Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists

• URL: http://arxiv.org/abs/2305.05601v1
• Date: Tue, 9 May 2023 16:50:36 GMT
• Title: Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists
• Authors: R. Fioresi, F. Zanchetta
• Abstract summary: We discuss the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We provide some appendices to complement our treatment discussing Kullback-Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation Theorem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph Neural Networks. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We do not aim to give a complete and exhaustive treatment, but we isolate few concepts to give a fast introduction to the subject. We provide some appendices to complement our treatment discussing Kullback-Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation Theorem.

Related papers

• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• A Unified Framework for Neural Computation and Learning Over Time [56.44910327178975]
  Hamiltonian Learning is a novel unified framework for learning with neural networks "over time" It is based on differential equations that: (i) can be integrated without the need of external software solvers; (ii) generalize the well-established notion of gradient-based learning in feed-forward and recurrent networks; (iii) open to novel perspectives.
  arXiv  Detail & Related papers  (2024-09-18T14:57:13Z)
• Foundations and Frontiers of Graph Learning Theory [81.39078977407719]
  Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. This article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models.
  arXiv  Detail & Related papers  (2024-07-03T14:07:41Z)
• Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory [4.066869900592636]
  This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail.
  arXiv  Detail & Related papers  (2023-10-31T11:01:23Z)
• Bayesian Learning for Neural Networks: an algorithmic survey [95.42181254494287]
  This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective.
  arXiv  Detail & Related papers  (2022-11-21T21:36:58Z)
• A Study of the Mathematics of Deep Learning [1.14219428942199]
  "Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This thesis takes several steps towards building strong theoretical foundations for these new paradigms of deep-learning.
  arXiv  Detail & Related papers  (2021-04-28T22:05:54Z)
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges [50.22269760171131]
  The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. This text is concerned with exposing pre-defined regularities through unified geometric principles. It provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers.
  arXiv  Detail & Related papers  (2021-04-27T21:09:51Z)
• Fusing the Old with the New: Learning Relative Camera Pose with Geometry-Guided Uncertainty [91.0564497403256]
  We present a novel framework that involves probabilistic fusion between the two families of predictions during network training. Our network features a self-attention graph neural network, which drives the learning by enforcing strong interactions between different correspondences. We propose motion parmeterizations suitable for learning and show that our method achieves state-of-the-art performance on the challenging DeMoN and ScanNet datasets.
  arXiv  Detail & Related papers  (2021-04-16T17:59:06Z)
• A Survey of Deep Meta-Learning [1.2891210250935143]
  Deep neural networks can achieve great successes when presented with large data sets and sufficient computational resources. However, their ability to learn new concepts quickly is limited. Deep Meta-Learning is one approach to address this issue, by enabling the network to learn how to learn.
  arXiv  Detail & Related papers  (2020-10-07T17:09:02Z)
• Learning the Travelling Salesperson Problem Requires Rethinking Generalization [9.176056742068813]
  End-to-end training of neural network solvers for graph optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently. While state-of-the-art learning-driven approaches perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural optimization pipeline that unifies several recent papers in order to identify the principled biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training.
  arXiv  Detail & Related papers  (2020-06-12T10:14:15Z)
• Structure preserving deep learning [1.2263454117570958]
  deep learning has risen to the foreground as a topic of massive interest. There are multiple challenging mathematical problems involved in applying deep learning. A growing effort to mathematically understand the structure in existing deep learning methods.
  arXiv  Detail & Related papers  (2020-06-05T10:59:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.