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Information plane (IP) analysis has been suggested to study the training dynamics of deep neural networks through mutual information (MI) between inputs, representations, and targets. However, its statistical validity is often compromised…

Machine Learning · Computer Science 2026-05-06 Maximilian Nothnagel , Bernhard C. Geiger

The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization…

Machine Learning · Statistics 2017-02-14 Alessandro Achille , Stefano Soatto

Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases,…

Machine Learning · Computer Science 2017-02-17 Xuezhe Ma , Yingkai Gao , Zhiting Hu , Yaoliang Yu , Yuntian Deng , Eduard Hovy

We review the current literature concerned with information plane analyses of neural network classifiers. While the underlying information bottleneck theory and the claim that information-theoretic compression is causally linked to…

Machine Learning · Computer Science 2022-12-02 Bernhard C. Geiger

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…

Machine Learning · Statistics 2016-10-05 Yarin Gal , Zoubin Ghahramani

The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the…

Quantum Physics · Physics 2024-11-05 Nathan Haboury , Mo Kordzanganeh , Alexey Melnikov , Pavel Sekatski

Dropout is one of the most popular regularization techniques in neural network training. Because of its power and simplicity of idea, dropout has been analyzed extensively and many variants have been proposed. In this paper, several…

Machine Learning · Statistics 2022-06-23 Masanari Kimura , Hideitsu Hino

We study the flow of information and the evolution of internal representations during deep neural network (DNN) training, aiming to demystify the compression aspect of the information bottleneck theory. The theory suggests that DNN training…

Machine Learning · Computer Science 2019-05-31 Ziv Goldfeld , Ewout van den Berg , Kristjan Greenewald , Igor Melnyk , Nam Nguyen , Brian Kingsbury , Yury Polyanskiy

Integrated Information Theory (IIT) is an audacious attempt to pin down the abstract, phenomenological experiences of consciousness into a rigorous, mathematical framework. We show that IIT's stance in regards to neuronal noise is…

Neurons and Cognition · Quantitative Biology 2021-12-10 Refath Bari

Dropout regularization of deep neural networks has been a mysterious yet effective tool to prevent overfitting. Explanations for its success range from the prevention of "co-adapted" weights to it being a form of cheap Bayesian inference.…

Machine Learning · Statistics 2019-05-30 Eric Nalisnick , José Miguel Hernández-Lobato , Padhraic Smyth

Dropout is used to avoid overfitting by randomly dropping units from the neural networks during training. Inspired by dropout, this paper presents GI-Dropout, a novel dropout method integrating with global information to improve neural…

Computation and Language · Computer Science 2018-10-11 Hengru Xu , Shen Li , Renfen Hu , Si Li , Sheng Gao

Measuring model performance is a key issue for deep learning practitioners. However, we often lack the ability to explain why a specific architecture attains superior predictive accuracy for a given data set. Often, validation accuracy is…

Machine Learning · Computer Science 2022-04-01 Marius C. Landverk , Signe Riemer-Sørensen

Dropout is a regularization technique widely used in training artificial neural networks to mitigate overfitting. It consists of dynamically deactivating subsets of the network during training to promote more robust representations. Despite…

Machine Learning · Statistics 2025-09-10 Francesco Mori , Francesca Mignacco

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the \textit{Information Plane}; i.e.,…

Machine Learning · Computer Science 2017-05-02 Ravid Shwartz-Ziv , Naftali Tishby

This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…

Information Theory · Computer Science 2023-08-29 Pieter Adriaans

Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random…

Machine Learning · Computer Science 2021-08-30 Christopher Sun , Jai Sharma , Milind Maiti

Uncertainty estimation for machine learning models is of high importance in many scenarios such as constructing the confidence intervals for model predictions and detection of out-of-distribution or adversarially generated points. In this…

Machine Learning · Computer Science 2022-05-06 Kirill Fedyanin , Evgenii Tsymbalov , Maxim Panov

Transformer-based language models are widely deployed for reasoning, yet their behavior under inference-time stochasticity remains underexplored. While dropout is common during training, its inference-time effects via Monte Carlo sampling…

Machine Learning · Computer Science 2026-03-19 Antônio Junior Alves Caiado , Michael Hahsler

Dropout is a very effective method in preventing overfitting and has become the go-to regularizer for multi-layer neural networks in recent years. Hierarchical mixture of experts is a hierarchically gated model that defines a soft decision…

Machine Learning · Computer Science 2018-12-27 Ozan İrsoy , Ethem Alpaydın

Understanding the influence of a training instance on a neural network model leads to improving interpretability. However, it is difficult and inefficient to evaluate the influence, which shows how a model's prediction would be changed if a…

Machine Learning · Computer Science 2021-11-22 Sosuke Kobayashi , Sho Yokoi , Jun Suzuki , Kentaro Inui
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