# Is Grokking Worthwhile? Functional Analysis and Transferability of Generalization Circuits in Transformers

arXiv: https://arxiv.org/abs/2601.09049 · HTML: https://mlsanity.com/paper/2601.09049/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Steering and interpreting LLM reasoning, one of 13 directions in Mechanistic interpretability.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Placed in

- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks](https://mlsanity.com/paper/2303.11873/) (2023)
- [Grokking of Hierarchical Structure in Vanilla Transformers](https://mlsanity.com/paper/2305.18741/) (2023)
- [A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task](https://mlsanity.com/paper/2402.11917/) (2024)
- [Grokfast: Accelerated Grokking by Amplifying Slow Gradients](https://mlsanity.com/paper/2405.20233/) (2024)
- [Unified View of Grokking, Double Descent and Emergent Abilities: A Perspective from Circuits Competition](https://mlsanity.com/paper/2402.15175/) (2024)
- [How Do LLMs Perform Two-Hop Reasoning in Context?](https://mlsanity.com/paper/2502.13913/) (2025)
- [Lessons from Studying Two-Hop Latent Reasoning](https://mlsanity.com/paper/2411.16353/) (2024)
- [How do Transformers Learn Implicit Reasoning?](https://mlsanity.com/paper/2505.23653/) (2025)
- [Towards Empirical Interpretation of Internal Circuits and Properties in Grokked Transformers on Modular Polynomials](https://mlsanity.com/paper/2402.16726/) (2024)
- [Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model](https://mlsanity.com/paper/2504.13292/) (2025)
- [Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers](https://mlsanity.com/paper/2504.20752/) (2025)
- [What Can Grokking Teach Us About Learning Under Nonstationarity?](https://mlsanity.com/paper/2507.20057/) (2025)
- [Mechanistic Insights into Grokking from the Embedding Layer](https://mlsanity.com/paper/2505.15624/) (2025)
- [Unveiling the Mechanisms of Multi-Hop Reasoning in Transformers via Identity Bridge](https://mlsanity.com/paper/2509.24653/) (2025)
- [Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation](https://mlsanity.com/paper/2405.16658/) (2024)
- [NeuralGrok: Accelerate Grokking by Neural Gradient Transformation](https://mlsanity.com/paper/2504.17243/) (2025)
- [Beyond Progress Measures: Theoretical Insights into the Mechanism of Grokking](https://mlsanity.com/paper/2504.03162/) (2025)

## Built on by (most cited first, 1 of 1)

- [Where Grokking Happens: Distributed Utility and Fourier Recoding Without a Module Switch](https://mlsanity.com/paper/2609.17571/) (2026)

## Abstract (arXiv)

While Large Language Models (LLMs) excel at factual retrieval, they often struggle with the "curse of two-hop reasoning" in compositional tasks. Recent research suggests that parameter-sharing transformers can bridge this gap by forming a "Generalization Circuit" during a prolonged "grokking" phase. A fundamental question arises: Is a grokked model superior to its non-grokked counterparts on downstream tasks? Furthermore, is the extensive computational cost of waiting for the grokking phase worthwhile? In this work, we conduct a mechanistic study to evaluate the Generalization Circuit's role in knowledge assimilation and transfer. We demonstrate that: (i) The inference paths established by non-grokked and grokked models for in-distribution compositional queries are identical. This suggests that the "Generalization Circuit" does not represent the sudden acquisition of a new reasoning paradigm. Instead, we argue that grokking is the process of integrating memorized atomic facts into an naturally established reasoning path. (ii) Achieving high accuracy on unseen cases after prolonged training and the formation of a certain reasoning path are not bound; they can occur independently under specific data regimes. (iii) Even a mature circuit exhibits limited transferability when integrating new knowledge, suggesting that "grokked" Transformers do not achieve a full mastery of compositional logic.