What is a feedforward neural network and how does it process inputs?

Question

AcadiFi · Accepted Answer

A feedforward neural network is a directed acyclic graph of neurons organized in layers: input layer, one or more hidden layers, and an output layer. Data flows forward only - no cycles.

Each neuron in a hidden layer computes:
z = w1 x1 + w2 x2 + ... + wn xn + b
a = f(z)
where w are weights, b is bias, and f is an activation function (ReLU, sigmoid, tanh).

Example: Predicting 1-year stock return from four inputs: trailing PE (15), revenue growth (8%), debt-to-equity (0.6), earnings surprise (+2%).

Hidden layer 1 has three neurons. Neuron 1 weights: [-0.4, 2.5, -1.2, 3.0], bias 0.1. z = -0.4(15) + 2.5(0.08) - 1.2(0.6) + 3.0(0.02) + 0.1 = -6 + 0.2 - 0.72 + 0.06 + 0.1 = -6.36. ReLU(-6.36) = 0. Neuron dies for this sample.

Neuron 2 weights: [0.05, 4.0, -0.5, 2.5], bias 0.3. z = 0.75 + 0.32 - 0.3 + 0.05 + 0.3 = 1.12. ReLU = 1.12.

Output layer combines hidden activations into final prediction: y_hat = w_out . a_hidden + b_out.

```mermaid
graph LR
  I1[PE 15] --> H1
  I2[Growth 8%] --> H1
  I3[D/E 0.6] --> H1
  I4[Surprise 2%] --> H1
  I1 --> H2
  I2 --> H2
  I3 --> H2
  I4 --> H2
  H1[Neuron 1] --> O[Return prediction]
  H2[Neuron 2] --> O
```

Why it works: the network learns non-linear interactions that linear regression can't capture. A ReLU-activated hidden neuron can effectively learn 'high revenue growth matters only when D/E is low' without a manually specified interaction term.

What is a feedforward neural network and how does it process inputs?

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