# Post-Hoc Concept Disentanglement: From Correlated to Isolated Concept Representations

arXiv: https://arxiv.org/abs/2503.05522 · HTML: https://mlsanity.com/paper/2503.05522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 30 of 36)

- [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)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Learning to Generate Reviews and Discovering Sentiment](https://mlsanity.com/paper/1704.01444/) (2017)
- [From Attribution Maps to Human-Understandable Explanations through Concept Relevance Propagation](https://mlsanity.com/paper/2206.03208/) (2022)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Multi-Level Variational Autoencoder: Learning Disentangled Representations from Grouped Observations](https://mlsanity.com/paper/1705.08841/) (2017)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [FineGAN: Unsupervised Hierarchical Disentanglement for Fine-Grained Object Generation and Discovery](https://mlsanity.com/paper/1811.11155/) (2018)
- [Software for Dataset-wide XAI: From Local Explanations to Global Insights with Zennit, CoRelAy, and ViRelAy](https://mlsanity.com/paper/2106.13200/) (2021)
- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [FunnyBirds: A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods](https://mlsanity.com/paper/2308.06248/) (2023)
- [Probing Classifiers are Unreliable for Concept Removal and Detection](https://mlsanity.com/paper/2207.04153/) (2022)

## Built on by (most cited first, 1 of 1)

- [ICON decomposition: Multivariate concept auditing reveals shortcuts that neural networks rely on](https://mlsanity.com/paper/2608.26083/) (2026)

## Abstract (arXiv)

Concept Activation Vectors (CAVs) are widely used to model human-understandable concepts as directions within the latent space of neural networks. They are trained by identifying directions from the activations of concept samples to those of non-concept samples. However, this method often produces similar, non-orthogonal directions for correlated concepts, such as "beard" and "necktie" within the CelebA dataset, which frequently co-occur in images of men. This entanglement complicates the interpretation of concepts in isolation and can lead to undesired effects in CAV applications, such as activation steering. To address this issue, we introduce a post-hoc concept disentanglement method that employs a non-orthogonality loss, facilitating the identification of orthogonal concept directions while preserving directional correctness. We evaluate our approach with real-world and controlled correlated concepts in CelebA and a synthetic FunnyBirds dataset with VGG16 and ResNet18 architectures. We further demonstrate the superiority of orthogonalized concept representations in activation steering tasks, allowing (1) the insertion of isolated concepts into input images through generative models and (2) the removal of concepts for effective shortcut suppression with reduced impact on correlated concepts in comparison to baseline CAVs.