How models learn

An interactive explainer

How models learn

Machine learning tends to be explained twice over: once in metaphors that leave nothing behind, once in equations that assume you already agree. This is the third way.

  1. A cook who has lost the recipe still gets there: taste, adjust, taste again. Learning is that loop, written down. Opens chapter 1, What a model is.

  3. Before anything can be fixed, one number has to say how wrong the answer was. Opens chapter 2, The loss.

  5. A slope is an exchange rate: turn one knob a little, see how much loss you get back. One of those per knob, stacked in a column, is the gradient. Opens chapter 3, The slope, and the gradient.

  7. Step against the gradient. Too short and you never arrive, too long and you fly over the valley. Opens chapter 4, Gradient descent.

  9. You cannot work on all of it at once. So the examples are cut into handfuls, and one handful is one step. Opens chapter 5, Batches.

  11. A network is a chain of small machines. Each one receives, transforms, and passes it on. Opens chapter 6, Neural network.

  13. Along a train of gears the ratios multiply. Sensitivities travel the same way. Opens chapter 7, The chain rule.

  15. Thirteen thousand knobs, and one pass backwards tells you what each of them owes the error. Opens chapter 8, Backpropagation.

  17. Predict, measure, hand out the blame, adjust. Then again, a few thousand times. Opens chapter 9, The training loop.

  19. None of it runs on words. Meaning has to become coordinates first. Opens chapter 10, Embeddings.

  21. Something has to read all of it, squeeze it down, and write something back, deciding at each word which part of the input still matters. Opens chapter 11, Encoder and decoder.

  23. None of that runs any more when the model answers you. One pass forward, one piece of a word, and round again. Opens chapter 12, Inference.

The whole of it, in order

Every step below is one chapter of the series. Read down the left and you have built a model; read down the right and you are using one. Almost nothing on the right is doing any learning.

While it is learning

Repeated a few thousand times, on examples whose answers are known.

  1. Start with a machine full of knobs, set at random.01What a model is
  2. Turn every example into numbers it can actually take in.10Embeddings
  3. Keep a tenth of the examples back, and shuffle the rest into batches.05Batches
  4. Run one batch forward, layer by layer, and get an answer.06Neural network
  5. Compare the answers with the truth: one number, the loss.02The loss
  6. Ask how much that number moves when each knob moves.03The slope, and the gradient
  7. Multiply the sensitivities along each path through the machine.07The chain rule
  8. One pass backwards hands every knob its share of the blame.08Backpropagation
  9. Step every knob the other way to its slope, by a chosen amount.04Gradient descent
  10. Go back four steps, a few thousand times, and watch the curve.09The training loop

When it answers you

Once per piece of a word, on something it has never seen.

  1. Freeze the knobs. Nothing below this line ever moves them again.12Inference
  2. Turn what was asked into numbers, the same way as before.10Embeddings
  3. Read all of it, deciding which parts matter for what comes next.11Encoder and decoder
  4. One pass forward through the layers, and no pass back.06Neural network
  5. Out comes one piece of a word: the one it finds most likely.12Inference
  6. Add the piece to what was written, keep what was already read, go round.12Inference