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30 Problems

Calculus for ML

From limits to multivariable calculus. Understand the math behind gradient descent, backpropagation, and optimization in neural networks.

5 Easy18 Medium7 Hard

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6 sections

Limit of a Learning Rate Schedule Continuity of Activation Functions Sigmoid Boundedness via Squeeze Theorem Softmax Numerical Stability & Log-Sum-Exp Calculus Foundations Quiz10 questions

Derivatives of Common Activation Functions Chain Rule Through a 3-Layer Network Higher-Order Derivatives & Loss Curvature Subgradients for Non-Smooth Functions Finite Difference Gradient Checking Single-Variable Differentiation Quiz10 questions

Expected Value via Numerical Integration KL Divergence: Discrete and Continuous Area Under the ROC Curve via Trapezoidal Rule Integration & Probability Calculus Quiz10 questions

Gradient of Multivariate Linear Regression Loss Directional Derivative & Steepest Descent Direction Jacobian of a Neural Network Layer Hessian Matrix & Convexity of Linear Regression Loss JVP and VJP for a 2-Layer Network Second-Order Partial Derivatives Jacobian of a Vector-Valued Polynomial Gradient of a Matrix-Valued Function Hessian Tensor of a Vector-Valued Function Multivariable & Matrix Calculus Quiz10 questions

Gradient Descent on a Non-Convex Loss Learning Rate Stability & Convergence Bounds Lagrange Multipliers: Regularization as Constrained Optimization Taylor Approximation of a Loss Landscape Calculus-Based Optimization Quiz10 questions

Forward-Mode Autodiff with Dual Numbers Backpropagation Through a Computation Graph Softmax + Cross-Entropy Gradient Gradient Clipping: Global Norm Rescaling Gradient of Multivariate Gaussian Log-PDF Calculus in ML Applications Quiz10 questions

Summary

Total30

Easy5

Medium18

Hard7

Progress0%

Quizzes0/6