quiz.json

{
  "questions": [
    {
      "stage": "pre",
      "question": "What does the dot product of two vectors measure?",
      "options": ["The distance between the two vectors", "How similar or aligned the two vectors are", "The angle between the vectors in degrees", "The number of dimensions the vectors share"],
      "correct": 1,
      "explanation": "The dot product measures alignment: positive means same direction (similar), zero means perpendicular (unrelated), negative means opposite direction (dissimilar). This is the basis of similarity search in AI."
    },
    {
      "stage": "pre",
      "question": "In AI, what does 'embedding' refer to?",
      "options": ["Inserting one model inside another", "A vector representation that captures the meaning of something (word, image, user)", "A technique for compressing model weights", "The process of converting code to machine instructions"],
      "correct": 1,
      "explanation": "An embedding maps discrete objects (words, images, users) to continuous vectors in a high-dimensional space where similar items are close together. It is the bridge between real-world concepts and mathematical operations."
    },
    {
      "stage": "post",
      "question": "Three vectors v1=[1,0,0], v2=[0,1,0], v3=[2,1,0] are given. Are they linearly independent?",
      "options": ["Yes, because there are three vectors in 3D space", "No, because v3 = 2*v1 + v2, so v3 is a linear combination of the others", "Yes, because none of the vectors are identical", "No, because they all have a zero component"],
      "correct": 1,
      "explanation": "v3 = 2*v1 + v2, making the set linearly dependent. All three vectors lie in the xy-plane and cannot reach [0,0,1]. Despite having 3 vectors in 3D, they only span a 2D subspace."
    },
    {
      "stage": "post",
      "question": "What does the rank of a matrix tell you in the context of machine learning?",
      "options": ["How fast the matrix can be multiplied", "The number of linearly independent columns, indicating how many dimensions of useful information it contains", "The maximum value in the matrix", "The number of non-zero entries in the matrix"],
      "correct": 1,
      "explanation": "Rank equals the number of linearly independent columns. In ML, a rank-deficient feature matrix means redundant features, infinitely many weight solutions, and the need for regularization."
    },
    {
      "stage": "post",
      "question": "How does LoRA (Low-Rank Adaptation) use linear algebra to efficiently fine-tune large language models?",
      "options": ["It removes unused rows from weight matrices to shrink the model", "It decomposes weight updates into two small low-rank matrices instead of updating the full weight matrix", "It converts all weights from float32 to int8", "It freezes the embedding layer and only trains the output head"],
      "correct": 1,
      "explanation": "LoRA decomposes a 4096x4096 weight update into two matrices of size 4096x16 and 16x4096 (rank-16), reducing trainable parameters from 16M to 131K by assuming updates live in a low-dimensional subspace."
    }
  ]
}