# Multilinear Latent Conditioning for Generating Unseen Attribute Combinations

arXiv: https://arxiv.org/abs/2009.04075 · HTML: https://mlsanity.com/paper/2009.04075/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2020.

## Built on by (most cited first, 14 of 14)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Multilinear Mixture of Experts: Scalable Expert Specialization through Factorization](https://mlsanity.com/paper/2402.12550/) (2024)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)
- [Augmenting Deep Classifiers with Polynomial Neural Networks](https://mlsanity.com/paper/2104.07916/) (2021)
- [Tensor Component Analysis for Interpreting the Latent Space of GANs](https://mlsanity.com/paper/2111.11736/) (2021)
- [CoPE: Conditional image generation using Polynomial Expansions](https://mlsanity.com/paper/2104.05077/) (2021)
- [Multilinear Operator Networks](https://mlsanity.com/paper/2401.17992/) (2024)
- [Hadamard product in deep learning: Introduction, Advances and Challenges](https://mlsanity.com/paper/2504.13112/) (2025)
- [Going beyond Compositions, DDPMs Can Produce Zero-Shot Interpolations](https://mlsanity.com/paper/2405.19201/) (2024)
- [Large-Scale Attribute-Object Compositions](https://mlsanity.com/paper/2105.11373/) (2021)
- [Cluster-guided Image Synthesis with Unconditional Models](https://mlsanity.com/paper/2112.12911/) (2021)
- [MI-NeRF: Learning a Single Face NeRF from Multiple Identities](https://mlsanity.com/paper/2403.19920/) (2024)
- [MIGS: Multi-Identity Gaussian Splatting via Tensor Decomposition](https://mlsanity.com/paper/2407.07284/) (2024)
- [DualVAE: Controlling Colours of Generated and Real Images](https://mlsanity.com/paper/2305.18769/) (2023)

## Abstract (arXiv)

Deep generative models rely on their inductive bias to facilitate generalization, especially for problems with high dimensional data, like images. However, empirical studies have shown that variational autoencoders (VAE) and generative adversarial networks (GAN) lack the generalization ability that occurs naturally in human perception. For example, humans can visualize a woman smiling after only seeing a smiling man. On the contrary, the standard conditional VAE (cVAE) is unable to generate unseen attribute combinations. To this end, we extend cVAE by introducing a multilinear latent conditioning framework that captures the multiplicative interactions between the attributes. We implement two variants of our model and demonstrate their efficacy on MNIST, Fashion-MNIST and CelebA. Altogether, we design a novel conditioning framework that can be used with any architecture to synthesize unseen attribute combinations.