fnn

Feedforward neural network (FNN) is a class of artificial neural networks in which information propagates in one direction from input to output through a sequence of layers, with no cycles or loops. In a typical FNN, data enters at the input layer, passes through one or more hidden layers, and produces an output. Each neuron computes a weighted sum of its inputs, adds a bias, and applies a nonlinear activation function such as ReLU, sigmoid, or tanh. If all layers are densely connected, the network is called a fully connected or dense feedforward network; convolutional layers and other specialized layers may be used within a feedforward architecture as well.

FNNs are trained using supervised learning. During training, a forward pass computes predictions, and a loss function measures the discrepancy between predictions and true targets. The gradients of the loss with respect to the network’s weights are computed by backpropagation, and iterative optimization (commonly stochastic gradient descent or its variants such as Adam) updates the weights. The goal is to minimize the loss over the training data and achieve good generalization to unseen data.

The expressive power of FNNs is characterized by the universal approximation theorem, which states that a feedforward network with at least one hidden layer and sufficient neurons can approximate a wide class of functions. Practical networks vary from shallow architectures (one hidden layer) to deep neural networks with many layers.

Limitations include difficulty modeling temporal or sequential data without modifications, and potential overfitting or training instability without regularization. FNNs underpin many foundational models and are often extended with architectural ideas from other networks, such as residual connections or convolutional operations, which integrate into a feedforward computation.

Common applications include classification, regression, function approximation, and pattern recognition across fields such as image and signal processing.