Related papers: Progress measures for grokking via mechanistic int…

We study the well-known grokking phenomena in neural networks (NNs) using a 3-layer MLP trained on 1 k-sample subset of MNIST, with and without weight decay, and discover a novel third phase -- \emph{anti-grokking} -- that occurs very late…

This paper investigates the grokking phenomenon, which refers to the sudden transition from a long memorization to generalization observed during neural networks training, in the context of learning multiplication in finite-dimensional…

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:…

This paper demonstrates that grokking behavior in modular arithmetic with a modulus P in a neural network can be controlled by modifying the profile of the activation function as well as the depth and width of the model. Plotting the even…

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…

A principled understanding of generalization in deep learning may require unifying disparate observations under a single conceptual framework. Previous work has studied \emph{grokking}, a training dynamic in which a sustained period of…

\emph{Memorization} in neural networks lacks a precise operational definition and is often inferred from the grokking regime, where training accuracy saturates while test accuracy remains very low. We identify a previously unreported third…

Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network -- a phenomenon often called "emergence''. Beyond scientific understanding, establishing the causal factors underlying such emergent…

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…

We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking…

While Large Language Models (LLMs) excel at factual retrieval, they often struggle with the "curse of two-hop reasoning" in compositional tasks. Recent research suggests that parameter-sharing transformers can bridge this gap by forming a…

We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and…

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.…

Emergence in machine learning refers to the spontaneous appearance of complex behaviors or capabilities that arise from the scale and structure of training data and model architectures, despite not being explicitly programmed. We introduce…

Neural networks readily learn a subset of the modular arithmetic tasks, while failing to generalize on the rest. This limitation remains unmoved by the choice of architecture and training strategies. On the other hand, an analytical…

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…

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…

Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or…

Measuring learning progress is essential for curiosity-driven exploration in reinforcement learning, but widely used signals such as prediction error often fail to distinguish meaningful, learnable patterns from random noise. This paper…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…