class netket.models.DeepSetRelDistance[source]#

Bases: Module

Implements an equivariant version of the DeepSets architecture given by (

\[f(x_1,...,x_N) = \rho\left(\sum_i \phi(x_i)\right)\]

that is suitable for the simulation of periodic systems. Additionally one can add a cusp condition by specifying the asymptotic exponent. For helium the Ansatz reads (

\[\psi(x_1,...,x_N) = \rho\left(\sum_i \phi(d_{\sin}(x_i,x_j))\right) \cdot \exp\left[-\frac{1}{2}\left(b/d_{\sin}(x_i,x_j)\right)^5\right]\]
cusp_exponent: Optional[int] = None#

exponent of Katos cusp condition

output_activation: Optional[Callable] = None#

The nonlinear activation function at the output layer.

use_bias: bool = True#

if True uses a bias in all layers.


Returns the variables in this module.

hilbert: ContinuousHilbert#

The hilbert space defining the periodic box where this ansatz is defined.

layers_phi: int#

Number of layers in phi network.

layers_rho: int#

Number of layers in rho network.

features_phi: Union[Tuple, int]#

Number of features in each layer for phi network.

features_rho: Union[Tuple, int]#

Number of features in each layer for rho network. If specified as a list, the last layer must have 1 feature.


Gaussian error linear unit activation function.

If approximate=False, computes the element-wise function:

\[\mathrm{gelu}(x) = \frac{x}{2} \left(1 + \mathrm{erf} \left( \frac{x}{\sqrt{2}} \right) \right)\]

If approximate=True, uses the approximate formulation of GELU:

\[\mathrm{gelu}(x) = \frac{x}{2} \left(1 + \mathrm{tanh} \left( \sqrt{\frac{2}{\pi}} \left(x + 0.044715 x^3 \right) \right) \right)\]

For more information, see Gaussian Error Linear Units (GELUs), section 2.

  • x (Any) – input array

  • approximate (bool) – whether to use the approximate or exact formulation.

Return type:


bias_init(shape, dtype=<class 'jax.numpy.float64'>)#

An initializer that returns a constant array full of zeros.

The key argument is ignored.

>>> import jax, jax.numpy as jnp
>>> jax.nn.initializers.zeros(jax.random.PRNGKey(42), (2, 3), jnp.float32)
:rtype: :py:data:`~typing.Any`
Array([[0., 0., 0.],

[0., 0., 0.]], dtype=float32)

Return type:


distance(x, sdim, L)[source]#

Returns true if a PRNGSequence with name name exists.

Return type:



name (str) –


Returns True if running under self.init(…) or nn.init(…)().

This is a helper method to handle the common case of simple initialization where we wish to have setup logic occur when only called under module.init or nn.init. For more complicated multi-phase initialization scenarios it is better to test for the mutability of particular variable collections or for the presence of particular variables that potentially need to be initialized.

Return type:


kernel_init(shape, dtype=<class 'jax.numpy.float64'>)#
Return type:


lazy_init(rngs, *args, method=None, mutable=DenyList(deny='intermediates'), **kwargs)#

Initializes a module without computing on an actual input.

lazy_init will initialize the variables without doing unnecessary compute. The input data should be passed as a jax.ShapeDtypeStruct which specifies the shape and dtype of the input but no concrete data.


model = nn.Dense(features=256)
variables = model.lazy_init(rng, jax.ShapeDtypeStruct((1, 128), jnp.float32))

The args and kwargs args passed to lazy_init can be a mix of concrete (jax arrays, scalars, bools) and abstract (ShapeDtypeStruct) values. Concrete values are only necessary for arguments that affect the initialization of variables. For example, the model might expect a keyword arg that enables/disables a subpart of the model. In this case, an explicit value (True/Flase) should be passed otherwise lazy_init cannot infer which variables should be initialized.

  • rngs (Union[Any, Dict[str, Any]]) – The rngs for the variable collections.

  • *args – arguments passed to the init function.

  • method (Optional[Callable[..., Any]]) – An optional method. If provided, applies this method. If not provided, applies the __call__ method.

  • mutable (Union[bool, str, Collection[str], DenyList]) – Can be bool, str, or list. Specifies which collections should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. By default all collections except β€œintermediates” are mutable.

  • **kwargs – Keyword arguments passed to the init function.

Return type:

FrozenDict[str, Mapping[str, Any]]


The initialized variable dict.

params_init(shape, dtype=<class 'jax.numpy.float64'>)#

An initializer that returns a constant array full of ones.

The key argument is ignored.

>>> import jax, jax.numpy as jnp
>>> jax.nn.initializers.ones(jax.random.PRNGKey(42), (3, 2), jnp.float32)
Array([[1., 1.],
:rtype: :py:data:`~typing.Any`

[1., 1.], [1., 1.]], dtype=float32)

Return type:


perturb(name, value, collection='perturbations')#

Add an zero-value variable (β€˜perturbation’) to the intermediate value.

The gradient of value would be the same as the gradient of this perturbation variable. Therefore, if you define your loss function with both params and perturbations as standalone arguments, you can get the intermediate gradients of value by running jax.grad on the perturbation argument.

Note: this is an experimental API and may be tweaked later for better performance and usability. At its current stage, it creates extra dummy variables that occupies extra memory space. Use it only to debug gradients in training.


import jax
import jax.numpy as jnp
import flax.linen as nn

class Foo(nn.Module):
    def __call__(self, x):
        x = nn.Dense(3)(x)
        x = self.perturb('dense3', x)
        return nn.Dense(2)(x)

def loss(params, perturbations, inputs, targets):
  variables = {'params': params, 'perturbations': perturbations}
  preds = model.apply(variables, inputs)
  return jnp.square(preds - targets).mean()

x = jnp.ones((2, 9))
y = jnp.ones((2, 2))
model = Foo()
variables = model.init(jax.random.PRNGKey(0), x)
intm_grads = jax.grad(loss, argnums=1)(variables['params'], variables['perturbations'], x, y)
print(intm_grads['dense3']) # ==> [[-1.456924   -0.44332537  0.02422847]
                            #      [-1.456924   -0.44332537  0.02422847]]

If perturbations are not passed to apply, perturb behaves like a no-op so you can easily disable the behavior when not needed:

model.apply({'params': params, 'perturbations': perturbations}, x) # works as expected
model.apply({'params': params}, x) # behaves like a no-op
Return type:


  • name (str) –

  • value (T) –

  • collection (str) –

pooling(axis=None, dtype=None, out=None, keepdims=False, initial=None, where=None, promote_integers=True)#

Sum of array elements over a given axis.

LAX-backend implementation of numpy.sum().

Original docstring below.

  • a (array_like) – Elements to sum.

  • axis (None or int or tuple of ints, optional) – Axis or axes along which a sum is performed. The default, axis=None, will sum all of the elements of the input array. If axis is negative it counts from the last to the first axis.

  • dtype (dtype, optional) – The type of the returned array and of the accumulator in which the elements are summed. The dtype of a is used by default unless a has an integer dtype of less precision than the default platform integer. In that case, if a is signed then the platform integer is used while if a is unsigned then an unsigned integer of the same precision as the platform integer is used.

  • keepdims (bool, optional) –

    If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

    If the default value is passed, then keepdims will not be passed through to the sum method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.

  • initial (scalar, optional) – Starting value for the sum. See ~numpy.ufunc.reduce for details.

  • where (array_like of bool, optional) – Elements to include in the sum. See ~numpy.ufunc.reduce for details.

  • promote_integers (bool, default True) – If True, then integer inputs will be promoted to the widest available integer dtype, following numpy’s behavior. If False, the result will have the same dtype as the input. promote_integers is ignored if dtype is specified.

  • out (None) –


sum_along_axis – An array with the same shape as a, with the specified axis removed. If a is a 0-d array, or if axis is None, a scalar is returned. If an output array is specified, a reference to out is returned.

Return type:


put_variable(col, name, value)#

Updates the value of the given variable if it is mutable, or an error otherwise.

  • col (str) – the variable collection.

  • name (str) – the name of the variable.

  • value (Any) – the new value of the variable.

tabulate(rngs, *args, depth=None, show_repeated=False, mutable=True, console_kwargs=None, **kwargs)#

Creates a summary of the Module represented as a table.

This method has the same signature and internally calls Module.init, but instead of returning the variables, it returns the string summarizing the Module in a table. tabulate uses jax.eval_shape to run the forward computation without consuming any FLOPs or allocating memory.

Additional arguments can be passed into the console_kwargs argument, for example, {β€˜width’: 120}. For a full list of console_kwargs arguments, see:


import jax
import jax.numpy as jnp
import flax.linen as nn

class Foo(nn.Module):
    def __call__(self, x):
        h = nn.Dense(4)(x)
        return nn.Dense(2)(h)

x = jnp.ones((16, 9))

print(Foo().tabulate(jax.random.PRNGKey(0), x))

This gives the following output:

                                Foo Summary
┃ path    ┃ module ┃ inputs        ┃ outputs       ┃ params               ┃
β”‚         β”‚ Foo    β”‚ float32[16,9] β”‚ float32[16,2] β”‚                      β”‚
β”‚ Dense_0 β”‚ Dense  β”‚ float32[16,9] β”‚ float32[16,4] β”‚ bias: float32[4]     β”‚
β”‚         β”‚        β”‚               β”‚               β”‚ kernel: float32[9,4] β”‚
β”‚         β”‚        β”‚               β”‚               β”‚                      β”‚
β”‚         β”‚        β”‚               β”‚               β”‚ 40 (160 B)           β”‚
β”‚ Dense_1 β”‚ Dense  β”‚ float32[16,4] β”‚ float32[16,2] β”‚ bias: float32[2]     β”‚
β”‚         β”‚        β”‚               β”‚               β”‚ kernel: float32[4,2] β”‚
β”‚         β”‚        β”‚               β”‚               β”‚                      β”‚
β”‚         β”‚        β”‚               β”‚               β”‚ 10 (40 B)            β”‚
β”‚         β”‚        β”‚               β”‚         Total β”‚ 50 (200 B)           β”‚

                      Total Parameters: 50 (200 B)

Note: rows order in the table does not represent execution order, instead it aligns with the order of keys in variables which are sorted alphabetically.

  • rngs (Union[Any, Dict[str, Any]]) – The rngs for the variable collections as passed to Module.init.

  • *args – The arguments to the forward computation.

  • depth (Optional[int]) – controls how many submodule deep the summary can go. By default its None which means no limit. If a submodule is not shown because of the depth limit, its parameter count and bytes will be added to the row of its first shown ancestor such that the sum of all rows always adds up to the total number of parameters of the Module.

  • show_repeated (bool) – If True, repeated calls to the same module will be shown in the table, otherwise only the first call will be shown. Default is False.

  • mutable (Union[bool, str, Collection[str], DenyList]) – Can be bool, str, or list. Specifies which collections should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. By default all collections except β€˜intermediates’ are mutable.

  • console_kwargs (Optional[Mapping[str, Any]]) – An optional dictionary with additional keyword arguments that are passed to rich.console.Console when rendering the table. Default arguments are {β€˜force_terminal’: True, β€˜force_jupyter’: False}.

  • **kwargs – keyword arguments to pass to the forward computation.

Return type:



A string summarizing the Module.


Returns an unbound copy of a Module and its variables.

unbind helps create a stateless version of a bound Module.

An example of a common use case: to extract a sub-Module defined inside setup() and its corresponding variables: 1) temporarily bind the parent Module; and then 2) unbind the desired sub-Module. (Recall that setup() is only called when the Module is bound.):

class AutoEncoder(nn.Module):
  def setup(self):
    self.encoder = Encoder()
    self.decoder = Decoder()

  def __call__(self, x):
    return self.decoder(self.encoder(x))

module = AutoEncoder()
variables = module.init(jax.random.PRNGKey(0), jnp.ones((1, 784)))
# Extract the Encoder sub-Module and its variables
encoder, encoder_vars = module.bind(variables).encoder.unbind()
Return type:

Tuple[TypeVar(M, bound= Module), Mapping[str, Mapping[str, Any]]]


A tuple with an unbound copy of this Module and its variables.


self (M) –