# Tensorized Linear Layers

Linear layers are parametrized by matrices. However, it is possible to
*tensorize* them, i.e. reshape them into higher-order tensors in order
to compress them.

You can do this easily in TensorLy-Torch:

```
import tltorch
import torch
```

Let’s create a batch of 4 data points of size 16 each:

```
data = torch.randn((4, 16), dtype=torch.float32)
```

Now, imagine you already have a linear layer:

```
linear = torch.nn.Linear(in_features=16, 10)
```

You can easily compress it into a tensorized linear layer: here we specify the shape to which to tensorize the weights, and use rank=0.5, which means automatically determine the rank so that the factorization uses approximately half the number of parameters.

```
fact_linear = tltorch.FactorizedLinear.from_linear(linear, auto_tensorize=False,
in_tensorized_features=(4, 4), out_tensorized_features=(2, 5), rank=0.5)
```

The tensorized weights will have the following shape:

```
torch.Size([4, 4, 2, 5])
```

Note that you can also let TensorLy-Torch automatically determine the tensorization shape. In this case we just instruct it to
find `in_tensorized_features`

and `out_tensorized_features`

to have length 2:

```
fact_linear = tltorch.FactorizedLinear.from_linear(linear, auto_tensorize=True, n_tensorized_modes=2, rank=0.5)
```

You can also create tensorized layers from scratch:

```
fact_linear = tltorch.FactorizedLinear(in_tensorized_features=(4, 4),
out_tensorized_features=(2, 5),
factorization='tucker', rank=0.5)
```

Finally, during the forward pass, you can reconstruct the full weights (`implementation='reconstructed'`

) and perform a regular linear layer forward pass.
ALternatively, you can let TensorLy-Torch automatically direction contract the input tensor with the *factors of the decomposition* (`implementation='factorized'`

),
which can be faster, particularly if you have a very small rank, e.g. very small factorization factors.