Learning with Algorithmic Supervision via Continuous Relaxations
This work addresses the need for more flexible and broadly applicable algorithmic supervision in machine learning, though it is incremental as it builds on existing relaxation ideas.
The paper tackles the problem of integrating algorithmic components into neural networks for supervision without ground truth labels, proposing a general continuous relaxation method for discrete conditions in control structures, and shows it performs competitively with task-specific relaxations on four challenging tasks.
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.