Seonglae ChoDeep Learning presents a challenge to classical statistical learning theory. Neural networks often achieve zero training error, yet they generalize well to unseen data. This contradicts traditional expectations and makes many classical generalization bounds ineffective.
Sparse activation and the Superposition Hypothesis have been proposed as possible explanations for the Grokking phenomenon, where models learn to activate sparsely and generalize well after initially overfitting when trained on very large datasets.
From OpenAI and Google researchers examines how neural networks generalize on small, algorithmically generated datasets. A network significantly improves its generalization performance after a point of overfitting, achieving perfect generalization in certain cases. This study is significant as it delves into the understanding of generalization in overparameterized neural networks beyond just memorizing finite training datasets.
Neel Nanda ICLR 2023 with Mechanistic interpretability
To find "progress measures," a transformer model was trained on modular addition tasks where grokking was observed. Reverse-engineering the implemented algorithm revealed that the model maps inputs to rotations on a circle and corresponds addition to rotation, specifically using discrete Fourier transforms and trigonometric identities to perform addition operations.
- Restricted Loss: Loss when non-key frequencies are removed
- Excluded Loss: Loss when only key frequencies are removed
Generalization
- Memorization (memorizing training data)
- Circuit formation (forming generalizable algorithms internally)
- Cleanup (removing memorization mechanisms)
