# Learning Simple Algorithms from Examples

arXiv: https://arxiv.org/abs/1511.07275 · HTML: https://mlsanity.com/paper/1511.07275/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2015.

## Built on by (most cited first, 12 of 12)

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- [Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors](https://mlsanity.com/paper/2402.01082/) (2024)
- [Evolutionary Training and Abstraction Yields Algorithmic Generalization of Neural Computers](https://mlsanity.com/paper/2105.07957/) (2021)
- [Learning Program Behavioral Models from Synthesized Input-Output Pairs](https://mlsanity.com/paper/2407.08597/) (2024)
- [Learning compositional programs with arguments and sampling](https://mlsanity.com/paper/2109.00619/) (2021)
- [Primitive Agentic First-Order Optimization](https://mlsanity.com/paper/2406.04841/) (2024)

## Abstract (arXiv)

We present an approach for learning simple algorithms such as copying, multi-digit addition and single digit multiplication directly from examples. Our framework consists of a set of interfaces, accessed by a controller. Typical interfaces are 1-D tapes or 2-D grids that hold the input and output data. For the controller, we explore a range of neural network-based models which vary in their ability to abstract the underlying algorithm from training instances and generalize to test examples with many thousands of digits. The controller is trained using Q-learning with several enhancements and we show that the bottleneck is in the capabilities of the controller rather than in the search incurred by Q-learning.