class Product(nengo.Network):
"""Computes the element-wise product of two equally sized vectors."""
def __init__(self, n_neurons, dimensions,
radius=1, encoders=nengo.Default, **ens_kwargs):
self.config[nengo.Ensemble].update(ens_kwargs)
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.dimensions = dimensions
if encoders is nengo.Default:
encoders = Choice([[1, 1], [1, -1], [-1, 1], [-1, -1]])
self.product = EnsembleArray(
n_neurons, n_ensembles=dimensions, ens_dimensions=2,
encoders=encoders, radius=np.sqrt(2) * radius)
nengo.Connection(
self.A, self.product.input[0::2], synapse=None)
nengo.Connection(
self.B, self.product.input[1::2], synapse=None)
self.output = self.product.add_output('product', lambda x: x[0] * x[1])
def dot_product_transform(self, scale=1.0):
"""Returns a transform for output to compute the scaled dot product."""
return scale*np.ones((1, self.dimensions))
class Product(nengo.Network):
"""Computes the element-wise product of two equally sized vectors."""
def __init__(self, neurons, dimensions, radius=1, encoders=None,
**ens_kwargs):
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.output = nengo.Node(size_in=dimensions, label="output")
self.dimensions = dimensions
if encoders is None and not isinstance(neurons, nengo.Direct):
encoders = np.tile(
[[1, 1], [1, -1], [-1, 1], [-1, -1]],
((neurons.n_neurons / 4) + 1, 1))[:neurons.n_neurons]
else:
encoders = None
self.product = EnsembleArray(
neurons, n_ensembles=dimensions, ens_dimensions=2,
encoders=encoders, radius=np.sqrt(2) * radius, **ens_kwargs)
nengo.Connection(
self.A, self.product.input[::2], synapse=None)
nengo.Connection(
self.B, self.product.input[1::2], synapse=None)
nengo.Connection(
self.product.add_output('product', lambda x: x[0] * x[1]),
self.output, synapse=None)
def dot_product_transform(self, scale=1.0):
"""Returns a transform for output to compute the scaled dot product."""
return scale*np.ones((1, self.dimensions))
class Product(nengo.Network):
"""Computes the element-wise product of two (scaled) unit vectors.
Requires Scipy.
"""
# def __init__(self, n_neurons, dimensions, radius=1.0,
# n_eval_points=nengo.Default, eval_points=nengo.Default,
# encoders=nengo.Default, **ens_kwargs):
def __init__(self, n_neurons, dimensions, radius=np.sqrt(2.0), encoders=nengo.Default, **ens_kwargs):
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.dimensions = dimensions
if encoders is nengo.Default:
encoders = Choice([[1, 1], [1, -1], [-1, 1], [-1, -1]])
self.product = EnsembleArray(
n_neurons,
n_ensembles=dimensions,
ens_dimensions=2,
encoders=encoders,
radius=np.sqrt(2) * radius,
**ens_kwargs
)
nengo.Connection(self.A, self.product.input[0::2], synapse=None)
nengo.Connection(self.B, self.product.input[1::2], synapse=None)
self.output = self.product.add_output("product", lambda x: x[0] * x[1])
class Product(nengo.Network):
"""Computes the element-wise product of two equally sized vectors."""
def __init__(self, n_neurons, dimensions,
radius=1, encoders=nengo.Default, **ens_kwargs):
self.config[nengo.Ensemble].update(ens_kwargs)
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.output = nengo.Node(size_in=dimensions, label="output")
self.dimensions = dimensions
if encoders is nengo.Default:
encoders = np.tile(
[[1, 1], [1, -1], [-1, 1], [-1, -1]],
((n_neurons // 4) + 1, 1))[:n_neurons]
self.product = EnsembleArray(
n_neurons, n_ensembles=dimensions, ens_dimensions=2,
encoders=encoders, radius=np.sqrt(2) * radius)
nengo.Connection(
self.A, self.product.input[::2], synapse=None)
nengo.Connection(
self.B, self.product.input[1::2], synapse=None)
nengo.Connection(
self.product.add_output('product', lambda x: x[0] * x[1]),
self.output, synapse=None)
def dot_product_transform(self, scale=1.0):
"""Returns a transform for output to compute the scaled dot product."""
return scale*np.ones((1, self.dimensions))
class Product(nengo.Network):
"""Computes the element-wise product of two (scaled) unit vectors.
Requires Scipy.
"""
def __init__(self,
n_neurons,
dimensions,
radius=1.0,
encoders=nengo.Default,
**ens_kwargs):
super(Product, self).__init__(self)
with self:
self.config[nengo.Ensemble].update(ens_kwargs)
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.dimensions = dimensions
if encoders is nengo.Default:
encoders = Choice([[1, 1], [1, -1], [-1, 1], [-1, -1]])
optimizer = SubvectorRadiusOptimizer(n_neurons,
2,
ens_kwargs=ens_kwargs)
scaled_r = radius * optimizer.find_optimal_radius(dimensions, 1)
self.product = EnsembleArray(n_neurons,
n_ensembles=dimensions,
ens_dimensions=2,
radius=scaled_r,
encoders=encoders,
**ens_kwargs)
nengo.Connection(self.A, self.product.input[::2], synapse=None)
nengo.Connection(self.B, self.product.input[1::2], synapse=None)
self.output = self.product.add_output('product',
lambda x: x[0] * x[1])
def dot_product_transform(self, scale=1.0):
"""Returns a transform for output to compute the scaled dot product."""
return scale * np.ones((1, self.dimensions))
class BinaryElementwiseOperation(nengo.Network):
'''Handles splitting high-dimensions stuff into ensemble arrays
which each handle one 'dimension' or 'element'.
the x.output object is of the same dimensions as the inputs'''
def __init__(self, neurons, dimensions, kernel=None,
input_transform=None):
self.kernel = kernel if kernel is not None else self.product
self.dimensions = dimensions
self.A = nengo.Node(size_in=dimensions, label='A')
self.B = nengo.Node(size_in=dimensions, label='B')
self.ensemble = EnsembleArray(neurons,
n_ensembles=dimensions,
dimensions=2,
radius=1,
label='elementwise_operation')
self.output = nengo.Node(size_in=dimensions, label='output')
if input_transform is None:
self.input_transform = self.elementwise_comparator_transform
else:
self.input_transform = input_transform
for ens in self.ensemble.ensembles:
if not isinstance(neurons, nengo.Direct):
ens.encoders = corners(ens.n_neurons)
nengo.Connection(self.A, self.ensemble.input, synapse=None,
transform=self.input_transform)
nengo.Connection(self.B, self.ensemble.input, synapse=None,
transform=self.input_transform)
nengo.Connection(self.ensemble.add_output('result', self.kernel),
self.output)
@property
def elementwise_comparator_transform(self):
I = np.eye(self.dimensions)
return np.vstack((I, I))
@staticmethod
def product(x):
return x[0] * x[1]
class Product(nengo.Network):
"""Computes the element-wise product of two (scaled) unit vectors.
Requires Scipy.
"""
def __init__(
self, n_neurons, dimensions, radius=1.0,
encoders=nengo.Default, **ens_kwargs):
super(Product, self).__init__(self)
with self:
self.config[nengo.Ensemble].update(ens_kwargs)
self.A = nengo.Node(size_in=dimensions, label="A")
self.B = nengo.Node(size_in=dimensions, label="B")
self.dimensions = dimensions
if encoders is nengo.Default:
encoders = Choice([[1, 1], [1, -1], [-1, 1], [-1, -1]])
optimizer = SubvectorRadiusOptimizer(
n_neurons, 2, ens_kwargs=ens_kwargs)
scaled_r = radius * optimizer.find_optimal_radius(dimensions, 1)
self.product = EnsembleArray(
n_neurons, n_ensembles=dimensions, ens_dimensions=2,
radius=scaled_r, encoders=encoders, **ens_kwargs)
nengo.Connection(
self.A, self.product.input[::2], synapse=None)
nengo.Connection(
self.B, self.product.input[1::2], synapse=None)
self.output = self.product.add_output(
'product', lambda x: x[0] * x[1])
def dot_product_transform(self, scale=1.0):
"""Returns a transform for output to compute the scaled dot product."""
return scale * np.ones((1, self.dimensions))
class BasalGanglia(nengo.Network):
"""Winner takes all; outputs 0 at max dimension, negative elsewhere."""
# connection weights from (Gurney, Prescott, & Redgrave, 2001)
mm = 1
mp = 1
me = 1
mg = 1
ws = 1
wt = 1
wm = 1
wg = 1
wp = 0.9
we = 0.3
e = 0.2
ep = -0.25
ee = -0.2
eg = -0.2
le = 0.2
lg = 0.2
def __init__(self, dimensions, n_neurons_per_ensemble=100, radius=1.5,
tau_ampa=0.002, tau_gaba=0.008, output_weight=-3,
input_bias=0.0, solver=None):
if solver is None:
try:
# Best, if we have SciPy
solver = NnlsL2nz()
except ImportError:
# If not, use default
warnings.warn("SciPy is not installed, so BasalGanglia will "
"use default decoder solver. Installing SciPy "
"may improve BasalGanglia performance.")
solver = nengo.Default
encoders = np.ones((n_neurons_per_ensemble, 1))
ea_params = {
'n_neurons': n_neurons_per_ensemble,
'n_ensembles': dimensions,
'radius': radius,
'encoders': encoders,
}
self.strD1 = EnsembleArray(label="Striatal D1 neurons",
intercepts=Uniform(self.e, 1), **ea_params)
self.strD2 = EnsembleArray(label="Striatal D2 neurons",
intercepts=Uniform(self.e, 1), **ea_params)
self.stn = EnsembleArray(label="Subthalamic nucleus",
intercepts=Uniform(self.ep, 1), **ea_params)
self.gpi = EnsembleArray(label="Globus pallidus internus",
intercepts=Uniform(self.eg, 1), **ea_params)
self.gpe = EnsembleArray(label="Globus pallidus externus",
intercepts=Uniform(self.ee, 1), **ea_params)
self.input = nengo.Node(label="input", size_in=dimensions)
self.output = nengo.Node(label="output", size_in=dimensions)
# add bias input (BG performs best in the range 0.5--1.5)
if abs(input_bias) > 0.0:
self.bias_input = nengo.Node([input_bias] * dimensions)
nengo.Connection(self.bias_input, self.input)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(self.input, self.strD1.input, synapse=None,
transform=self.ws * (1 + self.lg))
nengo.Connection(self.input, self.strD2.input, synapse=None,
transform=self.ws * (1 - self.le))
nengo.Connection(self.input, self.stn.input, synapse=None,
transform=self.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = self.strD1.add_output(
'func_str', self.str_func, solver=solver)
nengo.Connection(strD1_output,
self.gpi.input, synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
strD2_output = self.strD2.add_output(
'func_str', self.str_func, solver=solver)
nengo.Connection(strD2_output,
self.gpe.input, synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = self.wp * np.ones((dimensions, dimensions))
stn_output = self.stn.add_output(
'func_stn', self.stn_func, solver=solver)
nengo.Connection(stn_output, self.gpi.input,
transform=tr, synapse=tau_ampa)
nengo.Connection(stn_output, self.gpe.input,
transform=tr, synapse=tau_ampa)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = self.gpe.add_output(
'func_gpe', self.gpe_func, solver=solver)
nengo.Connection(gpe_output, self.gpi.input, synapse=tau_gaba,
transform=-self.we)
nengo.Connection(gpe_output, self.stn.input, synapse=tau_gaba,
transform=-self.wg)
# connect GPi to output (inhibitory)
gpi_output = self.gpi.add_output(
'func_gpi', self.gpi_func, solver=solver)
nengo.Connection(gpi_output, self.output, synapse=None,
transform=output_weight)
@classmethod
def str_func(cls, x):
if x < cls.e:
return 0
return cls.mm * (x - cls.e)
@classmethod
def stn_func(cls, x):
if x < cls.ep:
return 0
return cls.mp * (x - cls.ep)
@classmethod
def gpe_func(cls, x):
if x < cls.ee:
return 0
return cls.me * (x - cls.ee)
@classmethod
def gpi_func(cls, x):
if x < cls.eg:
return 0
return cls.mg * (x - cls.eg)
class AssociativeMemory(Module):
"""Associative memory module.
Parameters
----------
input_vocab: list of numpy.array, spa.Vocabulary
The vocabulary (or list of vectors) to match.
output_vocab: list of numpy.array, spa.Vocabulary, optional
The vocabulary (or list of vectors) to be produced for each match. If
not given, the associative memory will act like an auto-associative
memory (cleanup memory).
default_output_vector: numpy.array, spa.SemanticPointer, optional
The vector to be produced if the input value matches none of vectors
in the input vector list.
threshold: float, optional
The association activation threshold.
input_scale: float, optional
Scaling factor to apply on the input vectors.
inhibitable: boolean, optional
Flag to indicate if the entire associative memory module is
inhibitable (entire thing can be shut off).
inhibit_scale: float, optional
Scaling factor on the gating connections (must have inhibitable =
True). Setting a larger value will ensure that the cleanup memory
output is inhibited at a faster rate, however, recovery of the
network when inhibition is released will be slower.
wta_output: boolean, optional
Flag to indicate if output of the associative memory should contain
more than one vectors. Set to True if only one vectors output is
desired -- i.e. a winner-take-all (wta) output. Leave as default
(False) if (possible) combinations of vectors is desired.
wta_inhibit_scale: float, optional
Scaling factor on the winner-take-all (wta) inhibitory connections.
wta_synapse: float, optional
Synapse to use for the winner-take-all (wta) inhibitory connections.
output_utilities: boolean, optional
Flag to indicate if the direct utilities (in addition to the vectors)
are output as well.
output_thresholded_utilities: boolean, optional
Flag to indicate if the direct thresholded utilities (in addition to
the vectors) are output as well.
neuron_type: nengo.Neurons, optional
Neuron type to use in the associative memory. Defaults to
n_neurons_per_ensemble: int, optional
Number of neurons per ensemble in the associative memory. There is
one ensemble created per vector being compared.
"""
def __init__(
self,
input_vocab,
output_vocab=None, # noqa: C901
default_output_vector=None,
threshold=0.3,
input_scale=1.0,
inhibitable=False,
inhibit_scale=1.0,
wta_output=False,
wta_inhibit_scale=2.0,
wta_synapse=0.005,
precise=False,
output_utilities=False,
output_thresholded_utilities=False,
neuron_type=nengo.LIF(),
n_neurons_per_ensemble=10):
super(AssociativeMemory, self).__init__()
# If output vocabulary is not specified, use input vocabulary
# (i.e autoassociative memory)
if output_vocab is None:
output_vocab = input_vocab
# Handle different vocabulary types
if isinstance(input_vocab, Vocabulary):
input_vectors = input_vocab.vectors
elif is_iterable(input_vocab):
input_vectors = np.matrix(input_vocab)
else:
input_vectors = input_vocab
if isinstance(output_vocab, Vocabulary):
output_vectors = output_vocab.vectors
elif is_iterable(output_vocab):
output_vectors = np.matrix(output_vocab)
else:
output_vectors = output_vocab
# Fail if number of input items and number of output items don't match
if input_vectors.shape[0] != output_vectors.shape[0]:
raise ValueError(
'number of input vectors does not match number of output '
'vectors. %d != %d' %
(input_vectors.shape[0], output_vectors.shape[0]))
N = len(input_vectors)
n_eval_points = 1500
eval_point_margin = 0.0001 if precise == True else 0.1
eval_points = Uniform(
threshold + eval_point_margin,
1 + eval_point_margin).sample(n_eval_points).reshape(-1, 1)
# Ensemble array parameters
ea_params = {
'radius': 1.0,
'neuron_type': neuron_type,
'n_neurons': n_neurons_per_ensemble,
'n_ensembles': N,
'intercepts': Uniform(threshold, 1),
'max_rates':
Uniform(80, 100) if precise == True else Uniform(100, 200),
'encoders': np.ones((n_neurons_per_ensemble, 1)),
'eval_points': eval_points
}
# Thresholding function
def threshold_func(x):
return x > threshold
# Input and output nodes
self.input = nengo.Node(size_in=input_vectors.shape[1], label="input")
self.output = nengo.Node(size_in=output_vectors.shape[1],
label="output")
# Ensemble array to do the thresholding stuff
self.thresholded_ens_array = EnsembleArray(
label="thresholded ens array", **ea_params)
# Connect input and output nodes
nengo.Connection(self.input,
self.thresholded_ens_array.input,
synapse=None,
transform=input_vectors * input_scale)
nengo.Connection(self.thresholded_ens_array.add_output(
'thresholded_output', threshold_func),
self.output,
synapse=None,
transform=output_vectors.T)
# Configure associative memory to be inhibitable
if inhibitable:
# Input node for inhibitory gating signal (if enabled)
self.inhibit = nengo.Node(size_in=1, label="inhibit")
nengo.Connection(self.inhibit,
self.thresholded_ens_array.input,
synapse=None,
transform=-np.ones((N, 1)))
# Note: We can use decoded connection here because all the
# encoding vectors are [1]
# Configure associative memory to have mutually inhibited output
if wta_output:
nengo.Connection(self.thresholded_ens_array.output,
self.thresholded_ens_array.input,
synapse=wta_synapse,
transform=(np.eye(N) - 1) * inhibit_scale)
# Configure utilities output
if output_utilities:
self.utilities = nengo.Node(size_in=N, label="utilities")
nengo.Connection(self.thresholded_ens_array.output,
self.utilities,
synapse=None)
# Configure utilities output
if output_thresholded_utilities:
self.thresholded_utilities = nengo.Node(
size_in=N, label="thresholded_utilities")
nengo.Connection(self.thresholded_ens_array.thresholded_output,
self.thresholded_utilities,
synapse=None)
# Configure default output vector
if default_output_vector is not None:
eval_points = Uniform(0.8, 1).sample(n_eval_points).reshape(-1, 1)
bias = nengo.Node(output=[1])
default_vector_gate = nengo.Ensemble(
n_neurons_per_ensemble,
dimensions=1,
encoders=np.ones((n_neurons_per_ensemble, 1)),
intercepts=Uniform(0.5, 1),
max_rates=ea_params['max_rates'],
eval_points=eval_points,
label="default vector gate")
nengo.Connection(bias, default_vector_gate, synapse=None)
nengo.Connection(self.thresholded_ens_array.thresholded_output,
default_vector_gate,
transform=-np.ones((1, N)),
synapse=0.005)
nengo.Connection(default_vector_gate,
self.output,
synapse=None,
transform=np.matrix(default_output_vector).T)
if inhibitable:
nengo.Connection(self.inhibit,
default_vector_gate,
synapse=None,
transform=[[-1]])
if isinstance(input_vocab, Vocabulary):
self.inputs = dict(default=(self.input, input_vocab))
if isinstance(output_vocab, Vocabulary):
self.outputs = dict(default=(self.output, output_vocab))
class Product(nengo.Network):
"""Computes the element-wise product of two equally sized vectors.
The network used to calculate the product is described in
`Gosmann, 2015`_. A simpler version of this network can be found in the
:doc:`Multiplication example <examples/basic/multiplication>`.
Note that this network is optimized under the assumption that both input
values (or both values for each input dimensions of the input vectors) are
uniformly and independently distributed. Visualized in a joint 2D space,
this would give a square of equal probabilities for pairs of input values.
This assumption is violated with non-uniform input value distributions
(for example, if the input values follow a Gaussian or cosine similarity
distribution). In that case, no square of equal probabilities is obtained,
but a probability landscape with circular equi-probability lines. To obtain
the optimal network accuracy, scale the *input_magnitude* by a factor of
``1 / sqrt(2)``.
.. _Gosmann, 2015:
https://nbviewer.jupyter.org/github/ctn-archive/technical-reports/blob/
master/Precise-multiplications-with-the-NEF.ipynb
Parameters
----------
n_neurons : int
Number of neurons per dimension in the vector.
.. note:: These neurons will be distributed evenly across two
ensembles. If an odd number of neurons is specified, the
extra neuron will not be used.
dimensions : int
Number of dimensions in each of the vectors to be multiplied.
input_magnitude : float, optional (Default: 1.)
The expected magnitude of the vectors to be multiplied.
This value is used to determine the radius of the ensembles
computing the element-wise product.
**kwargs
Keyword arguments passed through to ``nengo.Network``
like 'label' and 'seed'.
Attributes
----------
input_a : Node
The first vector to be multiplied.
input_b : Node
The second vector to be multiplied.
output : Node
The resulting product.
sq1 : EnsembleArray
Represents the first squared term. See `Gosmann, 2015`_ for details.
sq2 : EnsembleArray
Represents the second squared term. See `Gosmann, 2015`_ for details.
"""
def __init__(self, n_neurons, dimensions, input_magnitude=1., **kwargs):
if 'net' in kwargs:
raise ObsoleteError("The 'net' argument is no longer supported.")
kwargs.setdefault('label', "Product")
super().__init__(**kwargs)
with self:
self.input_a = nengo.Node(size_in=dimensions, label="input_a")
self.input_b = nengo.Node(size_in=dimensions, label="input_b")
self.output = nengo.Node(size_in=dimensions, label="output")
self.sq1 = EnsembleArray(
max(1, n_neurons // 2),
n_ensembles=dimensions,
ens_dimensions=1,
radius=input_magnitude * np.sqrt(2),
)
self.sq2 = EnsembleArray(
max(1, n_neurons // 2),
n_ensembles=dimensions,
ens_dimensions=1,
radius=input_magnitude * np.sqrt(2),
)
tr = 1. / np.sqrt(2.)
nengo.Connection(self.input_a,
self.sq1.input,
transform=tr,
synapse=None)
nengo.Connection(self.input_b,
self.sq1.input,
transform=tr,
synapse=None)
nengo.Connection(self.input_a,
self.sq2.input,
transform=tr,
synapse=None)
nengo.Connection(self.input_b,
self.sq2.input,
transform=-tr,
synapse=None)
sq1_out = self.sq1.add_output('square', np.square)
nengo.Connection(sq1_out, self.output, transform=.5, synapse=None)
sq2_out = self.sq2.add_output('square', np.square)
nengo.Connection(sq2_out, self.output, transform=-.5, synapse=None)
@property
def A(self):
warnings.warn(DeprecationWarning("Use 'input_a' instead of 'A'."))
return self.input_a
@property
def B(self):
warnings.warn(DeprecationWarning("Use 'input_b' instead of 'B'."))
return self.input_b
def __init__(self, dimensions, n_neurons_per_ensemble=100, radius=1.5,
tau_ampa=0.002, tau_gaba=0.008, output_weight=-3,
decoder_solver=nnls_L2nz):
encoders = np.ones((n_neurons_per_ensemble, 1))
ea_params = {
'neurons': nengo.LIF(n_neurons_per_ensemble),
'n_ensembles': dimensions,
'radius': radius,
'encoders': encoders,
}
strD1 = EnsembleArray(label="Striatal D1 neurons",
intercepts=Uniform(self.e, 1), **ea_params)
strD2 = EnsembleArray(label="Striatal D2 neurons",
intercepts=Uniform(self.e, 1), **ea_params)
stn = EnsembleArray(label="Subthalamic nucleus",
intercepts=Uniform(self.ep, 1), **ea_params)
gpi = EnsembleArray(label="Globus pallidus internus",
intercepts=Uniform(self.eg, 1), **ea_params)
gpe = EnsembleArray(label="Globus pallidus externus",
intercepts=Uniform(self.ee, 1), **ea_params)
self.input = nengo.Node(label="input", size_in=dimensions)
self.output = nengo.Node(label="output", size_in=dimensions)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(self.input, strD1.input, synapse=None,
transform=self.ws * (1 + self.lg))
nengo.Connection(self.input, strD2.input, synapse=None,
transform=self.ws * (1 - self.le))
nengo.Connection(self.input, stn.input, synapse=None,
transform=self.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = strD1.add_output(
'func_str', self.str, decoder_solver=decoder_solver)
nengo.Connection(strD1_output,
gpi.input, synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
strD2_output = strD2.add_output(
'func_str', self.str, decoder_solver=decoder_solver)
nengo.Connection(strD2_output,
gpe.input, synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = self.wp * np.ones((dimensions, dimensions))
stn_output = stn.add_output(
'func_stn', self.stn, decoder_solver=decoder_solver)
nengo.Connection(stn_output, gpi.input,
transform=tr, synapse=tau_ampa)
nengo.Connection(stn_output, gpe.input,
transform=tr, synapse=tau_ampa)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = gpe.add_output(
'func_gpe', self.gpe, decoder_solver=decoder_solver)
nengo.Connection(gpe_output, gpi.input, synapse=tau_gaba,
transform=-self.we)
nengo.Connection(gpe_output, stn.input, synapse=tau_gaba,
transform=-self.wg)
# connect GPi to output (inhibitory)
gpi_output = gpi.add_output(
'func_gpi', self.gpi, decoder_solver=decoder_solver)
nengo.Connection(gpi_output, self.output, synapse=None,
transform=output_weight)
class Product(nengo.Network):
"""Computes the element-wise product of two equally sized vectors.
The network used to calculate the product is described in
`Gosmann, 2015`_. A simpler version of this network can be found in the
:doc:`Multiplication example <examples/basic/multiplication>`.
Note that this network is optimized under the assumption that both input
values (or both values for each input dimensions of the input vectors) are
uniformly and independently distributed. Visualized in a joint 2D space,
this would give a square of equal probabilities for pairs of input values.
This assumption is violated with non-uniform input value distributions
(for example, if the input values follow a Gaussian or cosine similarity
distribution). In that case, no square of equal probabilities is obtained,
but a probability landscape with circular equi-probability lines. To obtain
the optimal network accuracy, scale the *input_magnitude* by a factor of
``1 / sqrt(2)``.
.. _Gosmann, 2015:
https://nbviewer.jupyter.org/github/ctn-archive/technical-reports/blob/
master/Precise-multiplications-with-the-NEF.ipynb
Parameters
----------
n_neurons : int
Number of neurons per dimension in the vector.
.. note:: These neurons will be distributed evenly across two
ensembles. If an odd number of neurons is specified, the
extra neuron will not be used.
dimensions : int
Number of dimensions in each of the vectors to be multiplied.
input_magnitude : float, optional (Default: 1.)
The expected magnitude of the vectors to be multiplied.
This value is used to determine the radius of the ensembles
computing the element-wise product.
**kwargs
Keyword arguments passed through to ``nengo.Network``
like 'label' and 'seed'.
Attributes
----------
input_a : Node
The first vector to be multiplied.
input_b : Node
The second vector to be multiplied.
output : Node
The resulting product.
sq1 : EnsembleArray
Represents the first squared term. See `Gosmann, 2015`_ for details.
sq2 : EnsembleArray
Represents the second squared term. See `Gosmann, 2015`_ for details.
"""
def __init__(self, n_neurons, dimensions, input_magnitude=1., **kwargs):
if 'net' in kwargs:
raise ObsoleteError("The 'net' argument is no longer supported.")
kwargs.setdefault('label', "Product")
super().__init__(**kwargs)
with self:
self.input_a = nengo.Node(size_in=dimensions, label="input_a")
self.input_b = nengo.Node(size_in=dimensions, label="input_b")
self.output = nengo.Node(size_in=dimensions, label="output")
self.sq1 = EnsembleArray(
max(1, n_neurons // 2),
n_ensembles=dimensions,
ens_dimensions=1,
radius=input_magnitude * np.sqrt(2),
)
self.sq2 = EnsembleArray(
max(1, n_neurons // 2),
n_ensembles=dimensions,
ens_dimensions=1,
radius=input_magnitude * np.sqrt(2),
)
tr = 1. / np.sqrt(2.)
nengo.Connection(
self.input_a, self.sq1.input, transform=tr, synapse=None)
nengo.Connection(
self.input_b, self.sq1.input, transform=tr, synapse=None)
nengo.Connection(
self.input_a, self.sq2.input, transform=tr, synapse=None)
nengo.Connection(
self.input_b, self.sq2.input, transform=-tr, synapse=None)
sq1_out = self.sq1.add_output('square', np.square)
nengo.Connection(sq1_out, self.output, transform=.5, synapse=None)
sq2_out = self.sq2.add_output('square', np.square)
nengo.Connection(sq2_out, self.output, transform=-.5, synapse=None)
@property
def A(self):
warnings.warn(DeprecationWarning("Use 'input_a' instead of 'A'."))
return self.input_a
@property
def B(self):
warnings.warn(DeprecationWarning("Use 'input_b' instead of 'B'."))
return self.input_b
class BasalGanglia(nengo.Network):
"""Winner takes all; outputs 0 at max dimension, negative elsewhere."""
# connection weights from (Gurney, Prescott, & Redgrave, 2001)
mm = 1
mp = 1
me = 1
mg = 1
ws = 1
wt = 1
wm = 1
wg = 1
wp = 0.9
we = 0.3
e = 0.2
ep = -0.25
ee = -0.2
eg = -0.2
le = 0.2
lg = 0.2
def __init__(self,
dimensions,
n_neurons_per_ensemble=100,
radius=1.5,
tau_ampa=0.002,
tau_gaba=0.008,
output_weight=-3,
input_bias=0.0,
solver=None):
if solver is None:
try:
# Best, if we have SciPy
solver = NnlsL2nz()
except ImportError:
# If not, use default
warnings.warn("SciPy is not installed, so BasalGanglia will "
"use default decoder solver. Installing SciPy "
"may improve BasalGanglia performance.")
solver = nengo.Default
encoders = np.ones((n_neurons_per_ensemble, 1))
ea_params = {
'n_neurons': n_neurons_per_ensemble,
'n_ensembles': dimensions,
'radius': radius,
'encoders': encoders,
}
self.strD1 = EnsembleArray(label="Striatal D1 neurons",
intercepts=Uniform(self.e, 1),
**ea_params)
self.strD2 = EnsembleArray(label="Striatal D2 neurons",
intercepts=Uniform(self.e, 1),
**ea_params)
self.stn = EnsembleArray(label="Subthalamic nucleus",
intercepts=Uniform(self.ep, 1),
**ea_params)
self.gpi = EnsembleArray(label="Globus pallidus internus",
intercepts=Uniform(self.eg, 1),
**ea_params)
self.gpe = EnsembleArray(label="Globus pallidus externus",
intercepts=Uniform(self.ee, 1),
**ea_params)
self.input = nengo.Node(label="input", size_in=dimensions)
self.output = nengo.Node(label="output", size_in=dimensions)
# add bias input (BG performs best in the range 0.5--1.5)
if abs(input_bias) > 0.0:
self.bias_input = nengo.Node([input_bias] * dimensions)
nengo.Connection(self.bias_input, self.input)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(self.input,
self.strD1.input,
synapse=None,
transform=self.ws * (1 + self.lg))
nengo.Connection(self.input,
self.strD2.input,
synapse=None,
transform=self.ws * (1 - self.le))
nengo.Connection(self.input,
self.stn.input,
synapse=None,
transform=self.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = self.strD1.add_output('func_str',
self.str_func,
solver=solver)
nengo.Connection(strD1_output,
self.gpi.input,
synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
strD2_output = self.strD2.add_output('func_str',
self.str_func,
solver=solver)
nengo.Connection(strD2_output,
self.gpe.input,
synapse=tau_gaba,
transform=-np.eye(dimensions) * self.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = self.wp * np.ones((dimensions, dimensions))
stn_output = self.stn.add_output('func_stn',
self.stn_func,
solver=solver)
nengo.Connection(stn_output,
self.gpi.input,
transform=tr,
synapse=tau_ampa)
nengo.Connection(stn_output,
self.gpe.input,
transform=tr,
synapse=tau_ampa)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = self.gpe.add_output('func_gpe',
self.gpe_func,
solver=solver)
nengo.Connection(gpe_output,
self.gpi.input,
synapse=tau_gaba,
transform=-self.we)
nengo.Connection(gpe_output,
self.stn.input,
synapse=tau_gaba,
transform=-self.wg)
# connect GPi to output (inhibitory)
gpi_output = self.gpi.add_output('func_gpi',
self.gpi_func,
solver=solver)
nengo.Connection(gpi_output,
self.output,
synapse=None,
transform=output_weight)
@classmethod
def str_func(cls, x):
if x < cls.e:
return 0
return cls.mm * (x - cls.e)
@classmethod
def stn_func(cls, x):
if x < cls.ep:
return 0
return cls.mp * (x - cls.ep)
@classmethod
def gpe_func(cls, x):
if x < cls.ee:
return 0
return cls.me * (x - cls.ee)
@classmethod
def gpi_func(cls, x):
if x < cls.eg:
return 0
return cls.mg * (x - cls.eg)
class CircularConvolution(nengo.Network):
"""CircularConvolution docs XXX"""
def make(self, neurons, dimensions, radius=1,
invert_a=False, invert_b=False):
self.transformA = self._input_transform(
dimensions, first=True, invert=invert_a)
self.transformB = self._input_transform(
dimensions, first=False, invert=invert_b)
self.transformC = self._output_transform(dimensions)
self.A = nengo.Node(size_in=dimensions, label='A')
self.B = nengo.Node(size_in=dimensions, label='B')
self.ensemble = EnsembleArray(neurons,
self.transformC.shape[1],
dimensions=2,
radius=radius, label='conv')
self.output = nengo.Node(size_in=dimensions, label='output')
for ens in self.ensemble.ensembles:
if not isinstance(neurons, nengo.Direct):
ens.encoders = np.tile(
[[1, 1], [-1, 1], [1, -1], [-1, -1]],
(ens.n_neurons // 4, 1))
nengo.Connection(
self.A, self.ensemble.input, transform=self.transformA,
filter=None)
nengo.Connection(
self.B, self.ensemble.input, transform=self.transformB,
filter=None)
nengo.Connection(self.ensemble.add_output('product', self.product),
self.output,
filter=None,
transform=self.transformC)
@staticmethod
def _input_transform(dims, first, invert=False):
dims2 = 4 * (dims // 2 + 1)
T = np.zeros((dims2, 2, dims))
dft = _dft_half_cached(dims)
for i in range(dims2):
row = dft[i // 4] if not invert else dft[i // 4].conj()
if first:
T[i, 0] = row.real if i % 2 == 0 else row.imag
else:
T[i, 1] = row.real if i % 4 == 0 or i % 4 == 3 else row.imag
# --- Throw away rows that we don't need (b/c they're zero)
i = np.arange(dims2)
if dims % 2 == 0:
T = T[(i == 0) | (i > 3) & (i < len(i) - 3)]
else:
T = T[(i == 0) | (i > 3)]
return T.reshape((-1, dims))
@staticmethod
def _output_transform(dims):
dims2 = (dims // 2 + 1)
T = np.zeros((dims2, 4, dims))
idft = _dft_half_cached(dims).conj()
for i in range(dims2):
row = idft[i] if i == 0 or 2*i == dims else 2*idft[i]
T[i, 0] = row.real
T[i, 1] = -row.real
T[i, 2] = -row.imag
T[i, 3] = -row.imag
T = T.reshape(4*dims2, dims)
# --- Throw away rows that we don't need (b/c they're zero)
i = np.arange(4*dims2)
if dims % 2 == 0:
T = T[(i == 0) | (i > 3) & (i < len(i) - 3)]
else:
T = T[(i == 0) | (i > 3)]
# scaling is needed since we have 1./sqrt(dims) in DFT
T *= np.sqrt(dims)
return T.T
@staticmethod
def product(x):
return x[0] * x[1]
class BasalGanglia(nengo.Network):
"""Winner take all network, typically used for action selection.
The basal ganglia network outputs approximately 0 at the dimension with
the largest value, and is negative elsewhere.
While the basal ganglia is primarily defined by its winner-take-all
function, it is also organized to match the organization of the human
basal ganglia. It consists of five ensembles:
* Striatal D1 dopamine-receptor neurons (``strD1``)
* Striatal D2 dopamine-receptor neurons (``strD2``)
* Subthalamic nucleus (``stn``)
* Globus pallidus internus / substantia nigra reticulata (``gpi``)
* Globus pallidus externus (``gpe``)
Interconnections between these areas are also based on known
neuroanatomical connections. See [1]_ for more details, and [2]_ for
the original non-spiking basal ganglia model by
Gurney, Prescott & Redgrave that this model is based on.
.. note:: The default `.Solver` for the basal ganglia is `.NnlsL2nz`, which
requires SciPy. If SciPy is not installed, the global default
solver will be used instead.
Parameters
----------
dimensions : int
Number of dimensions (i.e., actions).
n_neurons_per_ensemble : int, optional (Default: 100)
Number of neurons in each ensemble in the network.
output_weight : float, optional (Default: -3.)
A scaling factor on the output of the basal ganglia
(specifically on the connection out of the GPi).
input_bias : float, optional (Default: 0.)
An amount by which to bias all dimensions of the input node.
Biasing the input node is important for ensuring that all input
dimensions are positive and easily comparable.
ampa_config : config, optional (Default: None)
Configuration for connections corresponding to biological connections
to AMPA receptors (i.e., connections from STN to to GPi and GPe).
If None, a default configuration using a 2 ms lowpass synapse
will be used.
gaba_config : config, optional (Default: None)
Configuration for connections corresponding to biological connections
to GABA receptors (i.e., connections from StrD1 to GPi, StrD2 to GPe,
and GPe to GPi and STN). If None, a default configuration using an
8 ms lowpass synapse will be used.
**kwargs
Keyword arguments passed through to ``nengo.Network``
like 'label' and 'seed'.
Attributes
----------
bias_input : Node or None
If ``input_bias`` is non-zero, this node will be created to bias
all of the dimensions of the input signal.
gpe : EnsembleArray
Globus pallidus externus ensembles.
gpi : EnsembleArray
Globus pallidus internus ensembles.
input : Node
Accepts the input signal.
output : Node
Provides the output signal.
stn : EnsembleArray
Subthalamic nucleus ensembles.
strD1 : EnsembleArray
Striatal D1 ensembles.
strD2 : EnsembleArray
Striatal D2 ensembles.
References
----------
.. [1] Stewart, T. C., Choo, X., & Eliasmith, C. (2010).
Dynamic behaviour of a spiking model of action selection in the
basal ganglia. In Proceedings of the 10th international conference on
cognitive modeling (pp. 235-40).
.. [2] Gurney, K., Prescott, T., & Redgrave, P. (2001).
A computational model of action selection in the basal
ganglia. Biological Cybernetics 84, 401-423.
"""
def __init__(self,
dimensions,
n_neurons_per_ensemble=100,
output_weight=-3.,
input_bias=0.,
ampa_config=None,
gaba_config=None,
**kwargs):
if 'net' in kwargs:
raise ObsoleteError("The 'net' argument is no longer supported.")
kwargs.setdefault('label', "Basal Ganglia")
super().__init__(**kwargs)
ampa_config, override_ampa = config_with_default_synapse(
ampa_config, nengo.Lowpass(0.002))
gaba_config, override_gaba = config_with_default_synapse(
gaba_config, nengo.Lowpass(0.008))
# Affects all ensembles / connections in the BG
# unless they've been overridden on `self.config`
config = nengo.Config(nengo.Ensemble, nengo.Connection)
config[nengo.Ensemble].radius = 1.5
config[nengo.Ensemble].encoders = Choice([[1]])
try:
# Best, if we have SciPy
config[nengo.Connection].solver = NnlsL2nz()
except ImportError:
# Warn if we can't use the better decoder solver.
warnings.warn("SciPy is not installed, so BasalGanglia will "
"use the default decoder solver. Installing SciPy "
"may improve BasalGanglia performance.")
ea_params = {'n_neurons': n_neurons_per_ensemble,
'n_ensembles': dimensions}
with self, config:
self.strD1 = EnsembleArray(label="Striatal D1 neurons",
intercepts=Uniform(Weights.e, 1),
**ea_params)
self.strD2 = EnsembleArray(label="Striatal D2 neurons",
intercepts=Uniform(Weights.e, 1),
**ea_params)
self.stn = EnsembleArray(label="Subthalamic nucleus",
intercepts=Uniform(Weights.ep, 1),
**ea_params)
self.gpi = EnsembleArray(label="Globus pallidus internus",
intercepts=Uniform(Weights.eg, 1),
**ea_params)
self.gpe = EnsembleArray(label="Globus pallidus externus",
intercepts=Uniform(Weights.ee, 1),
**ea_params)
self.input = nengo.Node(label="input", size_in=dimensions)
self.output = nengo.Node(label="output", size_in=dimensions)
# add bias input (BG performs best in the range 0.5--1.5)
if abs(input_bias) > 0.0:
self.bias_input = nengo.Node(np.ones(dimensions) * input_bias,
label="basal ganglia bias")
nengo.Connection(self.bias_input, self.input)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(self.input, self.strD1.input, synapse=None,
transform=Weights.ws * (1 + Weights.lg))
nengo.Connection(self.input, self.strD2.input, synapse=None,
transform=Weights.ws * (1 - Weights.le))
nengo.Connection(self.input, self.stn.input, synapse=None,
transform=Weights.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = self.strD1.add_output('func_str', Weights.str_func)
strD2_output = self.strD2.add_output('func_str', Weights.str_func)
with gaba_config:
nengo.Connection(strD1_output, self.gpi.input,
transform=-Weights.wm)
nengo.Connection(strD2_output, self.gpe.input,
transform=-Weights.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = Weights.wp * np.ones((dimensions, dimensions))
stn_output = self.stn.add_output('func_stn', Weights.stn_func)
with ampa_config:
nengo.Connection(stn_output, self.gpi.input, transform=tr)
nengo.Connection(stn_output, self.gpe.input, transform=tr)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = self.gpe.add_output('func_gpe', Weights.gpe_func)
with gaba_config:
nengo.Connection(
gpe_output, self.gpi.input, transform=-Weights.we)
nengo.Connection(
gpe_output, self.stn.input, transform=-Weights.wg)
# connect GPi to output (inhibitory)
gpi_output = self.gpi.add_output('func_gpi', Weights.gpi_func)
nengo.Connection(
gpi_output, self.output, synapse=None, transform=output_weight)
# Return ampa_config and gaba_config to previous states, if changed
if override_ampa:
del ampa_config[nengo.Connection].synapse
if override_gaba:
del gaba_config[nengo.Connection].synapse
class BasalGanglia(nengo.Network):
"""Winner take all network, typically used for action selection.
The basal ganglia network outputs approximately 0 at the dimension with
the largest value, and is negative elsewhere.
While the basal ganglia is primarily defined by its winner-take-all
function, it is also organized to match the organization of the human
basal ganglia. It consists of five ensembles:
* Striatal D1 dopamine-receptor neurons (``strD1``)
* Striatal D2 dopamine-receptor neurons (``strD2``)
* Subthalamic nucleus (``stn``)
* Globus pallidus internus / substantia nigra reticulata (``gpi``)
* Globus pallidus externus (``gpe``)
Interconnections between these areas are also based on known
neuroanatomical connections. See [1]_ for more details, and [2]_ for
the original non-spiking basal ganglia model by
Gurney, Prescott & Redgrave that this model is based on.
.. note:: The default `.Solver` for the basal ganglia is `.NnlsL2nz`, which
requires SciPy. If SciPy is not installed, the global default
solver will be used instead.
Parameters
----------
dimensions : int
Number of dimensions (i.e., actions).
n_neurons_per_ensemble : int, optional
Number of neurons in each ensemble in the network.
output_weight : float, optional
A scaling factor on the output of the basal ganglia
(specifically on the connection out of the GPi).
input_bias : float, optional
An amount by which to bias all dimensions of the input node.
Biasing the input node is important for ensuring that all input
dimensions are positive and easily comparable.
ampa_config : config, optional
Configuration for connections corresponding to biological connections
to AMPA receptors (i.e., connections from STN to to GPi and GPe).
If None, a default configuration using a 2 ms lowpass synapse
will be used.
gaba_config : config, optional
Configuration for connections corresponding to biological connections
to GABA receptors (i.e., connections from StrD1 to GPi, StrD2 to GPe,
and GPe to GPi and STN). If None, a default configuration using an
8 ms lowpass synapse will be used.
**kwargs
Keyword arguments passed through to ``nengo.Network``
like 'label' and 'seed'.
Attributes
----------
bias_input : Node or None
If ``input_bias`` is non-zero, this node will be created to bias
all of the dimensions of the input signal.
gpe : EnsembleArray
Globus pallidus externus ensembles.
gpi : EnsembleArray
Globus pallidus internus ensembles.
input : Node
Accepts the input signal.
output : Node
Provides the output signal.
stn : EnsembleArray
Subthalamic nucleus ensembles.
strD1 : EnsembleArray
Striatal D1 ensembles.
strD2 : EnsembleArray
Striatal D2 ensembles.
References
----------
.. [1] Stewart, T. C., Choo, X., & Eliasmith, C. (2010).
Dynamic behaviour of a spiking model of action selection in the
basal ganglia. In Proceedings of the 10th international conference on
cognitive modeling (pp. 235-40).
.. [2] Gurney, K., Prescott, T., & Redgrave, P. (2001).
A computational model of action selection in the basal
ganglia. Biological Cybernetics 84, 401-423.
"""
def __init__(self,
dimensions,
n_neurons_per_ensemble=100,
output_weight=-3.0,
input_bias=0.0,
ampa_config=None,
gaba_config=None,
**kwargs):
if "net" in kwargs:
raise ObsoleteError("The 'net' argument is no longer supported.")
kwargs.setdefault("label", "Basal Ganglia")
super().__init__(**kwargs)
ampa_config, override_ampa = config_with_default_synapse(
ampa_config, nengo.Lowpass(0.002))
gaba_config, override_gaba = config_with_default_synapse(
gaba_config, nengo.Lowpass(0.008))
# Affects all ensembles / connections in the BG
# unless they've been overridden on `self.config`
config = nengo.Config(nengo.Ensemble, nengo.Connection)
config[nengo.Ensemble].radius = 1.5
config[nengo.Ensemble].encoders = Choice([[1]])
try:
# Best, if we have SciPy
config[nengo.Connection].solver = NnlsL2nz()
except ImportError:
# Warn if we can't use the better decoder solver.
warnings.warn("SciPy is not installed, so BasalGanglia will "
"use the default decoder solver. Installing SciPy "
"may improve BasalGanglia performance.")
ea_params = {
"n_neurons": n_neurons_per_ensemble,
"n_ensembles": dimensions
}
with self, config:
self.strD1 = EnsembleArray(
label="Striatal D1 neurons",
intercepts=Uniform(Weights.e, 1),
**ea_params,
)
self.strD2 = EnsembleArray(
label="Striatal D2 neurons",
intercepts=Uniform(Weights.e, 1),
**ea_params,
)
self.stn = EnsembleArray(
label="Subthalamic nucleus",
intercepts=Uniform(Weights.ep, 1),
**ea_params,
)
self.gpi = EnsembleArray(
label="Globus pallidus internus",
intercepts=Uniform(Weights.eg, 1),
**ea_params,
)
self.gpe = EnsembleArray(
label="Globus pallidus externus",
intercepts=Uniform(Weights.ee, 1),
**ea_params,
)
self.input = nengo.Node(label="input", size_in=dimensions)
self.output = nengo.Node(label="output", size_in=dimensions)
# add bias input (BG performs best in the range 0.5--1.5)
if abs(input_bias) > 0.0:
self.bias_input = nengo.Node(np.ones(dimensions) * input_bias,
label="basal ganglia bias")
nengo.Connection(self.bias_input, self.input)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(
self.input,
self.strD1.input,
synapse=None,
transform=Weights.ws * (1 + Weights.lg),
)
nengo.Connection(
self.input,
self.strD2.input,
synapse=None,
transform=Weights.ws * (1 - Weights.le),
)
nengo.Connection(self.input,
self.stn.input,
synapse=None,
transform=Weights.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = self.strD1.add_output("func_str", Weights.str_func)
strD2_output = self.strD2.add_output("func_str", Weights.str_func)
with gaba_config:
nengo.Connection(strD1_output,
self.gpi.input,
transform=-Weights.wm)
nengo.Connection(strD2_output,
self.gpe.input,
transform=-Weights.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = Weights.wp * np.ones((dimensions, dimensions))
stn_output = self.stn.add_output("func_stn", Weights.stn_func)
with ampa_config:
nengo.Connection(stn_output, self.gpi.input, transform=tr)
nengo.Connection(stn_output, self.gpe.input, transform=tr)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = self.gpe.add_output("func_gpe", Weights.gpe_func)
with gaba_config:
nengo.Connection(gpe_output,
self.gpi.input,
transform=-Weights.we)
nengo.Connection(gpe_output,
self.stn.input,
transform=-Weights.wg)
# connect GPi to output (inhibitory)
gpi_output = self.gpi.add_output("func_gpi", Weights.gpi_func)
nengo.Connection(gpi_output,
self.output,
synapse=None,
transform=output_weight)
# Return ampa_config and gaba_config to previous states, if changed
if override_ampa:
del ampa_config[nengo.Connection].synapse
if override_gaba:
del gaba_config[nengo.Connection].synapse
class BasalGanglia(Network):
"""Winner take all network, typically used for action selection.
The basal ganglia network outputs approximately 0 at the dimension with
the largest value, and is negative elsewhere.
While the basal ganglia is primarily defined by its winner-take-all
function, it is also organized to match the organization of the human
basal ganglia. It consists of five ensembles:
* Striatal D1 dopamine-receptor neurons (*strD1*)
* Striatal D2 dopamine-receptor neurons (*strD2*)
* Subthalamic nucleus (*stn*)
* Globus pallidus internus / substantia nigra reticulata (*gpi*)
* Globus pallidus externus (*gpe*)
Interconnections between these areas are also based on known
neuroanatomical connections. See [1]_ for more details, and [2]_ for
the original non-spiking basal ganglia model by
Gurney, Prescott & Redgrave that this model is based on.
.. note:: The default `nengo.solvers.Solver` for the basal ganglia is
`nengo.solvers.NnlsL2nz`, which requires SciPy. If SciPy is not
installed, the global default solver will be used instead.
Parameters
----------
action_count : int
Number of actions.
n_neuron_per_ensemble : int, optional
Number of neurons in each ensemble in the network.
output_weight : float, optional
A scaling factor on the output of the basal ganglia
(specifically on the connection out of the GPi).
input_bias : float, optional
An amount by which to bias all dimensions of the input node.
Biasing the input node is important for ensuring that all input
dimensions are positive and easily comparable.
ampa_synapse : Synapse, optional
Synapse for connections corresponding to biological connections
to AMPA receptors (i.e., connections from STN to to GPi and GPe).
gaba_synapse : Synapse, optional
Synapse for connections corresponding to biological connections
to GABA receptors (i.e., connections from StrD1 to GPi, StrD2 to GPe,
and GPe to GPi and STN).
kwargs
Passed through the `nengo_spa.Network`.
Attributes
----------
bias_input : nengo.Node or None
If *input_bias* is non-zero, this node will be created to bias
all of the dimensions of the input signal.
gpe : nengo.networks.EnsembleArray
Globus pallidus externus ensembles.
gpi : nengo.networks.EnsembleArray
Globus pallidus internus ensembles.
input : nengo.Node
Accepts the input signal.
output : nengo.Node
Provides the output signal.
stn : nengo.networks.EnsembleArray
Subthalamic nucleus ensembles.
strD1 : nengo.networks.EnsembleArray
Striatal D1 ensembles.
strD2 : nengo.networks.EnsembleArray
Striatal D2 ensembles.
References
----------
.. [1] Stewart, T. C., Choo, X., & Eliasmith, C. (2010).
Dynamic behaviour of a spiking model of action selection in the
basal ganglia. In Proceedings of the 10th international conference on
cognitive modeling (pp. 235-40).
.. [2] Gurney, K., Prescott, T., & Redgrave, P. (2001).
A computational model of action selection in the basal
ganglia. Biological Cybernetics 84, 401-423.
"""
input_synapse = SynapseParam('input_synapse', default=Lowpass(0.002))
ampa_synapse = SynapseParam('ampa_synapse', default=Lowpass(0.002))
gaba_synapse = SynapseParam('gaba_synapse', default=Lowpass(0.008))
n_neurons_per_ensemble = IntParam('n_neurons_per_ensemble',
default=100,
low=1,
readonly=True)
output_weight = NumberParam('output_weight', default=-3., readonly=True)
input_bias = NumberParam('input_bias', default=0., readonly=True)
def __init__(self,
action_count,
n_neurons_per_ensemble=Default,
output_weight=Default,
input_bias=Default,
ampa_synapse=Default,
gaba_synapse=Default,
sBCBG_params=None,
**kwargs):
kwargs.setdefault('label', "Basal ganglia")
super(BasalGanglia, self).__init__(**kwargs)
self.action_count = action_count
self.input_connections = {}
self.input_bias = input_bias
if BasalGanglia.sBCBG:
# parameters
filter_tau = .01
if output_weight == Default:
self.output_weight = -0.001
import sBCBG
if sBCBG_params == None:
sBCBG_params = {}
sBCBG.nengo_instantiate(
self.action_count, self,
sBCBG_params if sBCBG_params != None else {})
with self:
# connect input to CSN
self.input = nengo.Node(label="input",
size_in=self.action_count)
scale = nengo.Ensemble(100, self.input.size_out)
nengo.Connection(self.input, scale)
for d in range(self.action_count):
nengo.Connection(scale[d],
self.pops['CSN'][d],
function=lambda x: 10 * x,
synapse=.01,
label='CSN input')
# add bias input (BG performs best in the range 0.5--1.5)
if abs(self.input_bias) > 0.0:
self.bias_input = nengo.Node(np.ones(self.action_count) *
input_bias,
label="basal ganglia bias")
nengo.Connection(self.bias_input, self.input)
# connect GPi to output (inhibitory)
decoding_weight = 1 # scaling of decoding GPi->out
self.output = nengo.Node(label="output",
size_in=self.action_count)
for d in range(self.action_count):
GPi_ens = self.pops["GPi"][d]
decoder_values = np.ones(
(GPi_ens.n_neurons, 1)) * decoding_weight
nengo.Connection(
GPi_ens,
self.output[d],
synapse=nengo.synapses.Lowpass(filter_tau),
transform=self.output_weight,
#eval_points=eval_points)
solver=nengo.solvers.NoSolver(decoder_values))
else:
self.n_neurons_per_ensemble = n_neurons_per_ensemble
self.ampa_synapse = ampa_synapse
self.gaba_synapse = gaba_synapse
self.output_weight = output_weight
# Affects all ensembles / connections in the BG
# unless overwritten with general_config
config = nengo.Config(nengo.Ensemble, nengo.Connection)
config[nengo.Ensemble].radius = 1.5
config[nengo.Ensemble].encoders = nengo.dists.Choice([[1]])
try:
# Best, if we have SciPy
config[nengo.Connection].solver = nengo.solvers.NnlsL2nz()
except ImportError:
warnings.warn("SciPy is not installed, so BasalGanglia will "
"use the default decoder solver. Installing "
"SciPy may improve BasalGanglia performance.")
ea_params = {
'n_neurons': self.n_neurons_per_ensemble,
'n_ensembles': self.action_count
}
with self, config:
self.strD1 = EnsembleArray(label="Striatal D1 neurons",
intercepts=nengo.dists.Uniform(
Weights.e, 1),
**ea_params)
self.strD2 = EnsembleArray(label="Striatal D2 neurons",
intercepts=nengo.dists.Uniform(
Weights.e, 1),
**ea_params)
self.stn = EnsembleArray(label="Subthalamic nucleus",
intercepts=nengo.dists.Uniform(
Weights.ep, 1),
**ea_params)
self.gpi = EnsembleArray(label="Globus pallidus internus",
intercepts=nengo.dists.Uniform(
Weights.eg, 1),
**ea_params)
self.gpe = EnsembleArray(label="Globus pallidus externus",
intercepts=nengo.dists.Uniform(
Weights.ee, 1),
**ea_params)
self.input = nengo.Node(label="input",
size_in=self.action_count)
self.output = nengo.Node(label="output",
size_in=self.action_count)
# add bias input (BG performs best in the range 0.5--1.5)
if abs(self.input_bias) > 0.0:
self.bias_input = nengo.Node(np.ones(self.action_count) *
self.input_bias,
label="basal ganglia bias")
nengo.Connection(self.bias_input, self.input)
# spread the input to StrD1, StrD2, and STN
nengo.Connection(self.input,
self.strD1.input,
synapse=None,
transform=Weights.ws * (1 + Weights.lg))
nengo.Connection(self.input,
self.strD2.input,
synapse=None,
transform=Weights.ws * (1 - Weights.le))
nengo.Connection(self.input,
self.stn.input,
synapse=None,
transform=Weights.wt)
# connect the striatum to the GPi and GPe (inhibitory)
strD1_output = self.strD1.add_output('func_str',
Weights.str_func)
strD2_output = self.strD2.add_output('func_str',
Weights.str_func)
self.gaba = nengo.Network("GABAergic connections")
self.gaba.config[nengo.Connection].synapse = self.gaba_synapse
with self.gaba:
nengo.Connection(strD1_output,
self.gpi.input,
transform=-Weights.wm)
nengo.Connection(strD2_output,
self.gpe.input,
transform=-Weights.wm)
# connect the STN to GPi and GPe (broad and excitatory)
tr = Weights.wp * np.ones(
(self.action_count, self.action_count))
stn_output = self.stn.add_output('func_stn', Weights.stn_func)
self.ampa = nengo.Network("AMPAergic connectiions")
self.ampa.config[nengo.Connection].synapse = self.ampa_synapse
with self.ampa:
nengo.Connection(stn_output, self.gpi.input, transform=tr)
nengo.Connection(stn_output, self.gpe.input, transform=tr)
# connect the GPe to GPi and STN (inhibitory)
gpe_output = self.gpe.add_output('func_gpe', Weights.gpe_func)
with self.gaba:
nengo.Connection(gpe_output,
self.gpi.input,
transform=-Weights.we)
nengo.Connection(gpe_output,
self.stn.input,
transform=-Weights.wg)
# connect GPi to output (inhibitory)
gpi_output = self.gpi.add_output('func_gpi', Weights.gpi_func)
nengo.Connection(gpi_output,
self.output,
synapse=None,
transform=self.output_weight)
def connect_input(self, source, transform=Default, index=None):
self.input_connections[index] = nengo.Connection(
source,
self.input[index],
transform=transform,
synapse=self.input_synapse)
class AssociativeMemory(Module):
"""Associative memory module.
Parameters
----------
input_vocab: list of numpy.array, spa.Vocabulary
The vocabulary (or list of vectors) to match.
output_vocab: list of numpy.array, spa.Vocabulary, optional
The vocabulary (or list of vectors) to be produced for each match. If
not given, the associative memory will act like an auto-associative
memory (cleanup memory).
default_output_vector: numpy.array, spa.SemanticPointer, optional
The vector to be produced if the input value matches none of vectors
in the input vector list.
threshold: float, optional
The association activation threshold.
input_scale: float, optional
Scaling factor to apply on the input vectors.
inhibitable: boolean, optional
Flag to indicate if the entire associative memory module is
inhibitable (entire thing can be shut off).
inhibit_scale: float, optional
Scaling factor on the gating connections (must have inhibitable =
True). Setting a larger value will ensure that the cleanup memory
output is inhibited at a faster rate, however, recovery of the
network when inhibition is released will be slower.
wta_output: boolean, optional
Flag to indicate if output of the associative memory should contain
more than one vectors. Set to True if only one vectors output is
desired -- i.e. a winner-take-all (wta) output. Leave as default
(False) if (possible) combinations of vectors is desired.
wta_inhibit_scale: float, optional
Scaling factor on the winner-take-all (wta) inhibitory connections.
wta_synapse: float, optional
Synapse to use for the winner-take-all (wta) inhibitory connections.
output_utilities: boolean, optional
Flag to indicate if the direct utilities (in addition to the vectors)
are output as well.
output_thresholded_utilities: boolean, optional
Flag to indicate if the direct thresholded utilities (in addition to
the vectors) are output as well.
neuron_type: nengo.Neurons, optional
Neuron type to use in the associative memory. Defaults to
n_neurons_per_ensemble: int, optional
Number of neurons per ensemble in the associative memory. There is
one ensemble created per vector being compared.
"""
def __init__(self, input_vocab, output_vocab=None, # noqa: C901
default_output_vector=None, threshold=0.3, input_scale=1.0,
inhibitable=False, inhibit_scale=1.0, wta_output=False,
wta_inhibit_scale=2.0, wta_synapse=0.005,
output_utilities=False, output_thresholded_utilities=False,
neuron_type=nengo.LIF(), n_neurons_per_ensemble=10):
super(AssociativeMemory, self).__init__()
# If output vocabulary is not specified, use input vocabulary
# (i.e autoassociative memory)
if output_vocab is None:
output_vocab = input_vocab
# Handle different vocabulary types
if isinstance(input_vocab, Vocabulary):
input_vectors = input_vocab.vectors
elif is_iterable(input_vocab):
input_vectors = np.matrix(input_vocab)
else:
input_vectors = input_vocab
if isinstance(output_vocab, Vocabulary):
output_vectors = output_vocab.vectors
elif is_iterable(output_vocab):
output_vectors = np.matrix(output_vocab)
else:
output_vectors = output_vocab
# Fail if number of input items and number of output items don't match
if input_vectors.shape[0] != output_vectors.shape[0]:
raise ValueError(
'number of input vectors does not match number of output '
'vectors. %d != %d'
% (input_vectors.shape[0], output_vectors.shape[0]))
N = len(input_vectors)
n_eval_points = 500
eval_point_margin = 0.1
eval_points = Uniform(
threshold + eval_point_margin, 1 + eval_point_margin)
# Ensemble array parameters
ea_params = {'radius': 1.0,
'neuron_type': neuron_type,
'n_neurons': n_neurons_per_ensemble,
'n_ensembles': N,
'intercepts': Uniform(threshold, 1),
'max_rates': Uniform(100, 200),
'encoders': Choice([[1]]),
'n_eval_points': n_eval_points,
'eval_points': eval_points}
# Thresholding function
def threshold_func(x):
return x > threshold
# Input and output nodes
self.input = nengo.Node(size_in=input_vectors.shape[1], label="input")
self.output = nengo.Node(size_in=output_vectors.shape[1],
label="output")
# Ensemble array to do the thresholding stuff
self.thresholded_ens_array = EnsembleArray(
label="thresholded ens array", **ea_params)
# Connect input and output nodes
nengo.Connection(self.input, self.thresholded_ens_array.input,
synapse=None, transform=input_vectors * input_scale)
nengo.Connection(
self.thresholded_ens_array.add_output(
'thresholded_output', threshold_func),
self.output, synapse=None, transform=output_vectors.T)
# Configure associative memory to be inhibitable
if inhibitable:
# Input node for inhibitory gating signal (if enabled)
self.inhibit = nengo.Node(size_in=1, label="inhibit")
nengo.Connection(self.inhibit, self.thresholded_ens_array.input,
synapse=None, transform=-np.ones((N, 1)))
# Note: We can use decoded connection here because all the
# encoding vectors are [1]
# Configure associative memory to have mutually inhibited output
if wta_output:
nengo.Connection(self.thresholded_ens_array.output,
self.thresholded_ens_array.input,
synapse=wta_synapse,
transform=(np.eye(N) - 1) * inhibit_scale)
# Configure utilities output
if output_utilities:
self.utilities = nengo.Node(size_in=N, label="utilities")
nengo.Connection(self.thresholded_ens_array.output,
self.utilities, synapse=None)
# Configure utilities output
if output_thresholded_utilities:
self.thresholded_utilities = nengo.Node(
size_in=N, label="thresholded_utilities")
nengo.Connection(self.thresholded_ens_array.thresholded_output,
self.thresholded_utilities, synapse=None)
# Configure default output vector
if default_output_vector is not None:
eval_points = Uniform(0.8, 1)
bias = nengo.Node(output=[1])
default_vector_gate = nengo.Ensemble(
n_neurons_per_ensemble, dimensions=1,
encoders=Choice([[1]]),
intercepts=Uniform(0.5, 1),
max_rates=ea_params['max_rates'],
n_eval_points=n_eval_points,
eval_points=eval_points,
label="default vector gate")
nengo.Connection(bias, default_vector_gate, synapse=None)
nengo.Connection(self.thresholded_ens_array.thresholded_output,
default_vector_gate, transform=-np.ones((1, N)),
synapse=0.005)
nengo.Connection(default_vector_gate, self.output, synapse=None,
transform=np.matrix(default_output_vector).T)
if inhibitable:
nengo.Connection(self.inhibit, default_vector_gate,
synapse=None, transform=[[-1]])
if isinstance(input_vocab, Vocabulary):
self.inputs = dict(default=(self.input, input_vocab))
if isinstance(output_vocab, Vocabulary):
self.outputs = dict(default=(self.output, output_vocab))