete Adversarial Trainingcited by 23
- 2021Self-Interpretable Model with TransformationEquivariant Interpretationcited by 21
- 2021Interpretable Compositional Convolutional Neural Networkscited by 16
- 2022Orthogonal Stochastic Configuration Networks with Adaptive Construction Parameter for Data Analyticscited by 1
Built on by
Citing papers per year: 2023: 1; 2024: 2; 2025: 2.
5 papers.
- 2023Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizercited by 29
- 2024SWEA: Updating Factual Knowledge in Large Language Models via Subject Word Embedding Alteringcited by 7
- 2024Harnessing Orthogonality to Train Low-Rank Neural Networkscited by 4
- 2025Self-Explaining Hypergraph Neural Networks for Diagnosis Predictioncited by 3
- 2025On the Fast Adaptation of Delayed Clients in Decentralized Federated Learning: A Centroid-Aligned Distillation Approachcited by 1
- 2025On the Fast Adaptation of Delayed Clients in Decentralized Federated Learning: A Centroid-Aligned Distillation Approach5 Aug 2025
- 2025Self-Explaining Hypergraph Neural Networks for Diagnosis Prediction15 Feb 2025
- 2024SWEA: Updating Factual Knowledge in Large Language Models via Subject Word Embedding Altering31 Jan 2024
- 2024Harnessing Orthogonality to Train Low-Rank Neural Networks16 Jan 2024
- 2023Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizer15 Oct 2023