# Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers

arXiv: https://arxiv.org/abs/2504.20752 · HTML: https://mlsanity.com/paper/2504.20752/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 18 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon](https://mlsanity.com/paper/2206.04817/) (2022)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [Unifying Grokking and Double Descent](https://mlsanity.com/paper/2303.06173/) (2023)
- [Grokfast: Accelerated Grokking by Amplifying Slow Gradients](https://mlsanity.com/paper/2405.20233/) (2024)
- [Multi-scale Feature Learning Dynamics: Insights for Double Descent](https://mlsanity.com/paper/2112.03215/) (2021)
- [Training Dynamics of Deep Network Linear Regions](https://mlsanity.com/paper/2310.12977/) (2023)

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

- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [Provable Scaling Laws of Feature Emergence from Learning Dynamics of Grokking](https://mlsanity.com/paper/2509.21519/) (2025)
- [Can LLMs Reconcile Knowledge Conflicts in Counterfactual Reasoning](https://mlsanity.com/paper/2506.15732/) (2025)
- [The Geometric Inductive Bias of Grokking: Bypassing Phase Transitions via Architectural Topology](https://mlsanity.com/paper/2603.05228/) (2026)
- [Is Grokking Worthwhile? Functional Analysis and Transferability of Generalization Circuits in Transformers](https://mlsanity.com/paper/2601.09049/) (2026)
- [The Scaling Properties of Implicit Deductive Reasoning in Transformers](https://mlsanity.com/paper/2605.04330/) (2026)
- [Input-Time Scaling: Adding Noise and Irrelevance into Less-Is-More Drastically Improves Reasoning Performance and Efficiency](https://mlsanity.com/paper/2508.13654/) (2025)
- [The Kinetics of Reasoning: How Chain-of-Thought Shapes Learning in Transformers?](https://mlsanity.com/paper/2510.25791/) (2025)
- [Fast Generalization after Interpolation via Critically Damped Momentum Optimization](https://mlsanity.com/paper/2606.01521/) (2026)
- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)
- [Why Knowing Both Hops Is Not Enough: Understanding Two-Hop Generalization in Language Models](https://mlsanity.com/paper/2608.07261/) (2026)
- [Misalignment of Low-Loss Regions Causes Grokking](https://mlsanity.com/paper/2610.00620/) (2026)

## Abstract (arXiv)

Transformers have achieved great success in numerous NLP tasks but continue to exhibit notable gaps in multi-step factual reasoning, especially when real-world knowledge is sparse. Recent advances in grokking have demonstrated that neural networks can transition from memorizing to perfectly generalizing once they detect underlying logical patterns - yet these studies have primarily used small, synthetic tasks. In this paper, for the first time, we extend grokking to real-world factual data and address the challenge of dataset sparsity by augmenting existing knowledge graphs with carefully designed synthetic data to raise the ratio φr of inferred facts to atomic facts above the threshold required for grokking. Surprisingly, we find that even factually incorrect synthetic data can strengthen emergent reasoning circuits rather than degrade accuracy, as it forces the model to rely on relational structure rather than memorization. When evaluated on multi-hop reasoning benchmarks, our approach achieves up to 95-100% accuracy on 2WikiMultiHopQA - substantially improving over strong baselines and matching or exceeding current state-of-the-art results. We further provide an in-depth analysis of how increasing φr drives the formation of generalizing circuits inside Transformers. Our findings suggest that grokking-based data augmentation can unlock implicit multi-hop reasoning capabilities, opening the door to more robust and interpretable factual reasoning in large-scale language models.