Summary of Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory, by Arnulf Jentzen et al.
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
by Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
First submitted to arxiv on: 31 Oct 2023
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Numerical Analysis (math.NA); Probability (math.PR); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Deep learning algorithms are introduced with full mathematical detail, covering essential components such as artificial neural network (ANN) architectures (fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and optimization algorithms (basic stochastic gradient descent method, accelerated methods, and adaptive methods). Theoretical aspects of deep learning are also explored, including approximation capacities of ANNs, optimization theory, and generalization errors. The book concludes by reviewing deep learning approximation methods for partial differential equations (PDEs), such as physics-informed neural networks (PINNs) and deep Galerkin methods. This comprehensive introduction is suitable for students and scientists with no prior knowledge of deep learning, as well as practitioners seeking a solid mathematical understanding. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Deep learning algorithms are explained in simple terms. The book covers the basics of artificial neural network architectures and optimization methods used in deep learning. It also explores theoretical aspects of deep learning, including how well ANNs can approximate functions and how they generalize to new data. Finally, the book shows how deep learning can be applied to solve partial differential equations (PDEs). This introduction is helpful for anyone curious about deep learning and its applications. |
Keywords
* Artificial intelligence * Batch normalization * Deep learning * Generalization * Neural network * Optimization * Stochastic gradient descent
