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To Grok or not to Grok: Disentangling Generalization and Memorization on Corrupted Algorithmic Datasets
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Studies how two-layer MLPs and Transformers trained on corrupted modular-arithmetic data both memorize corrupted labels and generalize, and how regularization (weight decay, dropout, BatchNorm) and IPR-based neuron pruning separate generalizing from memorizing sub-networks.
Problem
Neural networks can generalize and memorize label noise simultaneously, and it is hard to tell which representations implement the learned rule versus memorized examples. The paper asks how memorization and generalization coexist and how regularization changes this on corrupted algorithmic data.
Approach
Uses modular addition, where the analytic periodic solution of a quadratic-activation two-layer MLP is known, to quantify generalizing neurons via inverse participation ratio (IPR) of Fourier spectra. Low-IPR neurons are identified as memorizing; pruning them removes memorization, and weight decay, dropout and BatchNorm shift the network toward generalizing neurons, producing "inversion" (test acc
Key results
- Networks can memorize corrupted labels while reaching near 100% test accuracy; pruning low-IPR (memorizing) neurons lowers corrupted-train accuracy while keeping test accuracy high.
- Weight decay, dropout and BatchNorm enable 'Full Inversion' where train accuracy plateaus near 100(1-xi)% while test accuracy is 100%, with memorizing neurons eliminated (weight decay, dropout) or de-amplified (BatchNorm).
- Training with regularization shows grokking followed by unlearning of memorizing representations, with train accuracy dropping from 100% to about 100(1-xi)%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add weight decay | 2-layer MLP with quadratic activation · Modular Addition with corrupted labels | generalization accuracy: near-100% -> 100% | Helped |
| Add Dropout | 2-layer MLP with quadratic activation · Modular Addition with corrupted labels | generalization accuracy: near-100% -> 100% | Helped |
| Add BatchNorm | 2-layer MLP with quadratic activation · Modular Addition with corrupted labels | generalization accuracy: near-100% -> 100% | Helped |
| Increase weight decay | 2-layer MLP with quadratic activation · Modular Addition with corrupted labels | robustness to label corruption | Helped |
| Add weight decay | 4-layer ReLU MLP · MNIST with label corruption | generalization accuracy | Helped |
| Increase Dropout | 4-layer ReLU MLP · MNIST with label corruption | accuracy | Hurt |
| Prune neurons starting from the lowest IPR (ablation) | 2-layer MLP in the coexistence phase · Modular Addition, corrupted training examples | accuracy | Hurt |
| Prune neurons starting from the lowest IPR (ablation) | 2-layer MLP in the coexistence phase · Modular Addition, test set | accuracy | No clear effect |
| Prune neurons starting from the highest IPR (ablation) | 2-layer MLP in the coexistence phase · Modular Addition, test set | accuracy | Hurt |
| Use Dropout probability above 0.1 (ablation) | 1-layer Transformer · Modular Addition with corrupted labels | generalization: 0.1 | No clear effect |
| Use BatchNorm (ablation) | 3-layer ReLU MLP · Modular Addition with corrupted labels | phase outcome | No clear effect |
Surprising findings
- Partial inversion (test accuracy above train accuracy) occurs even without explicit regularization when training data is ample.
- Very high weight decay with quadratic activations and adaptive optimizers causes forgetting, where grokked networks collapse to random guessing as weight norms shrink.
Limitations
- Analysis restricted to exactly solvable two-layer models and algorithmic datasets; generalization to realistic settings untested.
- Training dynamics leading to the analytical solutions remain unsolved.
- 3-layer ReLU MLPs with even 0.05 dropout failed to memorize for some settings, with no explanation.
Experimental setup
Datasets: modular addition dataset (p=97) with synthetic symmetric label corruption MNIST (label corruption experiment in appendix)
Benchmarks: modular addition test accuracy MNIST with label corruption
Metrics: train accuracy test accuracy inverse participation ratio generalization gap
Baselines: weight decay dropout BatchNorm LayerNorm
Builds on: grokking (Power et al. 2022) analytical grokking solution (Gromov 2023)
Closest papers by meaning
- Unveiling Memorization–Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise (NeurIPS 2026 · similarity 0.90)
- Grokking in Linear Estimators -- A Solvable Model that Groks without Understanding (ICLR 2024 · similarity 0.90)
- Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model (ICLR 2025 · similarity 0.90)
- Grokking at the Edge of Numerical Stability (ICLR 2025 · similarity 0.90)
- Deep Networks Always Grok and Here is Why (ICML 2024 · similarity 0.90)
- The Pitfalls of Memorization: When Memorization Hurts Generalization (ICLR 2025 · similarity 0.89)
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