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.

  1. 01
    Introduction

    Why linear models are the first concrete neural-network building block.

  2. 02
    Affine Map

    A score as a weighted sum plus bias, computed by hand.

  3. 03
    Weights and Bias

    How feature weights and bias terms shape a linear score.

  4. 04
    Score Vector

    One score per class and score matrices for batches.

  5. 05
    Binary and Multiclass Scores

    How raw scores support binary and multiclass choices before probabilities.

  6. 06
    Decision Boundaries

    The score-zero boundary that separates positive and negative sides.

  7. 07
    Why Linear Models Are Limited

    Why one linear boundary cannot represent every useful pattern.

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

Chapter progress