A Differential Entropy Estimator for Training Neural Networks

TL;DR

This paper introduces KNIFE, a novel differentiable kernel-based estimator for differential entropy, enabling its use as a regularizer in neural network training across various high-dimensional tasks.

Contribution

The paper presents KNIFE, a fully parameterized, differentiable estimator for differential entropy and mutual information, overcoming previous limitations and broadening their application in neural network training.

Findings

KNIFE effectively estimates differential entropy in high-dimensional data.

Using KNIFE improves neural network training in tasks like domain adaptation and fair classification.

The method is validated on synthetic and real-world datasets, demonstrating versatility and accuracy.

Abstract

Mutual Information (MI) has been widely used as a loss regularizer for training neural networks. This has been particularly effective when learn disentangled or compressed representations of high dimensional data. However, differential entropy (DE), another fundamental measure of information, has not found widespread use in neural network training. Although DE offers a potentially wider range of applications than MI, off-the-shelf DE estimators are either non differentiable, computationally intractable or fail to adapt to changes in the underlying distribution. These drawbacks prevent them from being used as regularizers in neural networks training. To address shortcomings in previously proposed estimators for DE, here we introduce KNIFE, a fully parameterized, differentiable kernel-based estimator of DE. The flexibility of our approach also allows us to construct KNIFE-based estimators for conditional (on either discrete or continuous variables) DE, as well as MI. We empirically validate our method on high-dimensional synthetic data and further apply it to guide the training of neural networks for real-world tasks. Our experiments on a large variety of tasks, including visual domain adaptation, textual fair classification, and textual fine-tuning demonstrate the effectiveness of KNIFE-based estimation. Code can be found at https://github.com/g-pichler/knife.