nn.modules.Linear

class nn.modules.Linear(*args, **kwargs)

Bases: LinearMixin, Module

Encapsulates a linear weight matrix

Attributes overview

class_name	Class name of self
full_name	The full name of this module (class plus module name)
name	The name of this module, or an empty string if None
shape	The shape of this module
size	(DEPRECATED) The output size of this module
size_in	The input size of this module
size_out	The output size of this module
spiking_input	If True, this module receives spiking input.
spiking_output	If True, this module sends spiking output.
weight	Weight matrix of this module
bias	Bias vector of this module

Methods overview

__init__(shape[, weight, bias, has_bias, ...])	Encapsulate a linear weight matrix, with optional biases
as_graph()	Convert this module to a computational graph
attributes_named(name)	Search for attributes of this or submodules by time
evolve(input_data[, record])	Evolve the state of this module over input data
from_graph(graph)	from_graph constructs a LinearMixin object from the comptutational graph
modules()	Return a dictionary of all sub-modules of this module
parameters([family])	Return a nested dictionary of module and submodule Parameters
reset_parameters()	Reset all parameters in this module
reset_state()	Reset the state of this module
set_attributes(new_attributes)	Set the attributes and sub-module attributes from a dictionary
simulation_parameters([family])	Return a nested dictionary of module and submodule SimulationParameters
state([family])	Return a nested dictionary of module and submodule States
timed([output_num, dt, add_events])	Convert this module to a TimedModule

__init__(shape: tuple, weight=None, bias=None, has_bias: bool = False, weight_init_func: ~typing.Callable = <function kaiming>, bias_init_func: ~typing.Callable = <function uniform_sqrt>, *args, **kwargs)

Encapsulate a linear weight matrix, with optional biases

Linear wraps a single weight matrix, and passes data through by using the matrix as a set of weights. The shape of the matrix must be specified as a tuple (Nin, Nout). Linear provides optional biases.

A weight initialisation function may be specified. By default the weights will use Kaiming initialisation (kaiming()).

A bias initialisation function may be specified, if used. By default the biases will be initialised as uniform random over the range \((-\sqrt(1/N), \sqrt(1/N))\).

Warning

Standard DNN libraries by default include a bias on linear layers. These are usually not used for SNNs, where the bias is configured on the spiking neuron module. Linear layers in Rockpool use a default of has_bias = False. You can force the presence of a bias on the linear layer with has_bias = True on initialisation.

Examples

Build a linear weight matrix with shape (3, 4), and no biases:

>>> Linear((3, 4))
Linear  with shape (3, 4)

Build a linear weight matrix with shape (2, 5), which will be initialised with zeros:

>>> Linear((2, 5), weight_init_func = lambda s: np.zeros(s))
Linear  with shape (2, 5)

Provide a concrete initialisation for the linear weights:

>>> Linear((2, 2), weight = np.array([[1, 2], [3, 4]]))
Linear  with shape (2, 2)

Build a linear layer including biases:

>>> mod = Linear((2, 2), has_bias = True)
>>> mod.parameters()
Out:
{'weight': array([[ 0.56655314,  0.64411151],
        [-1.43016068, -1.538719  ]]),
 'bias': array([-0.58513867, -0.32314069])}

Parameters:

• shape (tuple) – The desired shape of the weight matrix. Must have two entries (Nin, Nout)

• weight_init_func (Callable) – The initialisation function to use for the weights. Default: Kaiming initialization; uniform on the range \((-\sqrt(6/Nin), \sqrt(6/Nin))\)

• weight (Optional[np.array]) – A concrete weight matrix to assign to the weights on initialisation. weight.shape must match the shape argument

• has_bias (bool) – A boolean flag indicating that this linear layer should have a bias parameter. Default: False, no bias parameter

• bias_init_func (Callable) – The initialisation function to use for the biases. Default: Uniform / sqrt(N); uniform on the range \((-\sqrt(1/N), \sqrt(1/N))\)

• bias (Optional[np.array]) – A concrete bias vector to assign to the biases on initialisation. bias.shape must be (N,)

_abc_impl = <_abc._abc_data object>

_auto_batch(data: ndarray, states: Tuple = (), target_shapes: Tuple | None = None) → Tuple[ndarray, Tuple[ndarray]]

Automatically replicate states over batches and verify input dimensions

Examples

>>> data, (state0, state1, state2) = self._auto_batch(data, (self.state0, self.state1, self.state2))

This will verify that data has the correct final dimension (i.e. self.size_in).

If data has only two dimensions (T, Nin), then it will be augmented to (1, T, Nin). The individual states will be replicated out from shape (a, b, c, ...) to (n_batches, a, b, c, ...) and returned.

If data has only a single dimension (T,), it will be expanded to (1, T, self.size_in).

state0, state1, state2 will be replicated out along the batch dimension.

>>> data, (state0,) = self._auto_batch(data, (self.state0,), ((10, -1, self.size_in),))

Attempt to replicate state0 to a specified size (10, -1, self.size_in).

Parameters:

• data (np.ndarray) – Input data tensor. Either (batches, T, Nin) or (T, Nin)

• states (Tuple) – Tuple of state variables. Each will be replicated out over batches by prepending a batch dimension

• target_shapes (Tuple) – A tuple of target size tuples, each corresponding to each state argument. The individual states will be replicated out to match the corresponding target sizes. If not provided (the default), then states will be only replicated along batches.

Returns:

(np.ndarray, Tuple[np.ndarray]) data, states

static _dot()

dot(a, b, out=None)

Dot product of two arrays. Specifically,

• If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).

• If both a and b are 2-D arrays, it is matrix multiplication, but using matmul() or a @ b is preferred.

• If either a or b is 0-D (scalar), it is equivalent to multiply() and using numpy.multiply(a, b) or a * b is preferred.

• If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

• If a is an N-D array and b is an M-D array (where M>=2), it is a sum product over the last axis of a and the second-to-last axis of b:

  dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
  

It uses an optimized BLAS library when possible (see numpy.linalg).

Parameters:

• a (array_like) – First argument.

• b (array_like) – Second argument.

• out (ndarray, optional) – Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.

Returns:

output – Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.

Return type:

ndarray

Raises:

ValueError – If the last dimension of a is not the same size as the second-to-last dimension of b.

See also

vdot

Complex-conjugating dot product.

tensordot

Sum products over arbitrary axes.

einsum

Einstein summation convention.

matmul

‘@’ operator as method with out parameter.

linalg.multi_dot

Chained dot product.

Examples

>>> np.dot(3, 4)
12

Neither argument is complex-conjugated:

>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)

For 2-D arrays it is the matrix product:

>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
       [2, 2]])

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128

_force_set_attributes

(bool) If True, do not sanity-check attributes when setting.

_get_attribute_family(type_name: str, family: Tuple | List | str | None = None) → dict

Search for attributes of this module and submodules that match a given family

This method can be used to conveniently get all weights for a network; or all time constants; or any other family of parameters. Parameter families are defined simply by a string: "weights" for weights; "taus" for time constants, etc. These strings are arbitrary, but if you follow the conventions then future developers will thank you (that includes you in six month’s time).

Parameters:

• type_name (str) – The class of parameters to search for. Must be one of ["Parameter", "SimulationParameter", "State"] or another future subclass of ParameterBase

• family (Union[str, Tuple[str]]) – A string or list or tuple of strings, that define one or more attribute families to search for

Returns:

A nested dictionary of attributes that match the provided type_name and family

Return type:

dict

_get_attribute_registry() → Tuple[Dict, Dict]

Return or initialise the attribute registry for this module

Returns:

registered_attributes, registered_modules

Return type:

(tuple)

_has_registered_attribute(name: str) → bool

Check if the module has a registered attribute

Parameters:

name (str) – The name of the attribute to check

Returns:

True if the attribute name is in the attribute registry, False otherwise.

Return type:

bool

_in_Module_init

(bool) If exists and True, indicates that the module is in the __init__ chain.

_name: str | None

Name of this module, if assigned

_register_attribute(name: str, val: ParameterBase)

Record an attribute in the attribute registry

Parameters:

• name (str) – The name of the attribute to register

• val (ParameterBase) – The ParameterBase subclass object to register. e.g. Parameter, SimulationParameter or State.

_register_module(name: str, mod: ModuleBase)

Register a sub-module in the module registry

Parameters:

• name (str) – The name of the module to register

• mod (ModuleBase) – The ModuleBase object to register

_reset_attribute(name: str) → ModuleBase

Reset an attribute to its initialisation value

Parameters:

name (str) – The name of the attribute to reset

Returns:

For compatibility with the functional API

Return type:

self (Module)

_shape

The shape of this module

_spiking_input: bool

Whether this module receives spiking input

_spiking_output: bool

Whether this module produces spiking output

_submodulenames: List[str]

Registry of sub-module names

_wrap_recorded_state(recorded_dict: dict, t_start: float) → Dict[str, TimeSeries]

Convert a recorded dictionary to a TimeSeries representation

This method is optional, and is provided to make the timed() conversion to a TimedModule work better. You should override this method in your custom Module, to wrap each element of your recorded state dictionary as a TimeSeries

Parameters:

• state_dict (dict) – A recorded state dictionary as returned by evolve()

• t_start (float) – The initial time of the recorded state, to use as the starting point of the time series

Returns:

The mapped recorded state dictionary, wrapped as TimeSeries objects

Return type:

Dict[str, TimeSeries]

as_graph() → GraphModuleBase

Convert this module to a computational graph

Returns:

The computational graph corresponding to this module

Return type:

GraphModuleBase

Raises:

NotImplementedError – If as_graph() is not implemented for this subclass

attributes_named(name: Tuple[str] | List[str] | str) → dict

Search for attributes of this or submodules by time

Parameters:

name (Union[str, Tuple[str]) – The name of the attribute to search for

Returns:

A nested dictionary of attributes that match name

Return type:

dict

bias

Bias vector of this module

property class_name: str

Class name of self

Type:

str

evolve(input_data, record: bool = False) → Tuple[Any, Any, Any]

Evolve the state of this module over input data

NOTE: THIS MODULE CLASS DOES NOT PROVIDE DOCUMENTATION FOR ITS EVOLVE METHOD. PLEASE UPDATE THE DOCUMENTATION FOR THIS MODULE.

Parameters:

• input_data – The input data with shape (T, size_in) to evolve with

• record (bool) – If True, the module should record internal state during evolution and return the record. If False, no recording is required. Default: False.

Returns:

(output, new_state, record)

output (np.ndarray): The output response of this module with shape (T, size_out) new_state (dict): A dictionary containing the updated state of this and all submodules after evolution record (dict): A dictionary containing recorded state of this and all submodules, if requested using the record argument

Return type:

tuple

classmethod from_graph(graph: LinearWeights) → LinearMixin

from_graph constructs a LinearMixin object from the comptutational graph

Parameters:

graph (LinearWeights) – the reference computational graph to restore computational module

Returns:

a LinearMixin object

Return type:

LinearMixin

property full_name: str

The full name of this module (class plus module name)

Type:

str

modules() → Dict

Return a dictionary of all sub-modules of this module

Returns:

A dictionary containing all sub-modules. Each item will be named with the sub-module name.

Return type:

dict

property name: str

The name of this module, or an empty string if None

Type:

str

parameters(family: Tuple | List | str | None = None) → Dict

Return a nested dictionary of module and submodule Parameters

Use this method to inspect the Parameters from this and all submodules. The optional argument family allows you to search for Parameters in a particular family — for example "weights" for all weights of this module and nested submodules.

Although the family argument is an arbitrary string, reasonable choises are "weights", "taus" for time constants, "biases" for biases…

Examples

Obtain a dictionary of all Parameters for this module (including submodules):

>>> mod.parameters()
dict{ ... }

Obtain a dictionary of Parameters from a particular family:

>>> mod.parameters("weights")
dict{ ... }

Parameters:

family (str) – The family of Parameters to search for. Default: None; return all parameters.

Returns:

A nested dictionary of Parameters of this module and all submodules

Return type:

dict

reset_parameters()

Reset all parameters in this module

Returns:

The updated module is returned for compatibility with the functional API

Return type:

Module

reset_state() → ModuleBase

Reset the state of this module

Returns:

The updated module is returned for compatibility with the functional API

Return type:

Module

set_attributes(new_attributes: dict) → ModuleBase

Set the attributes and sub-module attributes from a dictionary

This method can be used with the dictionary returned from module evolution to set the new state of the module. It can also be used to set multiple parameters of a module and submodules.

Examples

Use the functional API to evolve, obtain new states, and set those states:

>>> _, new_state, _ = mod(input)
>>> mod = mod.set_attributes(new_state)

Obtain a parameter dictionary, modify it, then set the parameters back:

>>> params = mod.parameters()
>>> params['w_input'] *= 0.
>>> mod.set_attributes(params)

Parameters:

new_attributes (dict) – A nested dictionary containing parameters of this module and sub-modules.

property shape: tuple

The shape of this module

Type:

tuple

simulation_parameters(family: Tuple | List | str | None = None) → Dict

Return a nested dictionary of module and submodule SimulationParameters

Use this method to inspect the SimulationParameters from this and all submodules. The optional argument family allows you to search for SimulationParameters in a particular family.

Examples

Obtain a dictionary of all SimulationParameters for this module (including submodules):

>>> mod.simulation_parameters()
dict{ ... }

Parameters:

family (str) – The family of SimulationParameters to search for. Default: None; return all SimulationParameter attributes.

Returns:

A nested dictionary of SimulationParameters of this module and all submodules

Return type:

dict

property size: int

(DEPRECATED) The output size of this module

Type:

int

property size_in: int

The input size of this module

Type:

int

property size_out: int

The output size of this module

Type:

int

property spiking_input: bool

If True, this module receives spiking input. If False, this module expects continuous input.

Type:

bool

property spiking_output

If True, this module sends spiking output. If False, this module sends continuous output.

Type:

bool

state(family: Tuple | List | str | None = None) → Dict

Return a nested dictionary of module and submodule States

Use this method to inspect the States from this and all submodules. The optional argument family allows you to search for States in a particular family.

Examples

Obtain a dictionary of all States for this module (including submodules):

>>> mod.state()
dict{ ... }

Parameters:

family (str) – The family of States to search for. Default: None; return all State attributes.

Returns:

A nested dictionary of States of this module and all submodules

Return type:

dict

timed(output_num: int = 0, dt: float | None = None, add_events: bool = False)

Convert this module to a TimedModule

Parameters:

• output_num (int) – Specify which output of the module to take, if the module returns multiple output series. Default: 0, take the first (or only) output.

• dt (float) – Used to provide a time-step for this module, if the module does not already have one. If self already defines a time-step, then self.dt will be used. Default: None

• add_events (bool) – Iff True, the TimedModule will add events occurring on a single timestep on input and output. Default: False, don’t add time steps.

Returns: TimedModule: A timed module that wraps this module

weight

Weight matrix of this module