# Principled Knowledge Extrapolation with GANs

arXiv: https://arxiv.org/abs/2205.13444 · HTML: https://mlsanity.com/paper/2205.13444/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 21 May 2022.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs](https://mlsanity.com/paper/2005.09635/) (2020)
- [StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation](https://mlsanity.com/paper/2011.12799/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [CounteRGAN: Generating Realistic Counterfactuals with Residual Generative Adversarial Nets](https://mlsanity.com/paper/2009.05199/) (2020)
- [Designing Counterfactual Generators using Deep Model Inversion](https://mlsanity.com/paper/2109.14274/) (2021)
- [The Counterfactual chi-GAN](https://mlsanity.com/paper/2001.03115/) (2020)

## Built on by (most cited first, 6 of 6)

- [HairCLIPv2: Unifying Hair Editing via Proxy Feature Blending](https://mlsanity.com/paper/2310.10651/) (2023)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)
- [Emerging Synergies in Causality and Deep Generative Models: A Survey](https://mlsanity.com/paper/2301.12351/) (2023)
- [Graph Community Augmentation with GMM-based Modeling in Latent Space](https://mlsanity.com/paper/2412.01163/) (2024)
- [Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences](https://mlsanity.com/paper/2603.20025/) (2026)
- [An Information Theoretic Framework for Graph Novelty Generation via Latent Mixture Modeling](https://mlsanity.com/paper/2606.19770/) (2026)

## Abstract (arXiv)

Human can extrapolate well, generalize daily knowledge into unseen scenarios, raise and answer counterfactual questions. To imitate this ability via generative models, previous works have extensively studied explicitly encoding Structural Causal Models (SCMs) into architectures of generator networks. This methodology, however, limits the flexibility of the generator as they must be carefully crafted to follow the causal graph, and demands a ground truth SCM with strong ignorability assumption as prior, which is a nontrivial assumption in many real scenarios. Thus, many current causal GAN methods fail to generate high fidelity counterfactual results as they cannot easily leverage state-of-the-art generative models. In this paper, we propose to study counterfactual synthesis from a new perspective of knowledge extrapolation, where a given knowledge dimension of the data distribution is extrapolated, but the remaining knowledge is kept indistinguishable from the original distribution. We show that an adversarial game with a closed-form discriminator can be used to address the knowledge extrapolation problem, and a novel principal knowledge descent method can efficiently estimate the extrapolated distribution through the adversarial game. Our method enjoys both elegant theoretical guarantees and superior performance in many scenarios.