Related papers: A rationale from frequency perspective for grokkin…

A theory of neural networks (NNs) built upon collective variables would provide scientists with the tools to better understand the learning process at every stage. In this work, we introduce two such variables, the entropy and the trace of…

This paper presents the first study of grokking in practical LLM pretraining. Specifically, we investigate when an LLM memorizes the training data, when its generalization on downstream tasks starts to improve, and what happens if there is…

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the…

The training dynamics and generalization properties of neural networks (NN) can be precisely characterized in function space via the neural tangent kernel (NTK). Structural changes to the NTK during training reflect feature learning and…

Recent works have partly attributed the generalization ability of over-parameterized neural networks to frequency bias -- networks trained with gradient descent on data drawn from a uniform distribution find a low frequency fit before high…

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training…

We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various…

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and…

Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a…

We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase. This view is supported by the shared temporal structure of three phenomena:…

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons…

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…

Background: It is still an open research area to theoretically understand why Deep Neural Networks (DNNs)---equipped with many more parameters than training data and trained by (stochastic) gradient-based methods---often achieve remarkably…

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…

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…

Grokking, the sudden transition from memorization to generalization, is characterized by the emergence of low-dimensional representations, yet the mechanism underlying this organization remains elusive. We propose that intrinsic task…

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work…

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…

Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function…