TransitionAmplitudeSum#

parametricmatrixmodels.modules.TransitionAmplitudeSum

class TransitionAmplitudeSum(num_observables=None, output_size=None, Ds=None, init_magnitude=0.01, centered=True)[source]#

Bases: BaseModule

A module that computes the sum of transition amplitudes of trainable observables given an input of state vectors. The output can be centered by subtracting half the operator norm squared of each observable.

To produce \(q\) output values, given a single input of \(r\) state vectors of size \(n\) (shape (n, r)), denoted by \(v_i\), \(i=1, \ldots, r\), this module uses \(q\times l\) trainable observables \(D_{11}, D_{12}, \ldots, D_{1l}, D_{21}, \ldots, D_{ql}\) (each of shape (n, n)) to compute the output:

\[\begin{split}z_k = \sum_{i,j=1}^r &\left( \sum_{m=1}^l |v_i^H D_{km} v_j|^2\\ &\quad - \frac{1}{2} ||D_{km}||^2_2 \right)\end{split}\]

for \(k=1, \ldots, q\). This is equivalent to

\[\begin{split}z_k &= \sum_{m=1}^l \left( \sum_{i,j=1}^r \left( |v_i^H D_{km} v_j|^2 \right)\\ &\quad - \frac{r^2}{2} ||D_{km}||^2_2 \right)\end{split}\]

where \(||\cdot||_2\) is the operator 2-norm (largest singular value) so for Hermitian \(D\), \(||D||_2\) is the largest absolute eigenvalue.

The \(-\frac{1}{2} ||D_{km}||^2_2\) term centers the value of each term and can be disabled by setting the centered parameter to False.

Warning

This module assumes that the input state vectors are normalized. If they are not, the output values will be scaled by the square of the norm of the input vectors.

Warning

Even though the math shows that the centering term should be multiplied by \(r^2\), in practice this doesn’t work well and instead setting the centering term to \(\frac{1}{2} ||D_{km}||^2_2\) works much better. This non-\(r^2\) scaling is used here.

See also

ExpectationValueSum: A similar module that computes the sum of expectation values (instead of transition amplitudes) of trainable observables.
LowRankTransitionAmplitudeSum: A similar module that uses low-rank observables to reduce the number of trainable parameters.

Parameters:

num_observables (int | None)
output_size (int | None)
Ds (Inexact[Array, 'q l n n'] | None)
init_magnitude (float)
centered (bool)

__init__(num_observables=None, output_size=None, Ds=None, init_magnitude=0.01, centered=True)[source]#

Initialize the module.

Parameters:

num_observables (int | None) – Number of observable matrices, shorthand \(l\).
output_size (int | None) – Number of output features, shorthand \(q\).
Ds (Inexact[Array, 'q l n n'] | None) – Optional 4D array of matrices \(D_{ql}\) that define the observables. Each \(D\) must be Hermitian. If not provided, the observables will be randomly initialized when the module is compiled.
init_magnitude (float) – Initial magnitude for the random matrices if Ms is not provided. Default 1e-2.
centered (bool) – Whether to center the output by subtracting half the operator norm squared of each observable. Default True.

Return type:

None

`__call__`	Call the module with the current parameters and given input, state, and rng.
`_get_callable`	Returns a `jax.jit`-able and `jax.grad`-able callable that represents the module's forward pass.
`astype`	Convenience wrapper to set_precision using the dtype argument, returns self.
`compile`	Compile the module to be used with the given input shape.
`deserialize`	Deserialize the module from a dictionary.
`get_hyperparameters`	Get the hyperparameters of the module.
`get_num_trainable_floats`	Returns the number of trainable floats in the module.
`get_output_shape`	Get the output shape of the module given the input shape.
`get_params`	Get the current trainable parameters of the module.
`get_state`	Get the current state of the module.
`is_ready`	Return True if the module is initialized and ready for training or inference.
`serialize`	Serialize the module to a dictionary.
`set_hyperparameters`	Set the hyperparameters of the module.
`set_params`	Set the trainable parameters of the module.
`set_precision`	Set the precision of the module parameters and state.
`set_state`	Set the state of the module.

name

Returns the name of the module, unless overridden, this is the class name.

__call__(data, /, *, training=False, state=(), rng=None)#

Call the module with the current parameters and given input, state, and rng.

Parameters:

data (pmm.typing.Data) – PyTree of input arrays of shape (num_samples, …). Only the first dimension (num_samples) is guaranteed to be the same for all input arrays.
training (bool) – Whether the module is in training mode, by default False.
state (pmm.typing.State) – State of the module, by default ().
rng (Any) – JAX random key, by default None.

Returns:

Output array of shape (num_samples, num_output_features) and new
state.

Raises:

ValueError – If the module is not ready (i.e., compile() has not been called).

Return type:

tuple[TypeAliasForwardRef(’pmm.typing.Data’), TypeAliasForwardRef(’pmm.typing.State’)]

See also

_get_callable: Returns a callable that can be used to compute the output and new state given the parameters, input, training flag, state, and rng.
Params: Typing for the module parameters.
Data: Typing for the input and output data.
State: Typing for the module state.

_get_callable()[source]#

Returns a jax.jit-able and jax.grad-able callable that represents the module’s forward pass.

This method must be implemented by all subclasses and must return a jax-jit-able and jax-grad-able callable in the form of

module_callable(
    params: parametricmatrixmodels.typing.Params,
    data: parametricmatrixmodels.typing.Data,
    training: bool,
    state: parametricmatrixmodels.typing.State,
    rng: Any,
) -> (
    output: parametricmatrixmodels.typing.Data,
    new_state: parametricmatrixmodels.typing.State,
    )

That is, all hyperparameters are traced out and the callable depends explicitly only on

the module’s parameters, as a PyTree with leaf nodes as JAX arrays,
the input data, as a PyTree with leaf nodes as JAX arrays, each of
which has shape (num_samples, …),
the training flag, as a boolean,
the module’s state, as a PyTree with leaf nodes as JAX arrays

and returns

the output data, as a PyTree with leaf nodes as JAX arrays, each of
which has shape (num_samples, …),
the new module state, as a PyTree with leaf nodes as JAX arrays. The
PyTree structure must match that of the input state and additionally all leaf nodes must have the same shape as the input state leaf nodes.

The training flag will be traced out, so it doesn’t need to be jittable

Returns:

A callable that takes the module’s parameters, input data,
training flag, state, and rng key and returns the output data and
new state.

Raises:

NotImplementedError – If the method is not implemented in the subclass.

Return type:

pmm.typing.ModuleCallable

See also

__call__: Calls the module with the current parameters and given input, state, and rng.
ModuleCallable: Typing for the callable returned by this method.
Params: Typing for the module parameters.
Data: Typing for the input and output data.
State: Typing for the module state.

astype(dtype, /)#

Convenience wrapper to set_precision using the dtype argument, returns self.

Parameters:

dtype (str | type[Any] | dtype | SupportsDType) – Precision to set for the module parameters. Valid options are: For 32-bit precision (all options are equivalent) np.float32, np.complex64, "float32", "complex64", "single", "f32", "c64", 32 For 64-bit precision (all options are equivalent) np.float64, np.complex128, "float64", "complex128", "double", "f64", "c128", 64

Returns:

BaseModule – The module itself, with updated precision.

Raises:

ValueError – If the precision is invalid or if 64-bit precision is requested but JAX_ENABLE_X64 is not set.
RuntimeError – If the module is not ready (i.e., compile() has not been called).

Return type:

BaseModule

See also

set_precision: Sets the precision of the module parameters and state.

compile(rng, input_shape)[source]#

Compile the module to be used with the given input shape.

This method initializes the module’s parameters and state based on the input shape and random key.

This is needed since Model s are built before the input data is given, so before training or inference can be done, the module needs to be compiled and each module passes its output shape to the next module’s compile method.

The RNG key is used to initialize random parameters, if needed.

This is not used to trace or jit the module’s callable, that is done automatically later.

Parameters:

rng (Any) – JAX random key.
input_shape (pmm.typing.DataShape) – PyTree of input shape tuples, e.g. ((num_features,),), to compile the module for. All data passed to the module later must have the same PyTree structure and shape in all leaf array dimensions except the leading batch dimension.

Raises:

NotImplementedError – If the method is not implemented in the subclass.

Return type:

None

See also

DataShape: Typing for the input shape.
get_output_shape: Get the output shape of the module

deserialize(data, /)#

Deserialize the module from a dictionary.

This method sets the module’s parameters and state based on the provided dictionary.

The default implementation expects the dictionary to contain the module’s name, trainable parameters, and state.

Parameters:: data (dict[str, Any]) – Dictionary containing the serialized module data.
Raises:: ValueError – If the serialized data does not contain the expected keys or if the version of the serialized data is not compatible with with the current package version.
Return type:: None

get_hyperparameters()[source]#

Get the hyperparameters of the module.

Hyperparameters are used to configure the module and are not trainable. They can be set via set_hyperparameters.

Returns:: Dictionary containing the hyperparameters of the module.
Return type:: pmm.typing.HyperParams

See also

set_hyperparameters: Set the hyperparameters of the module.
HyperParams: Typing for the hyperparameters. Simply an alias for Dict[str, Any].

get_num_trainable_floats()[source]#

Returns the number of trainable floats in the module. If the module does not have trainable parameters, returns 0. If the module is not ready, returns None.

Returns:

Number of trainable floats in the module, or None if the module
is not ready.

Return type:

int | None

get_output_shape(input_shape)[source]#

Get the output shape of the module given the input shape.

Parameters:

input_shape (pmm.typing.DataShape) – PyTree of input shape tuples, e.g. ((num_features,),), to get the output shape for.

Returns:

PyTree of output shape tuples, e.g. ((num_output_features,),),
corresponding to the output shape of the module for the given
input shape.

Raises:

NotImplementedError – If the method is not implemented in the subclass.

Return type:

pmm.typing.DataShape

See also

DataShape: Typing for the input and output shape.

get_params()[source]#

Get the current trainable parameters of the module. If the module has no trainable parameters, this method should return an empty tuple.

Returns:

PyTree with leaf nodes as JAX arrays representing the module’s
trainable parameters.

Raises:

NotImplementedError – If the method is not implemented in the subclass.

Return type:

pmm.typing.Params

See also

set_params: Set the trainable parameters of the module.
Params: Typing for the module parameters.

get_state()#

Get the current state of the module.

States are used to store “memory” or other information that is not passed between modules, is not trainable, but may be updated during either training or inference. e.g. batch normalization state.

The state is optional, in which case this method should return the empty tuple.

Returns:

PyTree with leaf nodes as JAX arrays representing the module’s
state.

Return type:

pmm.typing.State

See also

set_state: Set the state of the module.
State: Typing for the module state.

is_ready()[source]#

Return True if the module is initialized and ready for training or inference.

Returns:: True if the module is ready, False otherwise.
Raises:: NotImplementedError – If the method is not implemented in the subclass.
Return type:: bool

property name: str#

Returns the name of the module, unless overridden, this is the class name.

Returns:: Name of the module.

serialize()#

Serialize the module to a dictionary.

This method returns a dictionary representation of the module, including its parameters and state.

The default implementation serializes the module’s name, hyperparameters, trainable parameters, and state via a simple dictionary.

This only works if the module’s hyperparameters are auto-serializable. This includes basic types as well as numpy arrays.

Returns:: Dictionary containing the serialized module data.
Return type:: dict[str, Any]

set_hyperparameters(hyperparams)[source]#

Set the hyperparameters of the module.

Hyperparameters are used to configure the module and are not trainable. They can be set via this method.

The default implementation uses setattr to set the hyperparameters as attributes of the class instance.

Parameters:

hyperparameters – Dictionary containing the hyperparameters to set.
hyperparams (pmm.typing.HyperParams)

Raises:

TypeError – If hyperparameters is not a dictionary.

Return type:

None

See also

get_hyperparameters: Get the hyperparameters of the module.
HyperParams: Typing for the hyperparameters. Simply an alias for Dict[str, Any].

set_params(params)[source]#

Set the trainable parameters of the module.

Parameters:: params (pmm.typing.Params) – PyTree with leaf nodes as JAX arrays representing the new trainable parameters of the module.
Raises:: NotImplementedError – If the method is not implemented in the subclass.
Return type:: None

See also

get_params: Get the trainable parameters of the module.
Params: Typing for the module parameters.

set_precision(prec, /)#

Set the precision of the module parameters and state.

Parameters:

prec (Any | str | int) – Precision to set for the module parameters. Valid options are: For 32-bit precision (all options are equivalent) np.float32, np.complex64, "float32", "complex64", "single", "f32", "c64", 32. For 64-bit precision (all options are equivalent) np.float64, np.complex128, "float64", "complex128", "double", "f64", "c128", 64.

Raises:

ValueError – If the precision is invalid or if 64-bit precision is requested but JAX_ENABLE_X64 is not set.
RuntimeError – If the module is not ready (i.e., compile() has not been called).

Return type:

None

See also

astype: Convenience wrapper to set_precision using the dtype argument, returns self.

set_state(state, /)#

Set the state of the module.

This method is optional.

Parameters:: state (pmm.typing.State) – PyTree with leaf nodes as JAX arrays representing the new state of the module.
Return type:: None

See also

get_state: Get the state of the module.
State: Typing for the module state.

TransitionAmplitudeSum#

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