EasyTwo-class softmaxml-dl-llm-math-integration-1
Chapter 17 practice bank
100 questions:
ML & LLM Math
Solve on paper first. Reveal only the final answer when you want to check yourself. There are no worked solutions in this bank by design.
34 easy 33 medium 33 advanced
EasyCross-entropyml-dl-llm-math-integration-2
A classifier gives the correct class probability 1/2. Find its natural-log loss.
EasyGradient descentml-dl-llm-math-integration-3
θ=4, ∂L/∂θ=1, and η=0.1. Find θ after one gradient-descent step.
EasyEmbedding parameter countml-dl-llm-math-integration-4
A token embedding has vocabulary 10000 and dimension 128. How many scalar parameters are in its table?
EasyCosine similarityml-dl-llm-math-integration-5
Find cosine similarity between a=(1,1) and b=(1,0).
EasyAttention mixtureml-dl-llm-math-integration-6
An attention row assigns weights 0.2 and 0.8 to scalar values 2 and 8. Find the output.
EasyAttention scalingml-dl-llm-math-integration-7
With dₖ=16, a raw query-key dot product is 8. What scaled score enters softmax?
EasyTemperatureml-dl-llm-math-integration-8
Two token logits differ by ln 4. At temperature T=2, what is their probability ratio?
EasyTwo-class softmaxml-dl-llm-math-integration-9
Two logits are ln 3 and 0. What probabilities does softmax produce?
EasyCross-entropyml-dl-llm-math-integration-10