# FAIRFORMER: A transformer architecture for discrete fair division

arXiv: https://arxiv.org/abs/2601.22346 · HTML: https://mlsanity.com/paper/2601.22346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2026.

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

- [EF1-Constrained Nash Social Welfare with Identical Additive Valuations: Complexity, Guarantees, and Experiments](https://mlsanity.com/paper/2609.03846/) (2026)

## Abstract (arXiv)

We propose a deep neural network-based solution to the problem of allocating indivisible goods under additive subjective valuations without monetary transfers, trading off economic efficiency with envy-based fairness. We introduce FairFormer, an amortized, permutation-equivariant two-tower transformer that encodes items and agents as unordered token sets, applies self-attention within each set, and uses item-to-agent cross-attention to produce per-item assignment distributions in a single forward pass. FairFormer is trained end-to-end to maximize expected log-Nash welfare on sampled instances, requiring no solver supervision, unrolled allocation procedures, or fairness labels. At test time, we discretize by row-wise argmax and apply a lightweight post-processing routine that transfers items to eliminate violations of envy-freeness up to one item while prioritizing improvements in Nash welfare. Our approach generalizes beyond its training regime and achieves near-optimal welfare (e.g., for uniformly sampled valuations, 96--97% for Nash welfare; 95--96% for utilitarian welfare), outperforming strong baselines in solution quality and/or runtime.