{
  "lesson": "04-tree-of-thoughts-lats",
  "title": "Tree of Thoughts and LATS: Deliberate Search",
  "questions": [
    {
      "stage": "pre",
      "question": "Why does chain-of-thought struggle on Game of 24?",
      "options": [
        "A linear walk cannot backtrack when an early step is wrong, so later steps compound the error",
        "CoT requires a calculator tool that GPT-4 lacks",
        "The model cannot multiply integers",
        "The prompt is too short"
      ],
      "correct": 0,
      "explanation": "Without branching, a wrong early subexpression poisons the rest of the chain; the paper measures only 4 percent for CoT."
    },
    {
      "stage": "pre",
      "question": "What is a node in a Tree of Thoughts search?",
      "options": [
        "A tool registered with the runtime",
        "A weight update during fine-tuning",
        "A token produced by the model",
        "A coherent intermediate step or thought, with K possible child expansions"
      ],
      "correct": 3,
      "explanation": "ToT treats reasoning as a tree where each node is an intermediate thought that can expand into K children."
    },
    {
      "stage": "check",
      "question": "Which of these three is NOT one of LATS's roles for the LLM?",
      "options": [
        "Self-reflector that writes reflections on failure",
        "Optimizer that updates model weights between rollouts",
        "Value function that scores partial trajectories",
        "Policy that proposes next actions"
      ],
      "correct": 1,
      "explanation": "LATS is gradient-free; the three LLM roles are policy, value, and self-reflector. There are no weight updates."
    },
    {
      "stage": "check",
      "question": "Name the four MCTS phases the lesson lists.",
      "options": [
        "Sample, Score, Sort, Submit",
        "Plan, Execute, Reflect, Stop",
        "Select, Expand, Simulate, Backpropagate",
        "Search, Synthesize, Synthesize-Again, Stop"
      ],
      "correct": 2,
      "explanation": "MCTS proceeds in select, expand, simulate, backpropagate per iteration."
    },
    {
      "stage": "check",
      "question": "In UCT, what is the role of the exploration constant c?",
      "options": [
        "It scales the value estimate Q",
        "It sets the maximum tree depth",
        "It controls the number of rollouts",
        "It weights the exploration term sqrt(ln N / n) against the exploitation term Q"
      ],
      "correct": 3,
      "explanation": "c balances exploitation (Q) against the exploration term; tune per task."
    },
    {
      "stage": "post",
      "question": "When is search actively harmful compared to a single trajectory?",
      "options": [
        "Whenever tokens are cheap",
        "When the task is code generation",
        "When the task involves multiple correct answers",
        "When the evaluator is noisy and there is a single right answer, so the search converges on a good-scoring wrong answer"
      ],
      "correct": 3,
      "explanation": "A noisy value function plus a single correct answer is exactly when search overfits to the noise."
    },
    {
      "stage": "post",
      "question": "Roughly how much more token usage should you budget for ToT on Game of 24 compared with CoT?",
      "options": [
        "100x to 1000x",
        "Less than CoT because of pruning",
        "About 2x",
        "About 10x"
      ],
      "correct": 0,
      "explanation": "The lesson cites 100-1000x token cost for ToT on Game of 24 versus CoT."
    }
  ]
}