# Lie Access Neural Turing Machine

arXiv: https://arxiv.org/abs/1602.08671 · HTML: https://mlsanity.com/paper/1602.08671/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2016.

## Built on by (most cited first, 2 of 2)

- [Enhancing Reinforcement Learning with discrete interfaces to learn the Dyck Language](https://mlsanity.com/paper/2110.14350/) (2021)
- [Enhancing Length Extrapolation in Sequential Models with Pointer-Augmented Neural Memory](https://mlsanity.com/paper/2404.11870/) (2024)

## Abstract (arXiv)

Following the recent trend in explicit neural memory structures, we present a new design of an external memory, wherein memories are stored in an Euclidean key space mathbb Rn. An LSTM controller performs read and write via specialized read and write heads. It can move a head by either providing a new address in the key space (aka random access) or moving from its previous position via a Lie group action (aka Lie access). In this way, the "L" and "R" instructions of a traditional Turing Machine are generalized to arbitrary elements of a fixed Lie group action. For this reason, we name this new model the Lie Access Neural Turing Machine, or LANTM. We tested two different configurations of LANTM against an LSTM baseline in several basic experiments. We found the right configuration of LANTM to outperform the baseline in all of our experiments. In particular, we trained LANTM on addition of k-digit numbers for 2 ≤ k ≤ 16, but it was able to generalize almost perfectly to 17 ≤ k ≤ 32, all with the number of parameters 2 orders of magnitude below the LSTM baseline.