DL Foundations
The Math Behind Deep Learning — Linear Algebra, Calculus, Probability
Every neural network operation — from matrix multiplications to gradient updates — is built on mathematical principles. Mastering these foundations lets you understand why architectures work and debug training failures at the mathematical level.
- Linear Algebra — Vectors, matrices, eigendecomposition, and SVD underpin all neural network operations
- Calculus — The chain rule is the backbone of backpropagation, enabling efficient gradient computation
- Probability — Gaussian distributions, cross-entropy, and KL divergence shape loss functions and generative models
Math Foundations for Deep Learning
Deep learning is built on linear algebra, calculus, and probability. This tutorial covers the essential math you need to understand how neural networks learn.
Linear Algebra
Vectors and Matrices
Matrix Operations in Neural Networks
Eigenvalues and Eigenvectors
Singular Value Decomposition (SVD)
Calculus for Deep Learning
Gradients
The Chain Rule
Jacobian and Hessian
Probability Theory
Distributions
Information Theory
Practical Applications in Deep Learning
Summary
- Linear Algebra: Matrix multiplication, eigendecomposition, and SVD are the building blocks of all neural network operations
- Calculus: The chain rule enables efficient gradient computation through backpropagation
- Probability: Gaussian distributions, cross-entropy, and KL divergence shape loss functions and generative models
- Numerical Stability: Implementing math operations requires care to avoid overflow, underflow, and division by zero