netket.models.DeepSetRelDistance

class netket.models.DeepSetRelDistance

Bases: flax.linen.module.Module

Implements an equivariant version of the DeepSets architecture given by (https://arxiv.org/abs/1703.06114)

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

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 (https://arxiv.org/abs/2112.11957):

\[\psi(x_1,...,x_N) = \rho\left(\sum_i \phi(d_{\sin}(x_i,x_j))\right) \cdot \exp\left[-\frac{1}{2}\left(b/d_{\sin}(x_i,x_j)\right)^5\right]\]

Attributes

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.

variables

Returns the variables in this module.

Return type

Mapping[str, Mapping[str, Any]]

hilbert: netket.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.

Methods

activation(approximate=True)

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.

Parameters

• x (Any) – input array

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

Return type

Any

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

Return type

Any

Parameters

• key (jax._src.prng.PRNGKeyArray) –

• shape (Sequence[Union[int, Any]]) –

• dtype (Any) –

distance(x, sdim, L)

has_rng(name)

Returns true if a PRNGSequence with name name exists.

Return type

bool

Parameters

name (str) –

is_initializing()

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

bool

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

Return type

Any

Parameters

• key (jax._src.prng.PRNGKeyArray) –

• shape (Sequence[Union[int, Any]]) –

• dtype (Any) –

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

Return type

Any

Parameters

• key (jax._src.prng.PRNGKeyArray) –

• shape (Sequence[Union[int, Any]]) –

• dtype (Any) –

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

Add an zero-value variable (‘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.

Example:

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

class Foo(nn.Module):
    @nn.compact
    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]]

Return type

TypeVar(T)

Parameters

• name (str) –

• value (flax.linen.module.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.

Parameters

• 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) –

Returns

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

ndarray

put_variable(col, name, value)

Sets the value of a Variable.

Parameters

• col (str) – the variable collection.

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

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

Returns:

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.

Example:

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

class Foo(nn.Module):
    @nn.compact
    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               ┃
┡━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩
│         │ Foo    │ float32[16,9] │ float32[16,2] │                      │
├─────────┼────────┼───────────────┼───────────────┼──────────────────────┤
│ Dense_0 │ Dense  │ float32[16,9] │ float32[16,4] │ bias: float32[4]     │
│         │        │               │               │ kernel: float32[9,4] │
│         │        │               │               │                      │
│         │        │               │               │ 40 (160 B)           │
├─────────┼────────┼───────────────┼───────────────┼──────────────────────┤
│ Dense_1 │ Dense  │ float32[16,4] │ float32[16,2] │ bias: float32[2]     │
│         │        │               │               │ kernel: float32[4,2] │
│         │        │               │               │                      │
│         │        │               │               │ 10 (40 B)            │
├─────────┼────────┼───────────────┼───────────────┼──────────────────────┤
│         │        │               │         Total │ 50 (200 B)           │
└─────────┴────────┴───────────────┴───────────────┴──────────────────────┘

                      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.

Parameters

• 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 ‘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 {‘force_terminal’: True, ‘force_jupyter’: False}.

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

Return type

str

Returns

A string summarizing the Module.