Comprehensive Survey: Mathematical Foundations of Deep Learning -Linear Algebra, Statistics, Gradients, and Tensor Operations

Deep learning has emerged as a transformative field within machine learning, achieving unprecedented success across diverse applications from computer vision to natural language processing. However, the mathematical foundations underlying these powerful models remain crucial for understanding, implementing, and advancing deep learning systems. This comprehensive survey examines the essential mathematical components that form the backbone of deep learning: linear algebra operations, statistical concepts, gradient computations, and tensor manipulations. We provide detailed coverage of vector and matrix operations, probability distributions and statistical modeling, gradient computation through the chain rule, and multi-dimensional tensor operations. Additionally, we trace the evolution of deep learning from early perceptrons to modern deep networks, highlighting how these mathematical foundations enable the scalability and effectiveness of contemporary deep learning systems. This survey serves as a foundational reference for researchers and practitioners seeking to understand the mathematical underpinnings of deep learning technologies. Supplementary Material File (mathematical_foundations_deep_learning_survey.pdf) - Download - 196.49 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 307views 152downloads Citations Download citation Surya Rao Rayarao, Naga Donikena. Comprehensive Survey: Mathematical Foundations of Deep Learning -Linear Algebra, Statistics, Gradients, and Tensor Operations. Authorea. 26 August 2025. DOI: https://doi.org/10.22541/au.175623123.32795831/v1 DOI: https://doi.org/10.22541/au.175623123.32795831/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.