# Neural Power Units

arXiv: https://arxiv.org/abs/2006.01681 · HTML: https://mlsanity.com/paper/2006.01681/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)
- [Asynchronous Neural Networks for Learning in Graphs](https://mlsanity.com/paper/2205.12245/) (2022)
- [Learning Division with Neural Arithmetic Logic Modules](https://mlsanity.com/paper/2110.05177/) (2021)
- [Improving the Robustness of Neural Multiplication Units with Reversible Stochasticity](https://mlsanity.com/paper/2211.05624/) (2022)
- [Symbolic recovery of PDEs from measurement data](https://mlsanity.com/paper/2602.15603/) (2026)
- [TriPLU: Bypassing the Gate with Direct Trilinear Product FFNs in Tiny Language Models](https://mlsanity.com/paper/2608.20360/) (2026)
- [Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining](https://mlsanity.com/paper/2609.21876/) (2026)

## Abstract (arXiv)

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.