class Test(object):
ntp = NeuronTypeParam('ntp', default=None)
class Ensemble(NengoObject):
"""A group of neurons that collectively represent a vector.
Parameters
----------
n_neurons : int
The number of neurons.
dimensions : int
The number of representational dimensions.
radius : int, optional
The representational radius of the ensemble.
encoders : Distribution or ndarray (`n_neurons`, `dimensions`), optional
The encoders, used to transform from representational space
to neuron space. Each row is a neuron's encoder, each column is a
representational dimension.
intercepts : Distribution or ndarray (`n_neurons`), optional
The point along each neuron's encoder where its activity is zero. If
e is the neuron's encoder, then the activity will be zero when
dot(x, e) <= c, where c is the given intercept.
max_rates : Distribution or ndarray (`n_neurons`), optional
The activity of each neuron when dot(x, e) = 1, where e is the neuron's
encoder.
eval_points : Distribution or ndarray (`n_eval_points`, `dims`), optional
The evaluation points used for decoder solving, spanning the interval
(-radius, radius) in each dimension, or a distribution from which to
choose evaluation points. Default: ``UniformHypersphere``.
n_eval_points : int, optional
The number of evaluation points to be drawn from the `eval_points`
distribution. If None (the default), then a heuristic is used to
determine the number of evaluation points.
neuron_type : Neurons, optional
The model that simulates all neurons in the ensemble.
noise : StochasticProcess, optional
Random noise injected directly into each neuron in the ensemble
as current. A sample is drawn for each individual neuron on
every simulation step.
seed : int, optional
The seed used for random number generation.
label : str, optional
A name for the ensemble. Used for debugging and visualization.
"""
n_neurons = IntParam(default=None, low=1)
dimensions = IntParam(default=None, low=1)
radius = NumberParam(default=1, low=1e-10)
neuron_type = NeuronTypeParam(default=LIF())
encoders = DistributionParam(default=UniformHypersphere(surface=True),
sample_shape=('n_neurons', 'dimensions'))
intercepts = DistributionParam(default=Uniform(-1.0, 1.0),
optional=True,
sample_shape=('n_neurons', ))
max_rates = DistributionParam(default=Uniform(200, 400),
optional=True,
sample_shape=('n_neurons', ))
n_eval_points = IntParam(default=None, optional=True)
eval_points = DistributionParam(default=UniformHypersphere(),
sample_shape=('*', 'dimensions'))
bias = DistributionParam(default=None,
optional=True,
sample_shape=('n_neurons', ))
gain = DistributionParam(default=None,
optional=True,
sample_shape=('n_neurons', ))
noise = StochasticProcessParam(default=None, optional=True)
seed = IntParam(default=None, optional=True)
label = StringParam(default=None, optional=True)
def __init__(self,
n_neurons,
dimensions,
radius=Default,
encoders=Default,
intercepts=Default,
max_rates=Default,
eval_points=Default,
n_eval_points=Default,
neuron_type=Default,
gain=Default,
bias=Default,
noise=Default,
seed=Default,
label=Default):
self.n_neurons = n_neurons
self.dimensions = dimensions
self.radius = radius
self.encoders = encoders
self.intercepts = intercepts
self.max_rates = max_rates
self.label = label
self.n_eval_points = n_eval_points
self.eval_points = eval_points
self.bias = bias
self.gain = gain
self.neuron_type = neuron_type
self.noise = noise
self.seed = seed
self._neurons = Neurons(self)
def __getitem__(self, key):
return ObjView(self, key)
def __len__(self):
return self.dimensions
@property
def neurons(self):
return self._neurons
@neurons.setter
def neurons(self, dummy):
raise AttributeError("neurons cannot be overwritten.")
@property
def probeable(self):
return ["decoded_output", "input"]
@property
def size_in(self):
return self.dimensions
@property
def size_out(self):
return self.dimensions
class Test:
ntp = NeuronTypeParam("ntp", default=None)
class Ensemble(NengoObject):
"""A group of neurons that collectively represent a vector.
Parameters
----------
n_neurons : int
The number of neurons.
dimensions : int
The number of representational dimensions.
radius : int, optional (Default: 1.0)
The representational radius of the ensemble.
encoders : Distribution or (n_neurons, dimensions) array_like, optional \
(Default: UniformHypersphere(surface=True))
The encoders used to transform from representational space
to neuron space. Each row is a neuron's encoder; each column is a
representational dimension.
intercepts : Distribution or (n_neurons,) array_like, optional \
(Default: ``nengo.dists.Uniform(-1.0, 1.0)``)
The point along each neuron's encoder where its activity is zero. If
``e`` is the neuron's encoder, then the activity will be zero when
``dot(x, e) <= c``, where ``c`` is the given intercept.
max_rates : Distribution or (n_neurons,) array_like, optional \
(Default: ``nengo.dists.Uniform(200, 400)``)
The activity of each neuron when the input signal ``x`` is magnitude 1
and aligned with that neuron's encoder ``e``;
i.e., when ``dot(x, e) = 1``.
eval_points : Distribution or (n_eval_points, dims) array_like, optional \
(Default: ``nengo.dists.UniformHypersphere()``)
The evaluation points used for decoder solving, spanning the interval
(-radius, radius) in each dimension, or a distribution from which
to choose evaluation points.
n_eval_points : int, optional (Default: None)
The number of evaluation points to be drawn from the ``eval_points``
distribution. If None, then a heuristic is used to determine
the number of evaluation points.
neuron_type : `~nengo.neurons.NeuronType`, optional \
(Default: ``nengo.LIF()``)
The model that simulates all neurons in the ensemble
(see `~nengo.neurons.NeuronType`).
gain : Distribution or (n_neurons,) array_like (Default: None)
The gains associated with each neuron in the ensemble. If None, then
the gain will be solved for using ``max_rates`` and ``intercepts``.
bias : Distribution or (n_neurons,) array_like (Default: None)
The biases associated with each neuron in the ensemble. If None, then
the gain will be solved for using ``max_rates`` and ``intercepts``.
noise : Process, optional (Default: None)
Random noise injected directly into each neuron in the ensemble
as current. A sample is drawn for each individual neuron on
every simulation step.
normalize_encoders : bool, optional (Default: True)
Indicates whether the encoders should be normalized.
label : str, optional (Default: None)
A name for the ensemble. Used for debugging and visualization.
seed : int, optional (Default: None)
The seed used for random number generation.
Attributes
----------
bias : Distribution or (n_neurons,) array_like or None
The biases associated with each neuron in the ensemble.
dimensions : int
The number of representational dimensions.
encoders : Distribution or (n_neurons, dimensions) array_like
The encoders, used to transform from representational space
to neuron space. Each row is a neuron's encoder, each column is a
representational dimension.
eval_points : Distribution or (n_eval_points, dims) array_like
The evaluation points used for decoder solving, spanning the interval
(-radius, radius) in each dimension, or a distribution from which
to choose evaluation points.
gain : Distribution or (n_neurons,) array_like or None
The gains associated with each neuron in the ensemble.
intercepts : Distribution or (n_neurons) array_like or None
The point along each neuron's encoder where its activity is zero. If
``e`` is the neuron's encoder, then the activity will be zero when
``dot(x, e) <= c``, where ``c`` is the given intercept.
label : str or None
A name for the ensemble. Used for debugging and visualization.
max_rates : Distribution or (n_neurons,) array_like or None
The activity of each neuron when ``dot(x, e) = 1``,
where ``e`` is the neuron's encoder.
n_eval_points : int or None
The number of evaluation points to be drawn from the ``eval_points``
distribution. If None, then a heuristic is used to determine
the number of evaluation points.
n_neurons : int or None
The number of neurons.
neuron_type : NeuronType
The model that simulates all neurons in the ensemble
(see ``nengo.neurons``).
noise : Process or None
Random noise injected directly into each neuron in the ensemble
as current. A sample is drawn for each individual neuron on
every simulation step.
radius : int
The representational radius of the ensemble.
seed : int or None
The seed used for random number generation.
"""
probeable = ('decoded_output', 'input', 'scaled_encoders')
n_neurons = IntParam('n_neurons', low=1)
dimensions = IntParam('dimensions', low=1)
radius = NumberParam('radius', default=1.0, low=1e-10)
encoders = DistOrArrayParam('encoders',
default=UniformHypersphere(surface=True),
sample_shape=('n_neurons', 'dimensions'))
intercepts = DistOrArrayParam('intercepts',
default=Uniform(-1.0, 1.0),
optional=True,
sample_shape=('n_neurons', ))
max_rates = DistOrArrayParam('max_rates',
default=Uniform(200, 400),
optional=True,
sample_shape=('n_neurons', ))
eval_points = DistOrArrayParam('eval_points',
default=UniformHypersphere(),
sample_shape=('*', 'dimensions'))
n_eval_points = IntParam('n_eval_points', default=None, optional=True)
neuron_type = NeuronTypeParam('neuron_type', default=LIF())
gain = DistOrArrayParam('gain',
default=None,
optional=True,
sample_shape=('n_neurons', ))
bias = DistOrArrayParam('bias',
default=None,
optional=True,
sample_shape=('n_neurons', ))
noise = ProcessParam('noise', default=None, optional=True)
normalize_encoders = BoolParam('normalize_encoders',
default=True,
optional=True)
def __init__(self,
n_neurons,
dimensions,
radius=Default,
encoders=Default,
intercepts=Default,
max_rates=Default,
eval_points=Default,
n_eval_points=Default,
neuron_type=Default,
gain=Default,
bias=Default,
noise=Default,
normalize_encoders=Default,
label=Default,
seed=Default):
super(Ensemble, self).__init__(label=label, seed=seed)
self.n_neurons = n_neurons
self.dimensions = dimensions
self.radius = radius
self.encoders = encoders
self.intercepts = intercepts
self.max_rates = max_rates
self.n_eval_points = n_eval_points
self.eval_points = eval_points
self.bias = bias
self.gain = gain
self.neuron_type = neuron_type
self.noise = noise
self.normalize_encoders = normalize_encoders
def __getitem__(self, key):
return ObjView(self, key)
def __len__(self):
return self.dimensions
@property
def neurons(self):
"""A direct interface to the neurons in the ensemble."""
return Neurons(self)
@neurons.setter
def neurons(self, dummy):
raise ReadonlyError(attr="neurons", obj=self)
@property
def size_in(self):
"""The dimensionality of the ensemble."""
return self.dimensions
@property
def size_out(self):
"""The dimensionality of the ensemble."""
return self.dimensions
class EchoState(Network, Reservoir):
"""An Echo State Network (ESN) within a Nengo Reservoir.
This creates a standard Echo State Network (ENS) as a Nengo network,
defaulting to the standard set of assumptions of non-spiking Tanh units
and a random recurrent weight matrix [1]_. This is based on the
minimalist Python implementation from [2]_.
The network takes some arbitrary time-varying vector as input, encodes it
randomly, and filters it using nonlinear units and a random recurrent
weight matrix normalized by its spectral radius.
This class also inherits ``nengolib.networks.Reservoir``, and thus the
optimal linear readout is solved for in the same way: the network is
simulated on a test signal, and then a solver is used to optimize the
decoding connection weights.
References:
[1] http://www.scholarpedia.org/article/Echo_state_network
[2] http://minds.jacobs-university.de/mantas/code
"""
n_neurons = IntParam('n_neurons', default=None, low=1)
dimensions = IntParam('dimensions', default=None, low=1)
dt = NumberParam('dt', low=0, low_open=True)
recurrent_synapse = SynapseParam('recurrent_synapse')
gain = NumberParam('gain', low=0, low_open=True)
neuron_type = NeuronTypeParam('neuron_type')
def __init__(self,
n_neurons,
dimensions,
recurrent_synapse=0.005,
readout_synapse=None,
radii=1.0,
gain=1.25,
rng=None,
neuron_type=Tanh(),
include_bias=True,
ens_seed=None,
label=None,
seed=None,
add_to_container=None,
**ens_kwargs):
"""Initializes the Echo State Network.
Parameters
----------
n_neurons : int
The number of neurons to use in the reservoir.
dimensions : int
The dimensionality of the input signal.
recurrent_synapse : nengo.synapses.Synapse (Default: ``0.005``)
Synapse used to filter the recurrent connection.
readout_synapse : nengo.synapses.Synapse (Default: ``None``)
Optional synapse to filter all of the outputs before solving
for the linear readout. This is included in the connection to the
``output`` Node created within the network.
radii : scalar or array_like, optional (Default: ``1``)
The radius of each dimension of the input signal, used to normalize
the incoming connection weights.
gain : scalar, optional (Default: ``1.25``)
A scalar gain on the recurrent connection weight matrix.
rng : ``numpy.random.RandomState``, optional (Default: ``None``)
Random state used to initialize all weights.
neuron_type : ``nengo.neurons.NeuronType`` optional \
(Default: ``Tanh()``)
Neuron model to use within the reservoir.
include_bias : ``bool`` (Default: ``True``)
Whether to include a bias current to the neural nonlinearity.
This should be ``False`` if the neuron model already has a bias,
e.g., ``LIF`` or ``LIFRate``.
ens_seed : int, optional (Default: ``None``)
Seed passed to the ensemble of neurons.
"""
Network.__init__(self, label, seed, add_to_container)
self.n_neurons = n_neurons
self.dimensions = dimensions
self.recurrent_synapse = recurrent_synapse
self.radii = radii # TODO: make array or scalar parameter?
self.gain = gain
self.rng = np.random if rng is None else rng
self.neuron_type = neuron_type
self.include_bias = include_bias
self.W_in = (self.rng.rand(self.n_neurons, self.dimensions) -
0.5) / self.radii
if self.include_bias:
self.W_bias = self.rng.rand(self.n_neurons, 1) - 0.5
else:
self.W_bias = np.zeros((self.n_neurons, 1))
self.W = self.rng.rand(self.n_neurons, self.n_neurons) - 0.5
self.W *= self.gain / max(abs(eig(self.W)[0]))
with self:
self.ensemble = nengo.Ensemble(self.n_neurons,
1,
neuron_type=self.neuron_type,
seed=ens_seed,
**ens_kwargs)
self.input = nengo.Node(size_in=self.dimensions)
pool = self.ensemble.neurons
nengo.Connection(self.input,
pool,
transform=self.W_in,
synapse=None)
nengo.Connection( # note the bias will be active during training
nengo.Node(output=1, label="bias"),
pool,
transform=self.W_bias,
synapse=None)
nengo.Connection(self.ensemble.neurons,
pool,
transform=self.W,
synapse=self.recurrent_synapse)
Reservoir.__init__(self,
self.input,
pool,
readout_synapse=readout_synapse,
network=self)
class Test:
ntp = NeuronTypeParam('ntp', default=None)
