MIT 18.S096: Matrix Calculus For Machine Learning And Beyond
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MIT’s 18.S096 Matrix Calculus for Machine Learning and Beyond is an advanced mathematics course designed to provide a deep understanding of matrix calculus and its applications in machine learning, optimization, deep learning, and statistics. This course covers differentiation and optimization of matrix functions, which are essential for training machine learning models, computing gradients, and improving optimization techniques.
Why Study Matrix Calculus for Machine Learning?
- Essential for Understanding Deep Learning
- Backpropagation, the core algorithm for training deep neural networks, relies on matrix differentiation.
- Computing gradients efficiently is necessary for updating model parameters using gradient descent.
- Backpropagation, the core algorithm for training deep neural networks, relies on matrix differentiation.
- Crucial for Optimization and Training AI Models
- Optimization algorithms such as SGD, Adam, and Newton’s method require an understanding of matrix gradients.
- Hessian matrices improve convergence rates in second-order optimization techniques.
- Optimization algorithms such as SGD, Adam, and Newton’s method require an understanding of matrix gradients.
- Foundational for Probabilistic Models and Variational Inference
- Many probabilistic models involve matrix calculus for deriving gradients of likelihood functions.
- Gaussian Processes, Bayesian Neural Networks, and Expectation-Maximization (EM) algorithms rely on matrix derivatives.
- Many probabilistic models involve matrix calculus for deriving gradients of likelihood functions.
- Key for Natural Language Processing and Transformer Models
- Word embeddings, self-attention mechanisms, and transformer architectures depend on efficient computation of matrix derivatives.
- Understanding Jacobian and Hessian computations helps in designing stable and efficient NLP models.
- Word embeddings, self-attention mechanisms, and transformer architectures depend on efficient computation of matrix derivatives.
- Applied in Reinforcement Learning and Robotics
- Policy gradients in reinforcement learning require differentiation of expectation functions.
- Control systems and robotics involve matrix calculus for trajectory optimization and system modeling.
- Policy gradients in reinforcement learning require differentiation of expectation functions.