Hidden Monotonicity: Explaining Deep Neural Networks via their DC Decomposition
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Abstract (arXiv)
It has been demonstrated in various contexts that monotonicity leads to better explainability in neural networks. However, not every function can be well approximated by a monotone neural network. We demonstrate that monotonicity can still be used in two ways to boost explainability. First, we use an adaptation of the decomposition of a trained ReLU network into two monotone and convex parts, thereby overcoming numerical obstacles from an inherent blowup of the weights in this procedure. Our proposed saliency methods - SplitCAM and SplitLRP - improve on state of the art results on both VGG16 and Resnet18 networks on ImageNet-S across all Quantus saliency metric categories. Second, we exhibit that training a model as the difference between two monotone neural networks results in a system with strong self-explainability properties.
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References · 44
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
- 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,690
- 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
- 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,040
- 2017Axiomatic Attribution for Deep Networkscited by 3,350
- 2015Learning Deep Features for Discriminative Localizationcited by 2,430
- 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,348
- 2013Visualizing and Understanding Convolutional Networkscited by 2,278
- 2017Learning Important Features Through Propagating Activation Differencescited by 1,454
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- 2018Sanity Checks for Saliency Mapscited by 1,149
- 2017SmoothGrad: removing noise by adding noisecited by 1,097
- 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
- 2014Striving for Simplicity: The All Convolutional Netcited by 983
- 2017Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networkscited by 936
- 2017Interpretable Explanations of Black Boxes by Meaningful Perturbationcited by 611
- 2020Captum: A unified and generic model interpretability library for PyTorchcited by 542
- 2016Input Convex Neural Networkscited by 407
- 2017Methods for Interpreting and Understanding Deep Neural Networkscited by 342
- 2016Top-down Neural Attention by Excitation Backpropcited by 318
- 2019On the (In)fidelity and Sensitivity for Explanationscited by 309
- 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 253
- 2015Explaining NonLinear Classification Decisions with Deep Taylor Decompositioncited by 248
- 2021Towards Robust Vision Transformercited by 137
- 2018Tropical Geometry of Deep Neural Networkscited by 92
- 2019Towards Best Practice in Explaining Neural Network Decisions with LRPcited by 70
- 2020Certified Monotonic Neural Networkscited by 51
- 2022Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysiscited by 38
- 2023Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopescited by 36
- 2020Counterexample-Guided Learning of Monotonic Neural Networkscited by 34
- 2018Towards Explaining Anomalies: A Deep Taylor Decomposition of One-Class Modelscited by 24
- 2024The Real Tropical Geometry of Neural Networkscited by 23
- 2022Shortcomings of Top-Down Randomization-Based Sanity Checks for Evaluations of Deep Neural Network Explanationscited by 22
- 2020Deontological Ethics By Monotonicity Shape Constraintscited by 16
- 2020The Curious Case of Convex Neural Networkscited by 16
- 2020Piecewise Linear Regression via a Difference of Convex Functionscited by 14
- 2020The Clever Hans Effect in Anomaly Detectioncited by 13
- 2018Deep Learning of Nonnegativity-Constrained Autoencoders for Enhanced Understanding of Datacited by 9
- 2022Explaining Image Classifiers with Multiscale Directional Image Representationcited by 7
- 2023Representing Piecewise Linear Functions by Functions with Small Aritycited by 7
- 2021CDiNN -Convex Difference Neural Networkscited by 6
- 2021Novel convex decomposition of piecewise affine functionscited by 4
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