Neural Networks Explained

A single artificial neuron does one thing: it takes several numbers as inputs, multiplies each by a learned weight, sums them up, adds a bias term, and passes the result through an activation function to produce an output. That’s it. The magic of neural networks comes from combining millions of these simple operations, organized in layers, with weights adjusted through training to produce useful outputs.

A neural network is neurons organized into layers. The input layer receives raw data (pixels, text tokens, numbers). Hidden layers transform the representation through progressive abstraction — early layers learn simple features (edges in images, word co-occurrences in text), later layers learn complex features (faces, sentence meaning). The output layer produces the final prediction. “Deep” learning refers to networks with many hidden layers — the depth enables learning increasingly abstract representations.

Without activation functions, a neural network would just be a linear function — no matter how many layers, it could only learn linear relationships. Activation functions introduce non-linearity. Common functions: ReLU (sets negative values to zero — simple, widely used), Sigmoid (squashes to 0-1, used in output layers for probability), Softmax (used for multi-class classification outputs). The choice of activation function affects training stability and what the network can learn.

Training a neural network means adjusting millions of weights to minimize prediction error. Backpropagation is the algorithm that does this efficiently. Intuition: (1) make a prediction, (2) measure how wrong it was (loss function), (3) work backward through the network calculating how much each weight contributed to the error (gradients), (4) adjust each weight slightly in the direction that reduces error (gradient descent). Repeat millions of times across thousands of examples. The network gradually “learns” weights that minimize errors.

Large Language Models like Claude and GPT are neural networks with a specific architecture: the Transformer. The key innovation in Transformers is the attention mechanism — it lets each word/token in a sequence attend to every other token with learned importance weights, capturing long-range relationships that earlier architectures (RNNs) struggled with. LLMs are trained by predicting the next token in sequences across trillions of words of text, learning language, facts, reasoning patterns, and world knowledge in the process. The scale (billions of parameters) produces emergent capabilities that smaller networks don’t have.