MatMul#

parametricmatrixmodels.modules.MatMul

class MatMul(params=None, output_shape=None, path_order=None, trainable=False, init_magnitude=0.01, real=True, separator='.')[source]#

Bases: Einsum

Module for optionally trainable matrix multiplication. Just a special case of Einsum. Computes the matrix multiplication of all leaves in an input PyTree with an optional trainable or fixed matrix.

I.e. for a PyTree input with matrix leaves (A, B, C), and an optional trainable or fixed parameter matrix M, the output will be the single array M @ A @ B @ C

The order of the multiplication can be changed by providing the paths of each matrix in the parameter path_order. Paths are period-separated strings of keys/indices to reach each matrix in the input PyTree. A double period .. indicates the trainable/fixed parameter matrix if applicable.

The final input array may be a vector instead of a matrix.

All operations are applied over the batch dimension.

Examples

To create a module that takes a single vector input (ignoring batch dim) and multiplies it by a trainable weight matrix:

>>> m = MatMul(output_shape=2, trainable=True)
>>> m(np.ones((batch_dim, 4))) # vec of size 4 in, vec of size 2 out

To create a module that multiplies two input matrices together in an order different from the default:

>>> input_data = {
...     'x': np.ones((batch_dim, 3, 4)),
...     'y': [np.ones((batch_dim, 5, 3)),],
... }
>>> m = MatMul(path_order=['y.0', 'x'])

Parameters:

params (Inexact[Array, '...'] | None)
output_shape (Tuple[int] | Tuple[None, int] | Tuple[int, int] | Tuple[int, None] | int | None)
path_order (List[str] | None)
trainable (bool)
init_magnitude (float)
real (bool)
separator (str)

__init__(params=None, output_shape=None, path_order=None, trainable=False, init_magnitude=0.01, real=True, separator='.')[source]#

Initialize the MatMul module.

Parameters:

params (Inexact[Array, '...'] | None) – The parameter matrix to use for multiplication. If None and trainable is False (the default), then no parameter matrix is used. If None and trainable is True, then a randomly initialized trainable matrix is created during compilation.
output_shape (tuple[int] | tuple[None, int] | tuple[int, int] | tuple[int, None] | int | None) – The shape of the output matrix/vector (excluding batch dimension). If an integer is provided, it is treated as the size of a vector output. If None (the default), the output size is inferred during compilation based on the input shapes and the parameter matrix shape if applicable. Can be a tuple with None in one position to indicate that the size in that dimension should be inferred.
path_order (list[str] | None) – A list of period-separated strings indicating the order of the PyTree paths to multiply. A double separator .. indicates the position of the parameter matrix if applicable. If None (the default), the order of the matrices is the parameter matrix (if applicable) followed by the input PyTree leaves in the order returned by jax.tree.leaves. See jax.tree_util.keystr for more details on path strings.
trainable (bool) – Whether the params is trainable.
init_magnitude (float) – The magnitude of the random initialization for the trainable matrix if applicable.
real (bool) – Whether to use real or complex parameters for the trainable matrix if applicable.
separator (str) – The separator to use for path strings. Default is period (‘.’).

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()#

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:

Callable[[PyTree[jaxtyping.Inexact[Array, ’…’], ’Params’], PyTree[jaxtyping.Inexact[Array, ‘batch_size …’]] | Inexact[Array, ‘batch_size …’], bool, PyTree[jaxtyping.Num[Array, ’*?d’], ’State’], Any], tuple[PyTree[jaxtyping.Inexact[Array, ‘batch_size …’]] | Inexact[Array, ‘batch_size …’], PyTree[jaxtyping.Num[Array, ’*?d’], ’State’]]]

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.

_get_concrete_einsum_str(input_shape)#

Get the concrete einsum string by parsing the provided einsum string, adding batch indices and inferring any missing output indices. To account for batch dimensions. If the einsum string is a PyTree, it must have the same structure as the input data.

Parameters:: input_shape (PyTree[tuple[int | None, ...]] | tuple[int | None, ...]) – The shape of the input data, used to infer any missing output indices as well as validate existing indices. Should not include the batch dimension.
Return type:: str

Examples

>>> m = Einsum("ij,jk->ik")
>>> m._get_concrete_einsum_str(((2, 3), (3, 4)))
'aij,ajk->aik' # leading index 'a' added for batch dimension

>>> m = Einsum((('ij', 'jk'), 'ik'))
>>> m._get_concrete_einsum_str(((2, 3), (3, 4)))
'aij,ajk->aik'

>>> m = Einsum("ab,bc->ac")
>>> m._get_concrete_einsum_str(((5, 2), (2, 4)))
'dab,dbc->dac' # leading index 'd' added for batch dimension

>>> m = Einsum((['ij', 'jk'], 'ik'))
>>> m._get_concrete_einsum_str(((2, 3), (3, 4)))
ValueError: The structure of the einsum_str PyTree must match that
of the input data.
# (since the input data is a Tuple of two arrays, not a List)

>>> m = Einsum(('ij,jk', {'x': 'ik', 'y': 'ab'}, 'ab'))
>>> m._get_concrete_einsum_str({'x': (2, 3), 'y': (3, 4)})
'ij,jk,cik,cab->cab' # leading arrays don't have batch index
# all arrays from PyTrees are inserted in the same order as the
# list from jax.tree.leaves(...)

_get_dimension_map(concrete_einsum_str, input_shape)#

Fill in the dimension map by inferring sizes from the input shapes and parameter shapes based on the provided concrete einsum string and self.params if applicable.

Parameters:

concrete_einsum_str (str) – The concrete einsum string with all indices specified, including the output indices and batch index.
input_shape (PyTree[tuple[int | None, ...]] | tuple[int | None, ...]) – The shape of the input data, used to infer dimension sizes. Should not include the batch dimension.

Returns:

A complete dimension map with sizes for all indices in the
einsum string.

Return type:

dict[str, int]

_get_einsum_str_and_dim_map(input_shape)[source]#

Parameters:: input_shape (pmm.typing.DataShape)
Return type:: tuple[str, dict[str, int]]

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()#

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()#

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:

PyTree[jaxtyping.Inexact[Array, ’…’], ’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()#

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)#

Set the trainable parameters of the module.

Parameters:: params (PyTree[jaxtyping.Inexact[Array, '...'], '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.

MatMul#

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