LLM Fundamentals

The arithmetic behind the model

A model is a thing you send bytes to. This is the arithmetic of those bytes: what a line costs in tokens, what fits inside the window, what silently falls out when it does not, and what a temperature does to the distribution a word is drawn from. You leave holding a budget simulator you wrote.

Start this projectSee the modules
Modules
5
Drills
10
Build steps
2
Time
~4h

Walk out able to

Count the tokens in a request, say which message a window will drop and when, and predict what a sampling setting does to a stated distribution.

What you work out

01

Tokens, counted

What a line costs, and what a rewrite saves.

02

The window as a budget

What fits, what drops, what the tenth turn costs.

03

Temperature and filters

Exactly what each dial does to a distribution.

04

What it can see, and why

Which facts arrive, and where a wrong answer came from.

What you get

Skills that stick

Every project mixes short lessons, focused drills and real build steps, so you finish with working code and the judgement behind it.

You will practise

  • Counting tokens and costing a rewrite
  • What a window holds and what it drops
  • Temperature, top-k and top-p, exactly
  • Reading a failure back to its mechanism

Afterwards you can

  • Count the tokens before you send them
  • Say what the window will drop, and when
  • Predict what a temperature does to a gap
  • Name the mechanism behind a wrong answer

Modules

Step by step

Each module builds on the last. Read a short lesson, drill it until it's second nature, then put it to work.

  1. 1

    Count what you send

    ~48 min

    Produce a token count for any line, and say which of two spellings is cheaper.

    • LessonWhy count what you send4 min
    • LessonSee where a token boundary falls7 min
    • LessonSay where the cost actually lands6 min
    • DrillCount a line of tokens9 min
    • DrillSay what a rewrite saves8 min
    • Build stepWrite the counter14 min
  2. 2

    Fit it in the window

    ~51 min

    Say what a window holds, what falls out of it, and what the tenth turn costs.

    • LessonBudget the window in four terms9 min
    • LessonSay when it starts dropping6 min
    • DrillSay what falls out of the window10 min
    • DrillCost the tenth turn10 min
    • Build stepMake it drop the oldest turns16 min
  3. 3

    Turn the dials

    ~44 min

    Say exactly what a temperature, a top-k and a top-p do to a stated distribution.

    • LessonDivide the scores by a temperature5 min
    • LessonDelete candidates with a filter5 min
    • LessonTake the greedy path, and lose6 min
    • DrillScale a gap by a temperature9 min
    • DrillCut the tail off a distribution9 min
    • DrillTake the greedy path, and the best one10 min
  4. 4

    Write what it can see

    ~32 min

    Decide which facts reach a given turn, and name the change that supplies a missing one.

    • LessonDecide what it can actually see8 min
    • LessonName the repair that fits6 min
    • DrillName the fact that actually arrived9 min
    • DrillName the one change that helps9 min
  5. 5

    Read the failure back

    ~43 min

    Trace a wrong answer to the mechanism that made it, and ship the budget simulator.

    • LessonTrace a wrong answer to its cause7 min
    • LessonRead the settings, not the tone6 min
    • DrillName the mechanism behind it10 min
    • LessonShip the budget report20 min

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Ready when you are.

Work through it at your own pace and pick up right where you left off.

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