# Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning arXiv: https://arxiv.org/abs/2505.22308 ยท HTML: https://mlsanity.com/paper/2505.22308/ ## Key facts - Cited by 9 papers in the map (data through 14 Oct 2026). - Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. - Builds on 35 of its 37 references that are in the map. - First posted on arXiv 28 May 2025. ## Placed in - LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/) ## Builds on (most cited first, 30 of 35) - [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020) - [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023) - [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021) - [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022) - [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024) - [A Pretrainer's Guide to Training Data: Measuring the Effects of Data Age, Domain Coverage, Quality, & Toxicity](https://mlsanity.com/paper/2305.13169/) (2023) - [Learning to See by Looking at Noise](https://mlsanity.com/paper/2106.05963/) (2021) - [Mimetic Initialization of Self-Attention Layers](https://mlsanity.com/paper/2305.09828/) (2023) - [To Code, or Not To Code? Exploring Impact of Code in Pre-training](https://mlsanity.com/paper/2408.10914/) (2024) - [Neural Redshift: Random Networks are not Random Functions](https://mlsanity.com/paper/2403.02241/) (2024) - [Modeling rapid language learning by distilling Bayesian priors into artificial neural networks](https://mlsanity.com/paper/2305.14701/) (2023) - [Transferring Inductive Biases through Knowledge Distillation](https://mlsanity.com/paper/2006.00555/) (2020) - [Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models](https://mlsanity.com/paper/2411.12580/) (2024) - [Initializing Models with Larger Ones](https://mlsanity.com/paper/2311.18823/) (2023) - [Between Circuits and Chomsky: Pre-pretraining on Formal Languages Imparts Linguistic Biases](https://mlsanity.com/paper/2502.19249/) (2025) - [Injecting structural hints: Using language models to study inductive biases in language learning](https://mlsanity.com/paper/2304.13060/) (2023) - [Learning Universal Predictors](https://mlsanity.com/paper/2401.14953/) (2024) - [Pretraining with Artificial Language: Studying Transferable Knowledge in Language Models](https://mlsanity.com/paper/2203.10326/) (2022) - [Procedural Image Programs for Representation Learning](https://mlsanity.com/paper/2211.16412/) (2022) - [How Does Code Pretraining Affect Language Model Task Performance?](https://mlsanity.com/paper/2409.04556/) (2024) - [Insights into Pre-training via Simpler Synthetic Tasks](https://mlsanity.com/paper/2206.10139/) (2022) - [On the Transferability of Pre-trained Language Models: A Study from Artificial Datasets](https://mlsanity.com/paper/2109.03537/) (2021) - [Downstream Datasets Make Surprisingly Good Pretraining Corpora](https://mlsanity.com/paper/2209.14389/) (2022) - [Algorithmic Capabilities of Random Transformers](https://mlsanity.com/paper/2410.04368/) (2024) - [Scaling Backwards: Minimal Synthetic Pre-training?](https://mlsanity.com/paper/2408.00677/) (2024) - [Intelligence at the Edge of Chaos](https://mlsanity.com/paper/2410.02536/) (2024) - [Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wild](https://mlsanity.com/paper/2503.10065/) (2025) - [General Intelligence Requires Reward-based Pretraining](https://mlsanity.com/paper/2502.19402/) (2025) - [Emergent properties with repeated examples](https://mlsanity.com/paper/2410.07041/) (2024) - [Pre-training with Synthetic Data Helps Offline Reinforcement Learning](https://mlsanity.com/paper/2310.00771/) (2023) ## Built on by (most cited first, 9 of 9) - [Learning to See Before Seeing: Demystifying LLM Visual Priors from Language Pre-training](https://mlsanity.com/paper/2509.26625/) (2025) - [Training Language Models via Neural Cellular Automata](https://mlsanity.com/paper/2603.10055/) (2026) - [Can You Learn to See Without Images? Procedural Warm-Up for Vision Transformers](https://mlsanity.com/paper/2511.13945/) (2025) - [Synthetic Pre-Pre-Training Improves Language Model Robustness to Noisy Pre-Training Data](https://mlsanity.com/paper/2605.10129/) (2026) - [Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks](https://mlsanity.com/paper/2607.17624/) (2026) - [Structural priors for data-efficient language learning](https://mlsanity.com/paper/2609.11505/) (2026) - [Procedural Pretraining for Molecular Property Prediction](https://mlsanity.com/paper/2609.17831/) (2026) - [Procedural Core: A Compact Recurrent Initialization for Vision Transformers](https://mlsanity.com/paper/2609.37631/) (2026) - [Lasting Effects of Abstract Pretraining Beyond Perplexity](https://mlsanity.com/paper/2609.38764/) (2026) ## Abstract (arXiv) Pretraining on large, semantically rich datasets is key for developing language models. Surprisingly, recent studies have shown that even synthetic data, generated procedurally through simple semantic-free algorithms, can yield some of the same benefits as natural language pretraining. It is unclear what specific capabilities such simple synthetic data instils in a model, where these capabilities reside in the architecture, and how they manifest within its weights. In this short paper, we identify several beneficial forms of procedural data, together with specific algorithmic reasoning skills that improve in small transformers. Our core finding is that different procedural rules instil distinct but complementary inductive structures in the model. With extensive ablations and partial-transfer experiments, we discover that these structures reside in different parts of the model. Attention layers often carry the most transferable information, but some pretraining rules impart useful structure to MLP blocks instead. Most interestingly, the structures induced by multiple rules can be composed to jointly reinforce multiple capabilities. These results suggest an exciting possibility of disentangling the acquisition of knowledge from reasoning in language models, with the goal of improving their robustness and data efficiency.