Probability Distributions and PRNGs in JAX

Random number generation in functional programming environments requires a completely different approach than traditional stateful libraries. If you want to build reproducible machine learning models or run scientific simulations using JAX, mastering its unique pseudo-random number generator (PRNG) design and probability distribution handling is essential. This text-based course guides you from the fundamental math of randomness to practical implementation in modern numerical computing. You will transition from basic concepts to building robust, reproducible code structures. Through written explanations, structured code examples, and conceptual exercises, you will master the mechanics of functional randomness and probability. What you'll learn: - Understand the core principles of functional PRNG design and why JAX uses explicit state passing - Split and fold random keys safely to maintain reproducibility across parallel computations - Sample from standard continuous and discrete probability distributions using functional APIs - Implement modern array-based random transformations without side effects - Debug common state-related issues in random number generation within JAX transformations - Apply your knowledge to set up reproducible initializations for machine learning layers We start with the foundational definitions of pseudo-randomness and state management, then progress through key splitting techniques, and finish with practical distribution sampling. This course is designed for beginners in JAX, requiring only basic Python knowledge and a familiarity with foundational algebra. Start reading today to unlock reproducible, high-performance numerical computing.