# Decomposition of Evidence, Contradiction, and Fragility in Perturbation Responses

arXiv: https://arxiv.org/abs/2608.12935 · HTML: https://mlsanity.com/paper/2608.12935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 46 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 30 of 42)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Noise or Signal: The Role of Image Backgrounds in Object Recognition](https://mlsanity.com/paper/2006.09994/) (2020)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Explaining Image Classifiers by Counterfactual Generation](https://mlsanity.com/paper/1807.08024/) (2018)
- [Explaining Classifiers with Causal Concept Effect (CaCE)](https://mlsanity.com/paper/1907.07165/) (2019)

## Abstract (arXiv)

Perturbation methods explain model decisions by measuring prediction changes under altered inputs, but response magnitude tells us only how much a model reacts, not what that reaction means. The same magnitude can support the final factual-counterfactual difference, oppose it, or arise strongly along the perturbation path yet vanish at the endpoint. We therefore track how the contrast develops as paired inputs are progressively revealed, using the final contrast to interpret the trajectory. We introduce DECAF (Decomposition of Evidence, Contradiction, And Fragility), which routes aligned, opposed, and endpoint-null responses into evidence E, contradiction C, and fragility F. The decomposition preserves ordinary magnitude exactly, Abs = E + C + F, and is unique under endpoint-relative axioms. Across controlled vision and tabular settings, the three components track independently measured behavior. In a 72-model ImageNet-9 audit, we compare cases with nearly identical response magnitude but different independently measured behaviors. The largest DECAF component agrees with an observed behavior in 96.4% of cases, compared with 35.0% for magnitude alone. Changing only the reveal path increases total response by nearly 80%, yet evidence barely changes while fragility grows by more than 4x. On FunnyBirds and ImageNet-1k, short forward-only DECAF trajectories outperform the tested general-purpose attribution baselines. On a 1B-scale DINOv2 model, a short trajectory matches a strong gradient-based baseline with 4.75x lower wall time and 2.36x lower peak memory.