Anna's weighted sum: $z = 0.45 - 0.6 + 3.6 - 3.5 = -0.05$. Sigmoid: $\sigma(-0.05) \approx 0.49$. Just below 0.5 — borderline reject!

• This is exactly how a single neuron (or perceptron) works: weighted sum of inputs plus bias, passed through an activation function.
• Eva gets the lowest score because of her low income, high debt ratio, and low credit score.
• A real neural network stacks many neurons to capture more complex patterns.

A single neuron computes a weighted sum — it can only draw a straight line through the data. Complex patterns like "large AND unusual AND abroad" require non-linear combinations of features.

• Each hidden layer creates new, more abstract representations: raw features → simple patterns → complex patterns → decision.
• More layers ≠ always better: too many layers cause vanishing gradients (signals fade) and overfitting.
• Practical networks for tabular data use 2–5 layers.

This layered learning is what makes deep learning "deep."

Squared errors: Apple $(7.5-8.2)^2 = 0.49$, BMW $(5.0-3.1)^2 = 3.61$, Nestlé $(-2.0-(-1.5))^2 = 0.25$, HSBC $(1.2-4.0)^2 = 7.84$, Tesla $(15.3-12.0)^2 = 10.89$. MSE $= \frac{0.49 + 3.61 + 0.25 + 7.84 + 10.89}{5} = 4.616$.

• Tesla and HSBC contribute the most error — large individual mistakes are magnified by squaring.
• The loss function (here MSE: $L = \frac{1}{n}\sum(y_i - \hat{y}_i)^2$) tells the network HOW wrong it is overall.
• Gradient descent adjusts weights: $w \leftarrow w - \alpha \frac{\partial L}{\partial w}$, nudging them to reduce the biggest errors first.

Increasing $w_3$ to 0.3: new output = 3.0 $\times$ 0.3 = 0.9, error drops from 0.16 to 0.01 — a dramatic improvement!

• $w_3$ has the biggest effect only because $h_2$ is large (3.0). The impact of each weight depends on the values flowing through the network.
• This is backpropagation: compute the error at the output, then trace it backward through each layer using the chain rule.
• Each weight gets a gradient proportional to its contribution to the error — all weights are updated simultaneously.

This is how a network with millions of weights learns: one tiny coordinated nudge at a time.

Verdicts: Tiny — underfitting (too simple, poor on both). Small/Medium — good generalization. Large — starting to overfit (17% gap). Huge — severe overfitting (35% gap).

• The "Huge" model memorized the noise and individual quirks of the training data instead of learning general patterns.
• The bank's credit model did the same: it memorized historical applications rather than learning what creditworthiness actually means.
• Dropout (randomly disabling neurons during training) and regularization (penalizing large weights) help prevent this.
• Early stopping — halting training when test accuracy starts to fall — is the simplest and most effective remedy.

Each task maps cleanly to one architecture in the zoo:

• Check reading → CNN: convolutional networks scan images for local patterns (edges, curves, characters) regardless of where on the page they appear.
• Stock prediction → RNN/LSTM or Transformer: both handle sequences, but Transformers capture longer-range dependencies better. Risk: no architecture can reliably predict prices — markets are adversarial.
• Synthetic data → GAN: Generative Adversarial Networks create realistic transaction records that preserve statistical properties without exposing real customer data.

The Transformer has become the dominant architecture since 2018 (BERT, GPT) and powers most modern NLP in finance, including FinBERT from L06.