# Detecting overfitting in Neural Networks during long-horizon grokking using Random Matrix Theory

arXiv: https://arxiv.org/abs/2605.12394 · HTML: https://mlsanity.com/paper/2605.12394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 10 of 10)

- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [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)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [Grokfast: Accelerated Grokking by Amplifying Slow Gradients](https://mlsanity.com/paper/2405.20233/) (2024)
- [SETOL: A Semi-Empirical Theory of (Deep) Learning](https://mlsanity.com/paper/2507.17912/) (2025)
- [Risk Phase Transitions in Spiked Regression: Alignment Driven Benign and Catastrophic Overfitting](https://mlsanity.com/paper/2510.01414/) (2025)

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

- [Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics](https://mlsanity.com/paper/2605.20441/) (2026)

## Abstract (arXiv)

Training Neural Networks (NNs) without overfitting is difficult; detecting that overfitting is difficult as well. We present a novel Random Matrix Theory method that detects the onset of overfitting in deep learning models without access to train or test data. For each model layer, we randomize each weight matrix element-wise, W → Wrand, fit the randomized empirical spectral distribution with a Marchenko-Pastur distribution, and identify large outliers that violate self-averaging. We call these outliers Correlation Traps. During the onset of overfitting, which we call the "anti-grokking" phase in long-horizon grokking, Correlation Traps form and grow in number and scale as test accuracy decreases while train accuracy remains high. Traps may be benign or may harm generalization; we provide an empirical approach to distinguish between them by passing random data through the trained model and evaluating the JS divergence of output logits. Our findings show that anti-grokking is an additional grokking phase with high train accuracy and decreasing test accuracy, structurally distinct from pre-grokking through its Correlation Traps. More broadly, we find that some foundation-scale LLMs exhibit the same Correlation Traps, indicating potentially harmful overfitting.