# Counterfactual Explanations on Robust Perceptual Geodesics

arXiv: https://arxiv.org/abs/2601.18678 · HTML: https://mlsanity.com/paper/2601.18678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 77 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Generating Natural Adversarial Examples](https://mlsanity.com/paper/1710.11342/) (2017)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [An open access repository of images on plant health to enable the development of mobile disease diagnostics](https://mlsanity.com/paper/1511.08060/) (2015)
- [Constructing Unrestricted Adversarial Examples with Generative Models](https://mlsanity.com/paper/1805.07894/) (2018)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [Explaining in Style: Training a GAN to explain a classifier in StyleSpace](https://mlsanity.com/paper/2104.13369/) (2021)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [On the Connection Between Adversarial Robustness and Saliency Map Interpretability](https://mlsanity.com/paper/1905.04172/) (2019)

## Built on by (most cited first, 2 of 2)

- [Auditing Sybil: Explaining Deep Lung Cancer Risk Prediction Through Generative Interventional Attributions](https://mlsanity.com/paper/2602.02560/) (2026)
- [FCA-Guided Counterfactual Explanations for Multi-Modal Breast Cancer Diagnosis: A Framework Achieving Perfect Validity with Emergent Sparsity](https://mlsanity.com/paper/2609.20067/) (2026)

## Abstract (arXiv)

Latent-space optimization methods for counterfactual explanations - framed as minimal semantic perturbations that change model predictions - inherit the ambiguity of Wachter et al.'s objective: the choice of distance metric dictates whether perturbations are meaningful or adversarial. Existing approaches adopt flat or misaligned geometries, leading to off-manifold artifacts, semantic drift, or adversarial collapse. We introduce Perceptual Counterfactual Geodesics (PCG), a method that constructs counterfactuals by tracing geodesics under a perceptually Riemannian metric induced from robust vision features. This geometry aligns with human perception and penalizes brittle directions, enabling smooth, on-manifold, semantically valid transitions. Experiments on three vision datasets show that PCG outperforms baselines and reveals failure modes hidden under standard metrics.