# Achieving and Understanding Out-of-Distribution Generalization in Systematic Reasoning in Small-Scale Transformers

arXiv: https://arxiv.org/abs/2210.03275 · HTML: https://mlsanity.com/paper/2210.03275/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 7 Oct 2022.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Do Prompt-Based Models Really Understand the Meaning of their Prompts?](https://mlsanity.com/paper/2109.01247/) (2021)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Systematic Generalization and Emergent Structures in Transformers Trained on Structured Tasks](https://mlsanity.com/paper/2210.00400/) (2022)

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

- [Towards Understanding Inductive Bias in Transformers: A View From Infinity](https://mlsanity.com/paper/2402.05173/) (2024)
- [Do Transformers Have the Ability for Periodicity Generalization?](https://mlsanity.com/paper/2601.22690/) (2026)

## Abstract (arXiv)

Out-of-distribution generalization (OODG) is a longstanding challenge for neural networks. This challenge is quite apparent in tasks with well-defined variables and rules, where explicit use of the rules could solve problems independently of the particular values of the variables, but networks tend to be tied to the range of values sampled in their training data. Large transformer-based language models have pushed the boundaries on how well neural networks can solve previously unseen problems, but their complexity and lack of clarity about the relevant content in their training data obfuscates how they achieve such robustness. As a step toward understanding how transformer-based systems generalize, we explore the question of OODG in small scale transformers trained with examples from a known distribution. Using a reasoning task based on the puzzle Sudoku, we show that OODG can occur on a complex problem if the training set includes examples sampled from the whole distribution of simpler component tasks. Successful generalization depends on carefully managing positional alignment when absolute position encoding is used, but we find that suppressing sensitivity to absolute positions overcomes this limitation. Taken together our results represent a small step toward understanding and promoting systematic generalization in transformers.