Timezone: »
Poster
Explicit Regularisation in Gaussian Noise Injections
Alexander Camuto · Matthew Willetts · Umut Simsekli · Stephen J Roberts · Chris C Holmes
We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.
Author Information
Alexander Camuto (University of Oxford & The Alan Turing Institute)
Matthew Willetts (University of Oxford)
Umut Simsekli (Inria/ENS)
Stephen J Roberts (University of Oxford)
Chris C Holmes (University of Oxford)
More from the Same Authors
-
2021 Spotlight: Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms »
Alexander Camuto · George Deligiannidis · Murat Erdogdu · Mert Gurbuzbalaban · Umut Simsekli · Lingjiong Zhu -
2021 : HumBugDB: A Large-scale Acoustic Mosquito Dataset »
Ivan Kiskin · Marianne Sinka · Adam Cobb · Waqas Rafique · Lawrence Wang · Davide Zilli · Benjamin Gutteridge · Rinita Dam · Theodoros Marinos · Yunpeng Li · Dickson Msaky · Emmanuel Kaindoa · Gerard Killeen · Eva Herreros-Moya · Kathy Willis · Stephen J Roberts -
2021 : Certifiably Robust Variational Autoencoders »
Ben Barrett · Alexander Camuto · Matthew Willetts · Thomas Rainforth -
2021 : Relaxed-Responsibility Hierarchical Discrete VAEs »
Matthew Willetts · Xenia Miscouridou · Stephen J Roberts · Chris C Holmes -
2021 : Certifiably Robust Variational Autoencoders »
Ben Barrett · Alexander Camuto · Matthew Willetts · Thomas Rainforth -
2021 : On-the-fly Strategy Adaptation for ad-hoc Agent Coordination »
Jaleh Zand · Jack Parker-Holder · Stephen J Roberts -
2021 : Certifiably Robust Variational Autoencoders »
Ben Barrett · Alexander Camuto · Matthew Willetts · Thomas Rainforth -
2023 Poster: Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models »
Anant Raj · Umut Simsekli · Alessandro Rudi -
2023 Poster: Approximate Heavy Tails in Offline (Multi-Pass) Stochastic Gradient Descent »
Kruno Lehman · Alain Durmus · Umut Simsekli -
2023 Poster: Uniform-in-Time Wasserstein Stability Bounds for (Noisy) Stochastic Gradient Descent »
Lingjiong Zhu · Mert Gurbuzbalaban · Anant Raj · Umut Simsekli -
2023 Poster: Differentially Private Statistical Inference through $\beta$-Divergence One Posterior Sampling »
Jack Jewson · Sahra Ghalebikesabi · Chris C Holmes -
2023 Poster: A Unified Framework for U-Net Design and Analysis »
Christopher Williams · Fabian Falck · George Deligiannidis · Chris C Holmes · Arnaud Doucet · Saifuddin Syed -
2023 Poster: Learning via Wasserstein-Based High Probability Generalization Bounds »
Paul Viallard · Maxime Haddouche · Umut Simsekli · Benjamin Guedj -
2023 Workshop: Heavy Tails in ML: Structure, Stability, Dynamics »
Mert Gurbuzbalaban · Stefanie Jegelka · Michael Mahoney · Umut Simsekli -
2022 : Panel on Open Problems in Machine Learning Systems »
Ivana Dusparic · Stephen J Roberts · Morine Amutorine · Jerome White · Murtuza Shergadwala -
2022 Poster: A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEs »
Fabian Falck · Christopher Williams · Dominic Danks · George Deligiannidis · Christopher Yau · Chris C Holmes · Arnaud Doucet · Matthew Willetts -
2022 Poster: Chaotic Regularization and Heavy-Tailed Limits for Deterministic Gradient Descent »
Soon Hoe Lim · Yijun Wan · Umut Simsekli -
2022 Poster: Generalization Bounds for Stochastic Gradient Descent via Localized $\varepsilon$-Covers »
Sejun Park · Umut Simsekli · Murat Erdogdu -
2021 : Invite Talk 1 Q&A »
Chris C Holmes -
2021 : How to train your model when it's wrong: Bayesian nonparametric learning in M-open »
Chris C Holmes -
2021 Poster: Heavy Tails in SGD and Compressibility of Overparametrized Neural Networks »
Melih Barsbey · Milad Sefidgaran · Murat Erdogdu · Gaël Richard · Umut Simsekli -
2021 Poster: Multi-Facet Clustering Variational Autoencoders »
Fabian Falck · Haoting Zhang · Matthew Willetts · George Nicholson · Christopher Yau · Chris C Holmes -
2021 Poster: On Locality of Local Explanation Models »
Sahra Ghalebikesabi · Lucile Ter-Minassian · Karla DiazOrdaz · Chris C Holmes -
2021 : HumBugDB: A Large-scale Acoustic Mosquito Dataset »
Ivan Kiskin · Marianne Sinka · Adam Cobb · Waqas Rafique · Lawrence Wang · Davide Zilli · Benjamin Gutteridge · Rinita Dam · Theodoros Marinos · Yunpeng Li · Dickson Msaky · Emmanuel Kaindoa · Gerard Killeen · Eva Herreros-Moya · Kathy Willis · Stephen J Roberts -
2021 Poster: Conformal Bayesian Computation »
Edwin Fong · Chris C Holmes -
2021 Poster: Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks »
Tolga Birdal · Aaron Lou · Leonidas Guibas · Umut Simsekli -
2021 Poster: Tuning Mixed Input Hyperparameters on the Fly for Efficient Population Based AutoRL »
Jack Parker-Holder · Vu Nguyen · Shaan Desai · Stephen J Roberts -
2021 Poster: Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance »
Hongjian Wang · Mert Gurbuzbalaban · Lingjiong Zhu · Umut Simsekli · Murat Erdogdu -
2021 Poster: Neural Ensemble Search for Uncertainty Estimation and Dataset Shift »
Sheheryar Zaidi · Arber Zela · Thomas Elsken · Chris C Holmes · Frank Hutter · Yee Teh -
2021 Poster: Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections »
Kimia Nadjahi · Alain Durmus · Pierre E Jacob · Roland Badeau · Umut Simsekli -
2021 Poster: Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms »
Alexander Camuto · George Deligiannidis · Murat Erdogdu · Mert Gurbuzbalaban · Umut Simsekli · Lingjiong Zhu -
2020 Poster: Statistical and Topological Properties of Sliced Probability Divergences »
Kimia Nadjahi · Alain Durmus · Lénaïc Chizat · Soheil Kolouri · Shahin Shahrampour · Umut Simsekli -
2020 Poster: Effective Diversity in Population Based Reinforcement Learning »
Jack Parker-Holder · Aldo Pacchiano · Krzysztof M Choromanski · Stephen J Roberts -
2020 Spotlight: Statistical and Topological Properties of Sliced Probability Divergences »
Kimia Nadjahi · Alain Durmus · Lénaïc Chizat · Soheil Kolouri · Shahin Shahrampour · Umut Simsekli -
2020 Spotlight: Effective Diversity in Population Based Reinforcement Learning »
Jack Parker-Holder · Aldo Pacchiano · Krzysztof M Choromanski · Stephen J Roberts -
2020 : Chris Holmes Q&A »
Chris C Holmes -
2020 : Bayesian nowcasting of COVID-19 regional test results in England »
Chris C Holmes -
2020 Poster: Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks »
Umut Simsekli · Ozan Sener · George Deligiannidis · Murat Erdogdu -
2020 Poster: Quantitative Propagation of Chaos for SGD in Wide Neural Networks »
Valentin De Bortoli · Alain Durmus · Xavier Fontaine · Umut Simsekli -
2020 Poster: Provably Efficient Online Hyperparameter Optimization with Population-Based Bandits »
Jack Parker-Holder · Vu Nguyen · Stephen J Roberts -
2020 Spotlight: Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks »
Umut Simsekli · Ozan Sener · George Deligiannidis · Murat Erdogdu -
2019 : Poster Session »
Gergely Flamich · Shashanka Ubaru · Charles Zheng · Josip Djolonga · Kristoffer Wickstrøm · Diego Granziol · Konstantinos Pitas · Jun Li · Robert Williamson · Sangwoong Yoon · Kwot Sin Lee · Julian Zilly · Linda Petrini · Ian Fischer · Zhe Dong · Alexander Alemi · Bao-Ngoc Nguyen · Rob Brekelmans · Tailin Wu · Aditya Mahajan · Alexander Li · Kirankumar Shiragur · Yair Carmon · Linara Adilova · SHIYU LIU · Bang An · Sanjeeb Dash · Oktay Gunluk · Arya Mazumdar · Mehul Motani · Julia Rosenzweig · Michael Kamp · Marton Havasi · Leighton P Barnes · Zhengqing Zhou · Yi Hao · Dylan Foster · Yuval Benjamini · Nati Srebro · Michael Tschannen · Paul Rubenstein · Sylvain Gelly · John Duchi · Aaron Sidford · Robin Ru · Stefan Zohren · Murtaza Dalal · Michael A Osborne · Stephen J Roberts · Moses Charikar · Jayakumar Subramanian · Xiaodi Fan · Max Schwarzer · Nicholas Roberts · Simon Lacoste-Julien · Vinay Prabhu · Aram Galstyan · Greg Ver Steeg · Lalitha Sankar · Yung-Kyun Noh · Gautam Dasarathy · Frank Park · Ngai-Man (Man) Cheung · Ngoc-Trung Tran · Linxiao Yang · Ben Poole · Andrea Censi · Tristan Sylvain · R Devon Hjelm · Bangjie Liu · Jose Gallego-Posada · Tyler Sypherd · Kai Yang · Jan Nikolas Morshuis -
2019 : Poster Session »
Eduard Gorbunov · Alexandre d'Aspremont · Lingxiao Wang · Liwei Wang · Boris Ginsburg · Alessio Quaglino · Camille Castera · Saurabh Adya · Diego Granziol · Rudrajit Das · Raghu Bollapragada · Fabian Pedregosa · Martin Takac · Majid Jahani · Sai Praneeth Karimireddy · Hilal Asi · Balint Daroczy · Leonard Adolphs · Aditya Rawal · Nicolas Brandt · Minhan Li · Giuseppe Ughi · Orlando Romero · Ivan Skorokhodov · Damien Scieur · Kiwook Bae · Konstantin Mishchenko · Rohan Anil · Vatsal Sharan · Aditya Balu · Chao Chen · Zhewei Yao · Tolga Ergen · Paul Grigas · Chris Junchi Li · Jimmy Ba · Stephen J Roberts · Sharan Vaswani · Armin Eftekhari · Chhavi Sharma -
2019 : Poster session »
Sebastian Farquhar · Erik Daxberger · Andreas Look · Matt Benatan · Ruiyi Zhang · Marton Havasi · Fredrik Gustafsson · James A Brofos · Nabeel Seedat · Micha Livne · Ivan Ustyuzhaninov · Adam Cobb · Felix D McGregor · Patrick McClure · Tim R. Davidson · Gaurush Hiranandani · Sanjeev Arora · Masha Itkina · Didrik Nielsen · William Harvey · Matias Valdenegro-Toro · Stefano Peluchetti · Riccardo Moriconi · Tianyu Cui · Vaclav Smidl · Taylan Cemgil · Jack Fitzsimons · He Zhao · · mariana vargas vieyra · Apratim Bhattacharyya · Rahul Sharma · Geoffroy Dubourg-Felonneau · Jonathan Warrell · Slava Voloshynovskiy · Mihaela Rosca · Jiaming Song · Andrew Ross · Homa Fashandi · Ruiqi Gao · Hooshmand Shokri Razaghi · Joshua Chang · Zhenzhong Xiao · Vanessa Boehm · Giorgio Giannone · Ranganath Krishnan · Joe Davison · Arsenii Ashukha · Jeremiah Liu · Sicong (Sheldon) Huang · Evgenii Nikishin · Sunho Park · Nilesh Ahuja · Mahesh Subedar · · Artyom Gadetsky · Jhosimar Arias Figueroa · Tim G. J. Rudner · Waseem Aslam · Adrián Csiszárik · John Moberg · Ali Hebbal · Kathrin Grosse · Pekka Marttinen · Bang An · Hlynur Jónsson · Samuel Kessler · Abhishek Kumar · Mikhail Figurnov · Omesh Tickoo · Steindor Saemundsson · Ari Heljakka · Dániel Varga · Niklas Heim · Simone Rossi · Max Laves · Waseem Gharbieh · Nicholas Roberts · Luis Armando Pérez Rey · Matthew Willetts · Prithvijit Chakrabarty · Sumedh Ghaisas · Carl Shneider · Wray Buntine · Kamil Adamczewski · Xavier Gitiaux · Suwen Lin · Hao Fu · Gunnar Rätsch · Aidan Gomez · Erik Bodin · Dinh Phung · Lennart Svensson · Juliano Tusi Amaral Laganá Pinto · Milad Alizadeh · Jianzhun Du · Kevin Murphy · Beatrix Benkő · Shashaank Vattikuti · Jonathan Gordon · Christopher Kanan · Sontje Ihler · Darin Graham · Michael Teng · Louis Kirsch · Tomas Pevny · Taras Holotyak -
2019 Poster: Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance »
Kimia Nadjahi · Alain Durmus · Umut Simsekli · Roland Badeau -
2019 Spotlight: Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance »
Kimia Nadjahi · Alain Durmus · Umut Simsekli · Roland Badeau -
2019 Poster: First Exit Time Analysis of Stochastic Gradient Descent Under Heavy-Tailed Gradient Noise »
Thanh Huy Nguyen · Umut Simsekli · Mert Gurbuzbalaban · Gaël RICHARD -
2019 Poster: Generalized Sliced Wasserstein Distances »
Soheil Kolouri · Kimia Nadjahi · Umut Simsekli · Roland Badeau · Gustavo Rohde -
2018 Poster: Nonparametric learning from Bayesian models with randomized objective functions »
Simon Lyddon · Stephen Walker · Chris C Holmes -
2018 Poster: Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC »
Tolga Birdal · Umut Simsekli · Mustafa Onur Eken · Slobodan Ilic -
2017 : Cost-sensitive detection with variational autoencoders for environmental acoustic sensing »
Yunpeng Li · Stephen J Roberts -
2017 : Contributed talk: Safe Policy Search with Gaussian Process Models »
Kyriakos Polymenakos · Stephen J Roberts -
2017 Poster: Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding »
Mainak Jas · Tom Dupré la Tour · Umut Simsekli · Alexandre Gramfort -
2016 Poster: Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo »
Alain Durmus · Umut Simsekli · Eric Moulines · Roland Badeau · Gaël RICHARD -
2014 Poster: Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature »
Tom Gunter · Michael A Osborne · Roman Garnett · Philipp Hennig · Stephen J Roberts -
2012 Poster: Active Learning of Model Evidence Using Bayesian Quadrature »
Michael A Osborne · David Duvenaud · Roman Garnett · Carl Edward Rasmussen · Stephen J Roberts · Zoubin Ghahramani -
2011 Poster: Generalised Coupled Tensor Factorisation »
Kenan Y Yılmaz · Taylan Cemgil · Umut Simsekli -
2006 Poster: Bayesian Image Super-resolution, Continued »
Lyndsey C Pickup · David Capel · Stephen J Roberts · Andrew Zisserman -
2006 Spotlight: Bayesian Image Super-resolution, Continued »
Lyndsey C Pickup · David Capel · Stephen J Roberts · Andrew Zisserman