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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…

Machine Learning · Computer Science 2025-08-01 Thomas Walker , Ahmed Imtiaz Humayun , Randall Balestriero , Richard Baraniuk

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…

Machine Learning · Computer Science 2025-12-04 Yuanbang Liang , Yang Li

Modular addition tasks serve as a useful test bed for observing empirical phenomena in deep learning, including the phenomenon of \emph{grokking}. Prior work has shown that one-layer transformer architectures learn Fourier Multiplication…

Machine Learning · Computer Science 2025-03-31 Akshay Rangamani

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a…

Machine Learning · Computer Science 2023-10-31 Arthur Conmy , Augustine N. Mavor-Parker , Aengus Lynch , Stefan Heimersheim , Adrià Garriga-Alonso

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…

Machine Learning · Computer Science 2024-11-04 Alan Jeffares , Alicia Curth , Mihaela van der Schaar

Neural models have demonstrated remarkable performance across diverse ranking tasks. However, the processes and internal mechanisms along which they determine relevance are still largely unknown. Existing approaches for analyzing neural…

Information Retrieval · Computer Science 2025-02-04 Catherine Chen , Jack Merullo , Carsten Eickhoff

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…

Machine Learning · Statistics 2026-04-15 Abdessamed Qchohi , Simone Rossi

Grokking - the delayed transition from memorisation to generalisation in neural networks - remains poorly understood. We study this phenomenon through the geometry of learned representations and identify a consistent empirical signature…

Machine Learning · Computer Science 2026-05-13 Truong Xuan Khanh , Truong Quynh Hoa , Luu Duc Trung , Phan Thanh Duc

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…

Machine Learning · Computer Science 2024-03-06 Darshil Doshi , Aritra Das , Tianyu He , Andrey Gromov

Neural networks are often described as black boxes, reflecting the significant challenge of understanding their internal workings and interactions. We propose a different perspective that challenges the prevailing view: rather than being…

Machine Learning · Computer Science 2025-10-23 Shuchen Wu , Stephan Alaniz , Shyamgopal Karthik , Peter Dayan , Eric Schulz , Zeynep Akata

Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks…

Machine Learning · Computer Science 2024-02-20 Depen Morwani , Benjamin L. Edelman , Costin-Andrei Oncescu , Rosie Zhao , Sham Kakade

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…

Computation and Language · Computer Science 2025-02-07 Ang Lv , Ruobing Xie , Xingwu Sun , Zhanhui Kang , Rui Yan

Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…

Machine Learning · Computer Science 2026-04-24 Shreel Golwala

A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work…

We develop the neural network based "learning from regression uncertainty" approach for automated detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles…

Disordered Systems and Neural Networks · Physics 2023-11-09 Wei-Chen Guo , Bao-Quan Ai , Liang He

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to…

Neurons and Cognition · Quantitative Biology 2025-02-12 Udith Haputhanthri , Liam Storan , Yiqi Jiang , Tarun Raheja , Adam Shai , Orhun Akengin , Nina Miolane , Mark J. Schnitzer , Fatih Dinc , Hidenori Tanaka

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…

Machine Learning · Computer Science 2024-07-02 Jannik Brinkmann , Abhay Sheshadri , Victor Levoso , Paul Swoboda , Christian Bartelt

Reinforcement learning (RL) has catalyzed the emergence of Large Reasoning Models (LRMs) that have pushed reasoning capabilities to new heights. While their performance has garnered significant excitement, exploring the internal mechanisms…

Computation and Language · Computer Science 2026-01-29 Yi Hu , Jiaqi Gu , Ruxin Wang , Zijun Yao , Hao Peng , Xiaobao Wu , Jianhui Chen , Muhan Zhang , Liangming Pan

Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we…

Machine Learning · Computer Science 2026-04-16 Laura Gomezjurado Gonzalez

Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…

Computation and Language · Computer Science 2024-06-05 Henry Conklin , Kenny Smith
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