# Introduction to working with tensors in Vespa

Tensors allow Vespa to support more advanced ranking models such as large logistic regression models and neural networks. In this document tensors are introduced and some examples of their use are shown. For more detailed information, please refer to the tensor user guide and the tensor reference.

## Tensor concepts

In Vespa, we refer to tensors as a data structure which is a generalization of scalars, vectors and matrices:

1. A scalar is a tensor of order 0.
2. A vector is a tensor of order 1.
3. A matrix is a tensor of order 2.

Tensors can have any order.

Tensors consist of a set of double valued cells, with each cell having a unique address. A cells address is specified by its index or label along all dimensions. The number of dimensions in a tensor is the order of the tensor. Each dimension can be either sparse or dense. Sparse dimensions have labels designating their address, while dense dimensions have indices.

For instance, using literal form, the tensor:

{
{x:2, y:1}:1.0,
{x:0, y:2}:1.0
}


has two dimensions named x and y, and has two cells with defined values. A graphical representation is showed here:

When tensors are defined you need to declare it’s type. The following defines a sparse matrix:

tensor(x{},y{})


The following defines a dense matrix:

tensor(x[],y[])


Vespa needs to know the type of tensor to optimize the ranking pipeline. As seen above, the dimensions themselves define if they are sparse or dense. However, mixed tensors (sparse along one dimension, but dense along another) is currently not supported.

## Tensor examples

In the following examples, we will use the tensor playground to visualize tensor operations. The playground can be started by deploying the tensor sample app, and opening “http://[host]:[port]/playground/index.html”. By clicking on the links below, a setup string will be copied to the clipboard. Paste this string into the setup input box in the playground and press enter.

The neural network example is quite a bit more involved. Here, the network has 3 input neurons, 5 hidden neurons and a single output neuron. An example of neural networks in action can be found in the blog recommendation tutorial part 3.

## Using tensors in Vespa

Please refer to the the tensor user guide and for details of using tensors in Vespa. Also try the blog recommendation tutorial.