The Keras Functional API

A neural network can be understood as a route of tensor transformations. Data enters as a tensor, layers transform that tensor, and another tensor leaves the route. The Keras Functional API makes this route explicit: you create an input tensor, pass it through layers, retain the resulting tensors, and use the starting and ending tensors to define a Model.

The broader deep-learning picture has three connected parts. Neural networks represent data with tensors, manipulate tensors with mathematical operations, and improve parameter values through gradient-based optimization. Keras provides a framework-level way to describe neural-network models while running on a backend framework.

Tensor dimensionality describes how many axes are needed to organize values. A scalar is a 0D tensor, a vector is a 1D tensor, and a matrix is a 2D tensor. Tensors with more than two dimensions are higher-dimensional tensors. Data batches are also part of this representation discussion, so the useful first question is: which dimensions are needed to represent this data before a network applies operations to it?

Once data is represented as tensors, a network applies tensor operations. Important operations named in the source include element-wise operations, broadcasting, tensor dot, and tensor reshaping. Element-wise operations work across corresponding tensor values. Broadcasting allows tensor values to participate in an operation across compatible dimensions. Tensor dot combines tensors through a dot operation, while reshaping changes how tensor values are organized without changing the idea that the data remains tensor data.

Gradient-based optimization changes the network over repeated steps. The network begins with current parameter values. Derivatives provide information about change, and the gradient organizes that information for tensor operations. Stochastic gradient descent then uses the gradient to produce updated parameter values. The updated state becomes the starting point for another iteration. Backpropagation is the algorithm used for chaining derivatives.

This optimization loop is part of the same larger picture as the Functional API. The Functional API describes how tensors move through transformations; optimization describes how the network's parameter state changes as the network is improved.

Keras occupies a framework role in the deep-learning ecosystem. It can run on top of backend frameworks such as TensorFlow, Theano, or CNTK. This relationship separates the way a model is described from the underlying framework that runs the tensor computations.

When checking whether a Functional API model has been assembled correctly, trace the tensor handoff one step at a time. Begin at the model input. For each layer, identify the tensor entering it and the tensor it returns. Continue until the tensor selected as the model output. This route matters more than the visual order of lines in a file because the Model is assembled from the connected transformations between the chosen endpoints.