Chapter 3
Linear Models and Scores
Affine maps, weights, bias, raw scores, score vectors, and linear decision boundaries.
What this chapter does
Linear models are the first concrete model family. This chapter teaches weighted sums, bias terms, raw scores, class-score vectors, and the straight boundaries that make linear models both useful and limited.
Lessons
Read these in order.
Start with the chapter introduction, then move through the topic lessons. The order is chosen so each page can reuse ideas from the pages before it.
- 01Introduction
Why linear models are the first concrete neural-network building block.
- 02Affine Map
A score as a weighted sum plus bias, computed by hand.
- 03Weights and Bias
How feature weights and bias terms shape a linear score.
- 04Score Vector
One score per class and score matrices for batches.
- 05Binary and Multiclass Scores
How raw scores support binary and multiclass choices before probabilities.
- 06Decision Boundaries
The score-zero boundary that separates positive and negative sides.
- 07Why Linear Models Are Limited
Why one linear boundary cannot represent every useful pattern.
Review and practice
Close the chapter deliberately.
Use the conclusion and revision notes before the chapter exercises. Hints and solutions are collected here, while lesson-level exercises reveal their own help inline.
What Chapter 3 established before nonlinear activations.
Summary and Revision NotesA compact review of linear scores, score vectors, and decision boundaries.
ExercisesChapter-level practice for linear models and scores.
HintsLow-spoiler nudges for the Chapter 3 exercises.
SolutionsExplained solutions for the Chapter 3 exercises.
Before moving on
- Compute a linear score from features, weights, and bias.
- Read score vectors and score matrix shapes.
- Connect score zero to a decision boundary.
- Explain why nonlinear activations are needed after linear models.
Where this leads
- Activations and Nonlinearity
- Losses for Learning
- Multilayer Perceptrons