Mixture of Experts and task routing

01 / CHOOSE THE SOLVER

Choosing tools and specialist agents

Some tasks call for language: rewrite an explanation, summarize notes, or suggest possibilities. Others have a precise rule we can execute: add a column, search a game tree, or fit a statistical model. A useful agent can recognize the difference and hand work to an appropriate tool or specialist.

A basic text LLM predicts tokens. Its harness can use a classifier, routing rules, or a model decision to choose an expert. That expert could be another prompted agent, a calculator, a search service, or a program. Two specialist agents can even use the same underlying model with different instructions and tools.

QUESTION Could a harness route to several specialists while every model it calls is a dense model? Explain your answer.

02 / INFERENCE AND COMPUTATION

When should we turn it into a coding problem?

An LLM might infer a plausible answer from patterns in training and the current prompt. For arithmetic or a game with exact rules, we can ask it to write or call code that computes an answer we can test. Both routes may begin with the same model; the difference is the evidence behind the result.

For “17 × 23,” a calculator executes a defined operation and returns 391. For an NBA draft board, “best pick” needs a definition, data, and a way to evaluate predictions. A statistical model makes those choices inspectable.

03 / THE NBA DRAFT EXAMPLE

Using regression to evaluate NBA draft picks

Imagine an agent helping you choose your next NBA draft pick. One approach is to show it the board and ask for a recommendation based on what it already knows. It may draw on patterns in pretraining, including commentary about players. That knowledge can be stale, and it does not prove the agent checked current stats.

A stronger investigation gives the agent a concrete job: get a current, permitted raw dataset; record its source and timestamp; clean it; define a target; fit a model; and check its predictions against data it did not train on. Regression predicts a number. You still have to decide which number matters for your draft.

1. Fit the line and inspect its slope and intercept. Which prospect ranks first under this one-feature model?
2. Compare held-out mean absolute error (MAE) with the baseline that always predicts the training average. Lower MAE means smaller average errors on these held-out players.
3. Name two missing factors: injuries, role, age, competition level, team needs, or something else. Explain how one might change the pick.

Help investigate an NBA draft board using code. First ask me for the board, an instructor-approved current stats source, and the target to predict. Record source, season, and retrieval timestamp; save a reproducible data snapshot. Check units and missing values. Build a simple regression with a time-based held-out evaluation and a training-mean baseline; avoid future-data leakage. Run the code and report held-out MAE, the model ranking, assumptions, and missing factors. Keep synthetic examples clearly labeled. Do not invent live stats or claim a ranking guarantees the best pick.

04 / ASSIGNMENT

Ask an agent to analyze a game board.

We can check a board more completely than a future basketball career. Use tic-tac-toe, where the rules are small enough to search every possible legal continuation.

1. Choose a valid unfinished board. Before searching, write your own suggested move and why.
2. Copy its board prompt into VCC ↗. First ask the agent for a best-move guess without tools. Record its square and reasoning as a language prediction.
3. Then ask it to create and run a minimax solver. Tell it to validate the board, score every legal move, test immediate wins and blocks, and report ties. Keep the rules and board identical.
4. Compare the real agent’s first guess with its computed move scores and this browser’s search. Ask for the executed command, output, and tests.
5. Change one square to make a second valid board. Repeat. One correct guess does not show the method is always reliable.

Now solve the exact same tic-tac-toe board with code. X starts and turns alternate. Validate counts, winners, whose turn it is, and whether the game already ended. Write and run an exhaustive minimax solver that assumes perfect play by both sides. Score every legal move as win, draw, or loss for the player to move and report all tied best moves. Test an immediate win, a necessary block, a draw, and an invalid board. Show the command, actual output, and tests. Compare that evidence with your earlier no-tool guess. Keep the starter app working.

05 / NEXT: SPLITTING THE WORK

Dividing a task among agents

A harness can split a larger task into discrete parts: one specialist fetches data, another checks it, another fits a model, and another explains the results. The harness must track which results belong together and check that the combined answer still meets the goal. More handoffs also add coordination and token costs. Separate agents are useful when the work benefits from separate contexts or independent parallel tasks; they are not a requirement for every workflow. Lesson 7 follows how a model builds a response, and Lesson 8 explores sparse expert networks.

Turn in: your two valid boards, each no-tool guess, each executed solver result, tests, and a short comparison. Add one limitation of the draft regression and one sentence distinguishing MoE from harness routing.

Review: Describe a task you would give a language specialist, one you would give a code tool, and the evidence you would request from each. Save your work and stop your VCC workspace.