AI Systems · core
Gradient Descent
Loss surfaces, learning rate, SGD steps.
Mental model
Gradient descent is repeated tiny adjustments. At each step you move the weights a small amount in the direction that lowers the loss. The "learning rate" is how big each step is — too big and you overshoot the answer, too small and training crawls.
How to study Gradient Descent
Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Neural Networks: Zero to Hero (Karpathy), CS231n — Backpropagation & computational graphs, Gradient descent, how neural networks learn (3Blue1Brown) to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.
Next, compare Gradient Descent with Backpropagation. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete One SGD step on a quadratic and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.
Proof of understanding
- Explain the mechanism from first principles and identify the state it reads or changes.
- Give one situation where the concept is the right choice and one where it is not.
- Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
- Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.
Learn from primary sources
Practice and explain it back
One SGD step on a quadratic
Loss L(w)=(w−3)². At w=0 with lr=0.1, compute gradient and one gradient-descent update.
Expected evidence: ∇L=−6, w₁=0.6.
Open the interactive drill →Review prompts
- Loss goes down for a while, then spikes to NaN. What does that pattern point at first?
Build evidence
Synthesize: AI Models & Training
Move from transformer foundations through pre-training, fine-tuning, post-training, compression, and evaluation. Produce one working system, benchmark, or evidence-backed design that integrates the path.
- Implements or precisely models the core mechanisms from all three milestones
- Includes at least one injected failure or adversarial case and demonstrates recovery
- Reports quality, latency, resource, reliability, or usability measurements relevant to the domain
- Ships a concise architecture note explaining decisions, trade-offs, and remaining risks