# Measuring Arithmetic Extrapolation Performance

arXiv: https://arxiv.org/abs/1910.01888 · HTML: https://mlsanity.com/paper/1910.01888/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Exploring Generalization Ability of Pretrained Language Models on Arithmetic and Logical Reasoning](https://mlsanity.com/paper/2108.06743/) (2021)
- [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)
- [The Domain Mixed Unit: A New Neural Arithmetic Layer](https://mlsanity.com/paper/2509.08180/) (2025)

## Abstract (arXiv)

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.