Sign-In
Cart
Equivariant & Coordinate Independent Convolutional Networks
Hardcover
Series: Progress in Data Science, Book 1
ISBN13: 9789819806621
Publisher: World Scientific Publishing Company
Published: Jan 15 2026
Pages: 592
Weight: 2.10
Height: 1.25 Width: 6.00 Depth: 9.00
Language: English
What is the appropriate geometric structure for neural networks that process spatial signals on Euclidean spaces or more general manifolds? This question takes us on a journey which leads to a gauge field theory of convolutional networks.
Feature vector fields: The spatial signals we are interested in are fields of feature vectors. Feature fields allow to describe data like images, audio, videos, point clouds, or tensor fields, such as fluid flows and electromagnetic fields.
Equivariant networks commute with actions of some symmetry group on their feature spaces. The relevant group actions in this work are geometric transformations of feature fields, like translations, rotations, or reflections of images. Equivariant models generalize everything they learn over the considered group of transformations. This property makes them significantly more data efficient, interpretable, and robust in comparison to non-equivariant models.
Convolutional Neural Networks (CNNs) are the most common network architecture for processing feature fields. Conventional CNNs operate on Euclidean spaces and are translation equivariant, i.e. position independent. This work explains how to extend CNNs to be equivariant under more general symmetries of space.
Coordinate independence: Manifolds are in general not equipped with a canonical choice of coordinates. Feature fields and neural network layers are hence required to be coordinate independent, that is, expressible relative to different frames of reference. The ambiguity of local frames represents the gauge freedom of our neural field theory. We show that the demand for coordinate independence requires CNNs to be equivariant under local gauge transformations.
Also in
General Mathematics
The Golden Number: Pythagorean Rites and Rhythms in the Development of Western Civilization
Ghyka, Matila C.
Hardcover
How It All Works: All Scientific Laws and Phenomena Illustrated & Demonstrated
Clegg, Brian
Dant, Adam
Hardcover
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Feynman, Richard P.
Leighton, Robert B.
Sands, Matthew
Paperback
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Hardcover
Math Practice Workbook Grades 6-8: 1000+ Questions You Need to Kill in Middle School by Brain Hunter Prep
Brain Hunter Prep
Paperback
Who Gets What -- And Why: The New Economics of Matchmaking and Market Design
Roth, Alvin E.
Paperback
Tomoko Fuse's Amazing Kusudama Origami: Geometric Paper Art from Japan's Leading Expert!
Fuse, Tomoko
Paperback
The Art of Strategy: A Game Theorist's Guide to Success in Business and Life
Nalebuff, Barry J.
Dixit, Avinash K.
Paperback
Mastering Essential Math Skills Book 2, Bilingual Edition - English/Spanish
Fisher, Richard W.
Paperback
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Hardcover
The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics
Bardi, Jason Socrates
Hardcover
Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter
Orlin, Ben
Hardcover
Counting with - Contando Con Frida (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
Lundy, Miranda
Ashton, Anthony
Sutton, Daud
Hardcover
50 Math Tricks That Will Change Your Life: Mentally Solve the Impossible in Seconds
Zakowich, Tanya
Paperback
Graph Paper Composition Notebook: Quad Ruled 5x5, Grid Paper for Students in Math and Science
Wizo, Math
Paperback
New York Post Fiendish Sudoku: The Official Utterly Addictive Number-Placing Puzzle
Gould, Wayne
Paperback
Vector: A Surprising Story of Space, Time, and Mathematical Transformation
Arianrhod, Robyn
Hardcover
Touchthinklearn: Numbers: (Board Books for Baby Learners, Touch Feel Books for Children)
Deneux, Xavier
Hardcover
Quantum Mechanics Done Right: The Shortest Path from Novice to Researcher
Freericks, James K.
Hardcover
ALEKS Math Placement Test Prep 2026: 1200 Verified Practice Questions with Accurate Answer Keys, Step-by-Step Worked Solutions, and Clear Concept Expl
Reid, Marcus L.
Publishing, Kettford
Paperback
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
Oakley, Barbara
Paperback
Sudoku for Brain Fitness: 90-Day Challenge to Sharpen the Mind and Strengthen Cognitive Skills
Clontz, Steven
Demyanovich, Julie
Paperback
Un Elefante: Numbers / Números (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
WorkKeys Study Guide and Practice Test Questions: ACT WorkKeys Exam Prep and Review Book with Applied Mathematics, Locating Information, and Reading f
Trivium Exam Prep Team
Paperback
Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning
Liljedahl, Peter
Paperback
Talentos Ocultos: La Genialidad No Tiene Color. La Fuerza No Tiene Género. El Valor No Tiene Límite.
Shetterly, Margot Lee
Paperback
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Benjamin, Arthur
Shermer, Michael
Paperback
Concrete Mathematics: A Foundation for Computer Science
Knuth, Donald
Graham, Ronald
Patashnik, Oren
Hardcover
180 Days(r) Math for First Grade: Practice, Assess, Diagnose
Smith, Jodene
Smith, Jodene Lynn
Paperback
Number Systems and the Foundations of Analysis
Mathematics
Mendelson, Elliott
Dudley, Underwood
Paperback
Medical Dosage Calculations for Dummies
Snyder, Richard W.
Depuente, Vanessa
Schoenborn, Barry
Paperback
The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science
Schneider, Michael S.
Paperback
300 Math CrossWords: Addition, Subtraction, Multiplication, and Division Math CrossWords Grade 3 and Above, Age +8
Martin, Josh Ortiz
Paperback
Reaching for the Extreme: How the Quest for the Biggest, Fewest, and Weirdest Makes Math
Stewart, Ian
Hardcover
Sciencia: Mathematics, Physics, Chemistry, Biology, and Astronomy for All
Watkins, Matthew
Betts, Moff
Tweed, Matt
Hardcover
Math Fundamentals 3 - Geometry: For Middle School - A Quickstudy Laminated Reference Guide
Expolog
Warren, Peggy
Wright, Susan
Other
30 More Math Mysteries Kids Can't Resist!: Quick & Clever Mysteries That Boost Problem-Solving Skills
Lee, Martin
Paperback
Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python
Mirjalili, Vahid
Raschka, Sebastian
Liu, Yuxi (Hayden)
Paperback
It's All a Game: The History of Board Games from Monopoly to Settlers of Catan
Donovan, Tristan
Paperback