Related papers: Explaining Grokking and Information Bottleneck thr…

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…

Recent studies have uncovered intriguing phenomena in deep learning, such as grokking, double descent, and emergent abilities in large language models, which challenge human intuition and are crucial for a deeper understanding of neural…

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

Neural Collapse is a phenomenon where the last-layer representations of a well-trained neural network converge to a highly structured geometry. In this paper, we focus on its first (and most basic) property, known as NC1: the within-class…

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel…

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…

Deep learning has become the most powerful machine learning tool in the last decade. However, how to efficiently train deep neural networks remains to be thoroughly solved. The widely used minibatch stochastic gradient descent (SGD) still…

A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents -- valid in the limit of high information about the system state -- this picture…

Neural networks can be compressed to reduce memory and computational requirements, or to increase accuracy by facilitating the use of a larger base architecture. In this paper we focus on pruning individual neurons, which can simultaneously…

Neural Collapse is a phenomenon that helps identify sparse and low rank structures in deep classifiers. Recent work has extended the definition of neural collapse to regression problems, albeit only measuring the phenomenon at the last…

Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on…

The Information Bottleneck (IB) principle offers an information-theoretic framework for analyzing the training process of deep neural networks (DNNs). Its essence lies in tracking the dynamics of two mutual information (MI) values: between…

Modern practice for training classification deepnets involves a Terminal Phase of Training (TPT), which begins at the epoch where training error first vanishes; During TPT, the training error stays effectively zero while training loss is…

Deep neural networks (DNNs) at convergence consistently represent the training data in the last layer via a highly symmetric geometric structure referred to as neural collapse. This empirical evidence has spurred a line of theoretical…

The information bottleneck (IB) principle has been suggested as a way to analyze deep neural networks. The learning dynamics are studied by inspecting the mutual information (MI) between the hidden layers and the input and output. Notably,…

Grokking is an intriguing phenomenon of delayed generalization, where neural networks initially memorize training data with perfect accuracy but exhibit poor generalization, subsequently transitioning to a generalizing solution with…

Compact neural networks are essential for affordable and power efficient deep learning solutions. Binary Neural Networks (BNNs) take compactification to the extreme by constraining both weights and activations to two levels, $\{+1, -1\}$.…

As synthetic content increasingly infiltrates the web, generative AI models may be retrained on their own outputs: a process termed "autophagy". This leads to model collapse: a progressive loss of performance and diversity across…

Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…

\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…