# The Responsibility Problem in Neural Networks with Unordered Targets

arXiv: https://arxiv.org/abs/2304.09499 · HTML: https://mlsanity.com/paper/2304.09499/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 6 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [FSPool: Learning Set Representations with Featurewise Sort Pooling](https://mlsanity.com/paper/1906.02795/) (2019)
- [Deep Perm-Set Net: Learn to predict sets with unknown permutation and cardinality using deep neural networks](https://mlsanity.com/paper/1805.00613/) (2018)
- [Learning Sub-Patterns in Piecewise Continuous Functions](https://mlsanity.com/paper/2010.15571/) (2020)

## Built on by (most cited first, 4 of 4)

- [Object-centric architectures enable efficient causal representation learning](https://mlsanity.com/paper/2310.19054/) (2023)
- [Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching](https://mlsanity.com/paper/2506.07199/) (2025)
- [Mechanistic Independence: A Principle for Identifiable Disentangled Representations](https://mlsanity.com/paper/2509.22196/) (2025)
- [Improving Inference-Time Optimisation for Vocal Effects Style Transfer with a Gaussian Prior](https://mlsanity.com/paper/2505.11315/) (2025)

## Abstract (arXiv)

We discuss the discontinuities that arise when mapping unordered objects to neural network outputs of fixed permutation, referred to as the responsibility problem. Prior work has proved the existence of the issue by identifying a single discontinuity. Here, we show that discontinuities under such models are uncountably infinite, motivating further research into neural networks for unordered data.