Mathematics of Deep Learning
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Abstract (arXiv)
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain elusive. This tutorial will review recent work that aims to provide a mathematical justification for several properties of deep networks, such as global optimality, geometric stability, and invariance of the learned representations.
Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Dec 2017.
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Citing papers per year: 2021: 6; 2022: 3; 2023: 1; 2024: 1.
11 papers.
- 2022Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscapecited by 39
- 2022A Falsificationist Account of Artificial Neural Networkscited by 4
- 2021Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learningcited by 2
- 2021Combining Image Features and Patient Metadata to Enhance Transfer Learningcited by 2
- 2021A Reflection on Learning from Data: Epistemology Issues and Limitationscited by 0
- 2021Deep Neural Networks and PIDE discretizationscited by 0
- 2021Enhanced Transfer Learning Through Medical Imaging and Patient Demographic Data Fusioncited by 0
- 2021Towards the One Learning Algorithm Hypothesis: A System-theoretic Approachcited by 0
- 2022Scoliosis Detection using Deep Neural Networkcited by 0
- 2023On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenoncited by 0
- 2024On the Expressive Power of Graph Neural Networkscited by 0
- 2024On the Expressive Power of Graph Neural Networks3 Jan 2024
- 2023On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon21 Aug 2023
- 2022Scoliosis Detection using Deep Neural Network31 Oct 2022
- 2022A Falsificationist Account of Artificial Neural Networks3 May 2022
- 2022Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape20 Jan 2022
- 2021Towards the One Learning Algorithm Hypothesis: A System-theoretic Approach4 Dec 2021
- 2021Enhanced Transfer Learning Through Medical Imaging and Patient Demographic Data Fusion29 Nov 2021
- 2021Combining Image Features and Patient Metadata to Enhance Transfer Learning8 Oct 2021
- 2021Deep Neural Networks and PIDE discretizations5 Aug 2021
- 2021A Reflection on Learning from Data: Epistemology Issues and Limitations28 Jul 2021
- 2021Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning2 Jul 2021