Related papers: Grokking as Dimensional Phase Transition in Neural…
Recently, an interesting phenomenon called grokking has gained much attention, where generalization occurs long after the models have initially overfitted the training data. We try to understand this seemingly strange phenomenon through the…
Grokking in modular arithmetic has established itself as the quintessential fruit fly experiment, serving as a critical domain for investigating the mechanistic origins of model generalization. Despite its significance, existing research…
One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine…
Grokking is the phenomenon whereby, unlike the training performance, which peaks early in the training process, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close…
Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular arithmetic. Whether this mechanism extends beyond arithmetic…
Deep neural networks are strongly over-parameterized, often containing far more weights than required for their task. Although such redundancy can aid optimization, it leads to inefficient deployment and high computational cost, motivating…
Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or…
Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…
Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data. Here we study the generalisation dynamics of two-layer neural networks in a…
Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of…
Spectral bias, the tendency of neural networks to learn low frequencies first, can be both a blessing and a curse. While it enhances the generalization capabilities by suppressing high-frequency noise, it can be a limitation in scientific…
Grokking, referring to the abrupt improvement in test accuracy after extended overfitting, offers valuable insights into the mechanisms of model generalization. Existing researches based on progress measures imply that grokking relies on…
Neural networks sometimes exhibit grokking, a phenomenon where perfect or near-perfect performance is achieved on a validation set well after the same performance has been obtained on the corresponding training set. In this workshop paper,…
Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic…
Grokking-delayed generalization that emerges well after a model has fit the training data-has been linked to robustness and representation quality. We ask whether this training regime also helps with machine unlearning, i.e., removing the…
The complex and unpredictable nature of deep neural networks prevents their safe use in many high-stakes applications. There have been many techniques developed to interpret deep neural networks, but all have substantial limitations.…
We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region…
Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance…
We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the…
We examine the pre-training dynamics of language models, focusing on their ability to copy text from preceding context--a fundamental skill for various LLM applications, including in-context learning (ICL) and retrieval-augmented generation…