Sampling Methods
Sampling is how AI explores the space of possibilities. Language: Python Implement inverse CDF, rejection, and importance sampling from scratch using only uniform random numbers. Build temperature, top-k, and top-p (nucleus) sampling for language model token generation. Explain the reparameterization trick and why it enables backpropagation through sampling in VAEs. Run Metropolis-Hastings MCMC to sample from an unnormalized target distribution. A language model finishes processing your prompt and produces a vector of 50,000 logits. One for every token in its vocabulary. Now it has to pick one. How? If it always picks the highest-probability token, every response is identical. Deterministic. Boring. If it picks uniformly at random, the output is gibberish. The answer lives somewhere between these extremes, and that somewhere is controlled by sampling. Sampling is not limited to text generation. Reinforcement learning estimates policy gradients by sampling trajectories. VAEs learn latent representations by sampling from learned distributions and backpropagating through the randomness. Diffusion models generate images by sampling noise and iteratively denoising. Monte Carlo methods estimate integrals that have no closed-form solution. MCMC algorithms explore high-dimensional posterior distributions that are impossible to enumerate. Every generative AI system is a sampling system. The sampling strategy determines the quality, diversity, and controllability of the output. This lesson builds every major sampling method from scratch, starting from uniform random numbers and…
Sampling Methods: Sampling is how AI explores the space of possibilities. Language: Python Implement inverse CDF, rejection, and importance sampling from…
This free lesson is part of the AI Engineering from Scratch curriculum. Read the full explanation, run the lesson code, and verify the result in the interactive reader or from the repository source.
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