The Responsibility Problem in Neural Networks with Unordered Targets

TL;DR

This paper investigates the responsibility problem in neural networks handling unordered targets, revealing that discontinuities are uncountably infinite, which challenges existing assumptions and motivates further research into unordered data processing.

Contribution

It demonstrates that discontinuities in neural networks with unordered targets are uncountably infinite, extending prior work that identified only a single discontinuity.

Findings

Discontinuities are uncountably infinite in such models.

The responsibility problem is more complex than previously understood.

Results motivate new approaches for neural networks with unordered data.

Abstract

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.