kerrostoiminnoissa

Kerrostoiminnoissa, or layer operations, refer to the mathematical functions applied in individual layers of artificial neural networks. Each layer transforms its input vector through a combination of linear transformations and non‑linear activations, producing the output that serves as input for the next layer.

The core of a layer operation is an affine transformation: the input vector \(x\) is multiplied by a weight matrix \(W\) and a bias vector \(b\) is added, giving \(Wx+b\). This linear mapping captures weighted relationships between features. After the affine step, a point‑wise non‑linearity known as an activation function is applied element‑wise. Common activations include Sigmoid, hyperbolic tangent, Rectified Linear Unit (ReLU), and Softmax for classification tasks.

Layer operations come in several specialized forms beyond the standard fully connected (dense) layer. Convolutional layers use spatial filters to capture local patterns in image or signal data; recurrent layers, such as LSTMs or GRUs, maintain temporal dependencies; pooling layers reduce dimensionality by aggregating neighboring activations; and normalization layers like batch or layer normalisation improve training stability. Dropout layers randomly deactivate units during training to reduce over‑fitting.

In a network, successive kerrostoiminnoissa propagate activations forward from input to output. During training, backpropagation computes gradients of a loss function with respect to weights and biases in each layer, enabling gradient‑based optimisation. Layer operations thus form the building blocks that allow neural models to learn complex, hierarchical representations across domains such as computer vision, natural language processing, and time‑series forecasting.