import warnings
import nengo
import numpy as np
from nengo.networks.ensemblearray import EnsembleArray
from nengo.params import Default, IntParam, NumberParam
from nengo.synapses import Lowpass, SynapseParam
from nengo_spa.network import Network
# connection weights from (Gurney, Prescott, & Redgrave, 2001)
class Weights:
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
@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)
[docs]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 : dict
Keyword arguments 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=-3.0, readonly=True)
input_bias = NumberParam("input_bias", default=0.0, readonly=True)
def __init__(
self,
action_count,
n_neurons_per_ensemble=Default,
output_weight=Default,
input_bias=Default,
ampa_synapse=Default,
gaba_synapse=Default,
**kwargs
):
super(BasalGanglia, self).__init__(**kwargs)
self.action_count = action_count
self.n_neurons_per_ensemble = n_neurons_per_ensemble
self.output_weight = output_weight
self.input_bias = input_bias
self.ampa_synapse = ampa_synapse
self.gaba_synapse = gaba_synapse
self.input_connections = {}
# 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
)
