Lesson 10 · Book chapter pointer

Artificial neural networks

Read the chapter source: deeplearning.tex — do not treat this note as the book.

Learning goals

Write a neuron as a weighted sum plus a nonlinearity — no mysticism.
Explain what a loss is measuring and why we differentiate it.
See convolution in a net as the same local sum from the vision lesson, with learned weights.
Name overfitting as a robotics problem (the lab is not the warehouse).
Know when a classical feature pipeline is still the right tool.

Teaching note

Neural nets entered this textbook as a first-class chapter because students now meet perception as a weight file. That is fine, as long as the net is still a function: \(y=\sigma(Wx+b)\) stacked on itself. A layer is a linear map and a bend. Depth is composition. Nothing in that sentence requires a GPU, and everything later does. Start on paper with a two-input perceptron deciding “obstacle / no obstacle” from two range readings.

Learning is curve fitting with a lot of parameters. You pick a loss that says how wrong \(y\) is, then you walk the parameters downhill. Backpropagation is the chain rule on a computation graph — the appendix exists so this chapter can stay about robotics. If a student cannot differentiate a two-layer scalar net, they are not ready to debug a “the loss is NaN” night.

Convolutional nets share weights across space because the same edge can appear anywhere. Recurrent nets (and their modern cousins) carry state through time because a robot does. Neither architecture invents new physics. If your training images are noon in the atrium, night in the parking garage is another planet. Domain shift is not a footnote in robotics; it is the usual case.

Use nets where the representation is messy (pixels to “person / not”) and keep geometry explicit where you can write it (pinhole, Jacobian, occupancy). Hybrid stacks — a detector feeding a classical tracker, a net proposing grasps that statics then checks — are how grown systems look. A net that outputs a steering angle with no state and no map can work on a driveway and still be a bad syllabus for autonomy.

Classroom restraint: train a tiny classifier on a handful of hand-labeled patches before anyone downloads a foundation model. Measure train vs test. Then go read the book chapter and the backprop appendix. This note is a briefing, not a deep-learning course, and it is not a paste of the text.

Key equation

One layer: \(a = \sigma(Wx+b)\). Learning chooses \(W,b\) to shrink a loss \(\mathcal{L}(a,a^\star)\) on data you actually have.

Self-check

1. What does the nonlinearity do that a stack of linear maps cannot?

It makes the whole function able to bend. Without \(\sigma\), many layers collapse to one linear map.

2. The training loss is tiny and the robot still fails in a new room. Name the disease.

Overfitting / domain shift. The net memorized the lab’s lighting and furniture, not the task.

3. When should you not replace a Jacobian with a net?

When you already have a correct geometric model and need guarantees, calibration, or tiny data. Learn the residual, not the physics you can write.

Go read the book chapter Print edition