This book introduces approaches to generalize the benefits of equivariant deep learning to a broader set of learned structures through learned homomorphisms. In the field of machine learning, the idea of incorporating knowledge of data symmetries into artificial neural networks is known as equivariant deep learning and has led to the development of cutting edge architectures for image and physical data processing. The power of these models originates from data-specific structures ingrained in them through careful engineering. To-date however, the ability for practitioners to build such a structure into models is limited to situations where the data must exactly obey specific mathematical symmetries. The authors discuss naturally inspired inductive biases, specifically those which may provide types of efficiency and generalization benefits through what are known as homomorphic representations, a new general type of structured representation inspired from techniques in physics and neuroscience. A review of some of the first attempts at building models with learned homomorphic representations are introduced. The authors demonstrate that these inductive biases improve the ability of models to represent natural transformations and ultimately pave the way to the future of efficient and effective artificial neural networks.

In addition, this book;

• Offers a novel definition of generalized equivariance and a literature review on learned homomorphisms
• Provide clarity as to the unifying goals of the newly emerging subfield of learned approximate symmetries

• Emphasizes naturally intelligent systems have generalization capabilities and data efficiency beyond artificial models

  Autorentext

  Yue Song, Ph.D. is a Computing and Mathematical Sciences postdoctoral research fellow at Caltech. He pursued doctoral studies under the European Laboratory for Learning and Intelligent Systems (ELLIS), where he was affiliated with the Multimedia and Human Understanding Group (MHUG) at the University of Trento, Italy, and the Amsterdam Machine Learning Lab (AMLab) at the University of Amsterdam, the Netherlands. He researches structured representation learning, specifically leveraging beneficial inductive biases from scientific disciplines such as math, physics, and neuroscience to improve and explain existing machine learning models.

  Thomas Anderson Keller, Ph.D., is a postdoctoral research fellow at the Kempner Institute at Harvard University. He completed his doctorate under the supervision of Max Welling at the University of Amsterdam in the Amsterdam Machine Learning Lab (AMLab). His current research focuses on structured representation learning, probabilistic generative modeling, and biologically plausible learning. His research explores ways to develop deep probabilistic generative models that are meaningfully structured with respect to observed, real-world transformations. In the long term, the goal of Dr. Keller's research is to understand the abstract mechanisms underlying the apparent sample efficiency and generalizability of natural intelligence, and ultimately integrate these into artificially intelligent systems.

  Nicu Sebe, Ph.D., is a Professor at the University of Trento, Italy, where he is leading the research in the areas of multimedia analysis and human behavior understanding. He was the general co-chair of the IEEE FG 2008 and ACM Multimedia 2013. He was a program chair of ACM Multimedia 2011 and 2007, ECCV 2016, ICCV 2017, and ICPR 2020, and a general chair of ACM Multimedia 2022. He serves as the Co-Editor in Chief of the Computer Vision and Image Understanding journal. He is a fellow of IAPR and of .the European Lab for Learning and Intelligent Systems (ELLIS).

  Max Welling, Ph.D., is a Research Chair in Machine Learning at the University of Amsterdam and a Distinguished Scientist at MSR. He is a Fellow at the Canadian Institute for Advanced Research (CIFAR) and the European Lab for Learning and Intelligent Systems (ELLIS) where he also serves on the founding board. His previous appointments include VP at Qualcomm Technologies, professor at UC Irvine, postdoc at U. Toronto and UCL under the supervision of Prof. Geoffrey Hinton, and postdoc at Caltech under the supervision of Prof. Pietro Perona. He finished his Ph.D. in theoretical high energy physics under the supervision of Nobel laureate Prof. Gerard 't Hooft.