### Abstract

Original language | English |
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Title of host publication | Science meets Engineering of Deep Learning at 33rd Conference on Neural Information Processing Systems |

Number of pages | 5 |

Publication date | 2019 |

Publication status | Published - 2019 |

Event | Thirty-Third Annual Conference on Neural Information Processing Systems - Vancouver Convention Center, Vancouver, Canada Duration: 8 Dec 2019 → 14 Dec 2019 https://nips.cc/Conferences/2019/ |

### Conference

Conference | Thirty-Third Annual Conference on Neural Information Processing Systems |
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Location | Vancouver Convention Center |

Country | Canada |

City | Vancouver |

Period | 08/12/2019 → 14/12/2019 |

Internet address |

### Cite this

*Science meets Engineering of Deep Learning at 33rd Conference on Neural Information Processing Systems*

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*Science meets Engineering of Deep Learning at 33rd Conference on Neural Information Processing Systems.*Thirty-Third Annual Conference on Neural Information Processing Systems, Vancouver, Canada, 08/12/2019.

**Measuring Arithmetic Extrapolation Performance.** / Johansen, Alexander Rosenberg; Madsen, Andreas.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Measuring Arithmetic Extrapolation Performance

AU - Johansen, Alexander Rosenberg

AU - Madsen, Andreas

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

M3 - Article in proceedings

BT - Science meets Engineering of Deep Learning at 33rd Conference on Neural Information Processing Systems

ER -