Neural Power Units

TL;DR

The paper introduces the Neural Power Unit (NPU), a neural network component capable of learning arbitrary power functions over the full real domain, improving generalization and expressivity for arithmetic tasks.

Contribution

The NPU extends existing arithmetic units to operate on all real numbers using complex arithmetic without complex number conversion, enhancing their capabilities.

Findings

NPUs outperform competitors in accuracy and sparsity on artificial datasets.

RealNPU can discover governing equations of dynamical systems from data.

The model is highly transparent and interpretable.

Abstract

Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic units are either limited to operate on positive numbers or can only represent a subset of arithmetic operations. We introduce the Neural Power Unit (NPU) that operates on the full domain of real numbers and is capable of learning arbitrary power functions in a single layer. The NPU thus fixes the shortcomings of existing arithmetic units and extends their expressivity. We achieve this by using complex arithmetic without requiring a conversion of the network to complex numbers. A simplification of the unit to the RealNPU yields a highly transparent model. We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.