# Defining Custom Models¶

In this section we give some examples on how to define models for NetKet 3. There are mainly 3 ways to do that, and they all involve using some third party framework. Whatever you pick, we strongly advise you to read their documentation and whatch some examples.

The 3 frameworks that are supported are:

• Flax Linen API, which is an easy-to-use framework to define complex neural networks

• Barebone Jax/Stax, which is an experimental module of jax.

• Haiku, which is a competitor to Flax, and offers somewhat equivalent expressivity with a rather different syntax.

## Commonalities¶

Whatever the framework you pick, your model must be able to accept batches of states, so 2-Dimensonal matrices (B,N) where $$N$$ is the number of local degrees of freedom in the hilbert space (spatial sites) and $$B$$ is the number of batches. The result must be a (B,) vector where every element is the evaluation of your network for that entry.

If you have a model that is differnt to write in such a way to act on batches, you can use jax.vmap to vectorize it.

Your model will be compilde with jax.jit. Therefore in general you should NEVER (unless you know what you are doing) use numpy, but rather jax.numpy inside of it. If you want to understand why, read Jax 101 guide ( however, even if you don’t care, we think it’s hard to us a tool you don’t undrstand: so at least rad Jax for the Impatient, which is shorter).

### Defining models: init and apply functions¶

Internally, variational states don’t need a Flax model to work with, but only two functions: an initialization function, used to initialize the parameters and the state of the model, and an apply function, used to evaluate the model.

If you don’t want to use Flax, Haiku or other supported methods, you can define your own tuple of functions and pass it to the Variational State constructor. Keep in mind, however, that those two functions will be executed inside jax.jit blocks, so they must be jit-compatible.

## Using Flax Linen¶

To define a model using Flax Linen you need to define a Flax Module. Normally those functionalities are present in the flax.linen module, that people usually import with import flax.linen as nn (some day in a few months from now, import flax.nn will work, but at the moment it won’t, as it’s importing a different, legacy, deprecated module).

Flax supports complex numbers but does not make it overly easy to work with them. As such, netket exports a module, netket.nn which re-exports the functionality in flax.nn, but with the additional support of complex numbers.

To define a Flax Module, simply create a class that inherits from nn.Module. This class cannot have an __init__ method, but can have several class attributes. Class attributes should be hashable objects (so in general they can be strings, numbers, other classes, but cannot be numpy or jax arrays).

Models should define the __call__(self, x) function that represents their action on a batch of inputs x.

import netket.nn as nknn
import jax.numpy as jnp

class Model1(nknn.Module):

y : float = 1.0

def __call__(self, x):
return self.y * jnp.sum(x, axis=-1)


The example above does a very simple sum on the input and multiplies it by a number. To create the module, we simply construct it passing any optional class attribute, such as:

model = Model1(y=0.5)


If you want to use some layers inside your model, you can for example create them in the __call__ function by decorating it with the @nn.compact decorator. Don’t worry: they will only be initialised once.

import netket.nn as nknn
import jax.numpy as jnp

class RBM(nknn.Module):

y : float = 1.0
alpha : int = 1

@nknn.compact
def __call__(self, x):
# create a dense layers with alpha * N features, where N is the size of the system
dense = nknn.Dense(features=self.alpha*x.shape[-1])
# apply the dense layer
x = dense(x)
# sum the output
return self.y * jnp.sum(x, axis=-1)


For more advanced examples, you can check the source-code of the models included in netket  or Flax documentation.

## Using Jax/Stax¶

See tutorial Using Jax: Netket 3 preview

See this example