Learning with Algorithmic Supervision via Continuous Relaxations

TL;DR

This paper introduces a general method for integrating algorithms into neural networks by relaxing discrete conditions, enabling end-to-end training across various tasks with meaningful gradients.

Contribution

It proposes a unified approach to relax discrete algorithmic conditions, allowing differentiable integration into neural architectures for multiple applications.

Findings

The method performs comparably to task-specific relaxations.

It effectively relaxes control structures like conditionals and loops.

The approach is applicable to diverse challenging tasks.

Abstract

The integration of algorithmic components into neural architectures has gained increased attention recently, as it allows training neural networks with new forms of supervision such as ordering constraints or silhouettes instead of using ground truth labels. Many approaches in the field focus on the continuous relaxation of a specific task and show promising results in this context. But the focus on single tasks also limits the applicability of the proposed concepts to a narrow range of applications. In this work, we build on those ideas to propose an approach that allows to integrate algorithms into end-to-end trainable neural network architectures based on a general approximation of discrete conditions. To this end, we relax these conditions in control structures such as conditional statements, loops, and indexing, so that resulting algorithms are smoothly differentiable. To obtain meaningful gradients, each relevant variable is perturbed via logistic distributions and the expectation value under this perturbation is approximated. We evaluate the proposed continuous relaxation model on four challenging tasks and show that it can keep up with relaxations specifically designed for each individual task.