What are weights and biases in a neural network?

Weights and biases are the core learnable parameters in a neural network that enable it to model complex patterns in data. Weights determine the strength of connections between neurons in different layers. Each connection between two neurons has an associated weight, which scales the input signal from one neuron to the next. Biases, on the other hand, are constants added to the weighted sum of inputs before applying an activation function. They allow the network to shift the activation function’s output, providing flexibility to fit data that doesn’t pass through the origin. For example, in a simple neuron, the output is calculated as activation(weight * input + bias), where the weight adjusts how much the input influences the output, and the bias adjusts the baseline value before activation.

During training, weights and biases are iteratively adjusted to minimize prediction errors. The network starts with random initial values for weights and biases (e.g., sampled from a normal distribution) and uses optimization algorithms like gradient descent to update them. For instance, in a regression task, a neuron might learn that a weight of 2.5 for an input feature (like house size) and a bias of -10 effectively maps inputs to outputs (like predicting house prices). Biases are particularly important when the weighted sum of inputs alone can’t achieve the desired output. For example, if all inputs are zero, the bias ensures the neuron can still produce a non-zero output, preventing the network from getting “stuck” during training. Each neuron in a layer has its own bias, allowing the network to model offsets independently for different features.

The effectiveness of a neural network heavily depends on how well weights and biases are tuned. Poorly initialized weights (e.g., too large or small) can slow training or cause numerical instability, while biases help control the starting point of activation functions. For example, using a ReLU activation without a bias might result in “dead neurons” if weights are initialized such that the weighted sum is always negative. In practice, frameworks like TensorFlow or PyTorch automatically handle bias terms unless explicitly disabled. Regularization techniques like L2 regularization are often applied to weights (not biases) to prevent overfitting by penalizing large weight values. Understanding weights and biases is critical for debugging models—for instance, if a network fails to learn, checking whether biases are initialized to zero (a common default) might reveal issues in how the model adapts to data.