This video explains multi-layer neural networks, extending single-neuron models. Each node sums weighted inputs, applies an activation function (sigmoid, tanh, ReLU), and passes the result to subsequent layers. Hidden layers with non-linear activations enable complex function approximation, unlike linear networks. The network's architecture (layers, nodes) determines its representational power. Training uses gradient descent, minimizing a loss function (e.g., mean squared error) across all output neurons. The choice of activation function depends on the task (linear for regression, sigmoid for classification), but multi-layer networks benefit from additional functions like hyperbolic tangent and rectifier linear unit (ReLU). These offer flexibility and, importantly, their derivatives are needed for gradient descent-based training, which is explained in terms of the activation outputs for computational efficiency. Each node in a neural network performs a computation that can be divided into two stages: taking a weighted sum of inputs and applying an activation function. The key difference from a single neuron is that a neuron's input can come from previous neurons' activations, and its output is passed to later nodes, creating a flow of information through the network. A neural network makes predictions by setting input layer activations to data point values, then looping through layers, computing each neuron's activation (weighted sum of inputs plus activation function). The input and output layer sizes are determined by the data dimensionality, while the number and connectivity of hidden layers determine the network's representational capacity. Multi-layer networks with only linear activations offer no advantage over single neurons. However, non-linear activations are crucial. The video connects this to Boolean logic, showing how neurons can represent AND, OR, and NOT gates, implying that with non-linear activations, neural networks can, in principle, represent any computable function by combining these basic logical operations.