# Set Cross Entropy: Likelihood-based Permutation Invariant Loss Function for Probability Distributions

arXiv: https://arxiv.org/abs/1812.01217 · HTML: https://mlsanity.com/paper/1812.01217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

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

- [Multimodal Alignment and Fusion: A Survey](https://mlsanity.com/paper/2411.17040/) (2024)
- [Diffusion Is Your Friend in Show, Suggest and Tell](https://mlsanity.com/paper/2512.10038/) (2025)

## Abstract (arXiv)

We propose a permutation-invariant loss function designed for the neural networks reconstructing a set of elements without considering the order within its vector representation. Unlike popular approaches for encoding and decoding a set, our work does not rely on a carefully engineered network topology nor by any additional sequential algorithm. The proposed method, Set Cross Entropy, has a natural information-theoretic interpretation and is related to the metrics defined for sets. We evaluate the proposed approach in two object reconstruction tasks and a rule learning task.