# Sequence-to-Set Generative Models

arXiv: https://arxiv.org/abs/2209.08801 · HTML: https://mlsanity.com/paper/2209.08801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 9 of 9)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Orderless Recurrent Models for Multi-label Classification](https://mlsanity.com/paper/1911.09996/) (2019)
- [Conditional Set Generation with Transformers](https://mlsanity.com/paper/2006.16841/) (2020)
- [SHOPPER: A Probabilistic Model of Consumer Choice with Substitutes and Complements](https://mlsanity.com/paper/1711.03560/) (2017)

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

- [Beyond Triplet Plausibility: Relation Set Completion in Knowledge Graphs](https://mlsanity.com/paper/2606.29860/) (2026)

## Abstract (arXiv)

In this paper, we propose a sequence-to-set method that can transform any sequence generative model based on maximum likelihood to a set generative model where we can evaluate the utility/probability of any set. An efficient importance sampling algorithm is devised to tackle the computational challenge of learning our sequence-to-set model. We present GRU2Set, which is an instance of our sequence-to-set method and employs the famous GRU model as the sequence generative model. To further obtain permutation invariant representation of sets, we devise the SetNN model which is also an instance of the sequence-to-set model. A direct application of our models is to learn an order/set distribution from a collection of e-commerce orders, which is an essential step in many important operational decisions such as inventory arrangement for fast delivery. Based on the intuition that small-sized sets are usually easier to learn than large sets, we propose a size-bias trick that can help learn better set distributions with respect to the ℓ1-distance evaluation metric. Two e-commerce order datasets, TMALL and HKTVMALL, are used to conduct extensive experiments to show the effectiveness of our models. The experimental results demonstrate that our models can learn better set/order distributions from order data than the baselines. Moreover, no matter what model we use, applying the size-bias trick can always improve the quality of the set distribution learned from data.