Regular Polytope Networks

TL;DR

This paper introduces a novel fixed classifier approach using regular polytopes to generate stationary, maximally separated embeddings in neural networks, leading to improved performance and faster convergence.

Contribution

It extends fixed classifier concepts by leveraging regular polytopes for stationary embeddings, reducing memory, and enhancing neural network training.

Findings

The fixed polytope-based classifier achieves comparable accuracy to trainable classifiers.

The approach results in faster convergence during training.

Experimental results demonstrate improved generalization and performance.

Abstract

Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for classification. This transformation plays an important role in determining how the generated features change during the learning process. In this work, we argue that this transformation not only can be fixed (i.e. set as non-trainable) with no loss of accuracy and with a reduction in memory usage, but it can also be used to learn stationary and maximally separated embeddings. We show that the stationarity of the embedding and its maximal separated representation can be theoretically justified by setting the weights of the fixed classifier to values taken from the coordinate vertices of the three regular polytopes available in $\mathbb{R}^d$, namely: the $d$-Simplex, the $d$-Cube and the $d$-Orthoplex. These regular polytopes have the maximal amount of symmetry that can be exploited to generate stationary features angularly centered around their corresponding fixed weights. Our approach improves and broadens the concept of a fixed classifier, recently proposed in \cite{hoffer2018fix}, to a larger class of fixed classifier models. Experimental results confirm the theoretical analysis, the generalization capability, the faster convergence and the improved performance of the proposed method. Code will be publicly available.