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Deep Neural Networks in a Mathematical Framework 1st ed. 2018 [Mīkstie vāki]

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  • Formāts: Paperback / softback, 84 pages, height x width: 235x155 mm, weight: 454 g, XIII, 84 p., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 03-Apr-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319753037
  • ISBN-13: 9783319753034
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Deep Neural Networks in a Mathematical Framework 1st ed. 2018Palielināt
  • Formāts: Paperback / softback, 84 pages, height x width: 235x155 mm, weight: 454 g, XIII, 84 p., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 03-Apr-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319753037
  • ISBN-13: 9783319753034
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319753034.html
Keywords:

This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks.

This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.

1 Introduction and Motivation 1(10)
1.1 Introduction to Neural Networks
2(2)
1.1.1 Brief History
2(1)
1.1.2 Tasks Where Neural Networks Succeed
3(1)
1.2 Theoretical Contributions to Neural Networks
4(3)
1.2.1 Universal Approximation Properties
4(1)
1.2.2 Vanishing and Exploding Gradients
5(1)
1.2.3 Wasserstein GAN
6(1)
1.3 Mathematical Representations
7(1)
1.4 Book Layout
7(1)
References
8(3)
2 Mathematical Preliminaries 11(12)
2.1 Linear Maps, Bilinear Maps, and Adjoints
12(1)
2.2 Derivatives
13(2)
2.2.1 First Derivatives
13(1)
2.2.2 Second Derivatives
14(1)
2.3 Parameter-Dependent Maps
15(2)
2.3.1 First Derivatives
16(1)
2.3.2 Higher-Order Derivatives
16(1)
2.4 Elementwise Functions
17(5)
2.4.1 Hadamard Product
18(1)
2.4.2 Derivatives of Elementwise Functions
19(1)
2.4.3 The Softmax and Elementwise Log Functions
20(2)
2.5 Conclusion
22(1)
References
22(1)
3 Generic Representation of Neural Networks 23(12)
3.1 Neural Network Formulation
24(1)
3.2 Loss Functions and Gradient Descent
25(4)
3.2.1 Regression
25(1)
3.2.2 Classification
26(1)
3.2.3 Backpropagation
27(1)
3.2.4 Gradient Descent Step Algorithm
28(1)
3.3 Higher-Order Loss Function
29(4)
3.3.1 Gradient Descent Step Algorithm
32(1)
3.4 Conclusion
33(1)
References
34(1)
4 Specific Network Descriptions 35(24)
4.1 Multilayer Perceptron
36(4)
4.1.1 Formulation
36(1)
4.1.2 Single-Layer Derivatives
37(1)
4.1.3 Loss Functions and Gradient Descent
38(2)
4.2 Convolutional Neural Networks
40(12)
4.2.1 Single Layer Formulation
40(10)
4.2.2 Multiple Layers
50(1)
4.2.3 Single-Layer Derivatives
50(1)
4.2.4 Gradient Descent Step Algorithm
51(1)
4.3 Deep Auto-Encoder
52(5)
4.3.1 Weight Sharing
52(1)
4.3.2 Single-Layer Formulation
53(1)
4.3.3 Single-Layer Derivatives
54(1)
4.3.4 Loss Functions and Gradient Descent
55(2)
4.4 Conclusion
57(1)
References
58(1)
5 Recurrent Neural Networks 59(22)
5.1 Generic RNN Formulation
59(11)
5.1.1 Sequence Data
60(1)
5.1.2 Hidden States, Parameters, and Forward Propagation
60(2)
5.1.3 Prediction and Loss Functions
62(1)
5.1.4 Loss Function Gradients
62(8)
5.2 Vanilla RNNs
70(6)
5.2.1 Formulation
70(1)
5.2.2 Single-Layer Derivatives
71(1)
5.2.3 Backpropagation Through Time
72(2)
5.2.4 Real-Time Recurrent Learning
74(2)
5.3 RNN Variants
76(2)
5.3.1 Gated RNNs
77(1)
5.3.2 Bidirectional RNNs
78(1)
5.3.3 Deep RNNs
78(1)
5.4 Conclusion
78(1)
References
79(2)
6 Conclusion and Future Work 81(2)
References
82(1)
Glossary 83