Nengo frontend API

Nengo Objects

nengo.Network	A network contains ensembles, nodes, connections, and other networks.
nengo.Ensemble	A group of neurons that collectively represent a vector.
nengo.ensemble.Neurons	An interface for making connections directly to an ensemble’s neurons.
nengo.Node	Provide non-neural inputs to Nengo objects and process outputs.
nengo.Connection	Connects two objects together.
nengo.connection.LearningRule	An interface for making connections to a learning rule.
nengo.Probe	A probe is an object that collects data from the simulation.

class nengo.Network(label=None, seed=None, add_to_container=None)

A network contains ensembles, nodes, connections, and other networks.

A network is primarily used for grouping together related objects and connections for visualization purposes. However, you can also use networks as a nice way to reuse network creation code.

To group together related objects that you do not need to reuse, you can create a new Network and add objects in a with block. For example:

network = nengo.Network()
with network:
    with nengo.Network(label="Vision"):
        v1 = nengo.Ensemble(n_neurons=100, dimensions=2)
    with nengo.Network(label="Motor"):
        sma = nengo.Ensemble(n_neurons=100, dimensions=2)
    nengo.Connection(v1, sma)

To reuse a group of related objects, you can create a new subclass of Network, and add objects in the __init__ method. For example:

class OcularDominance(nengo.Network):
    def __init__(self):
        self.column = nengo.Ensemble(n_neurons=100, dimensions=2)

network = nengo.Network()
with network:
    left_eye = OcularDominance()
    right_eye = OcularDominance()
    nengo.Connection(left_eye.column, right_eye.column)

Parameters

labelstr, optional

Name of the network.

seedint, optional

Random number seed that will be fed to the random number generator. Setting the seed makes the network’s build process deterministic.

add_to_containerbool, optional

Determines if this network will be added to the current container. If None, this network will be added to the network at the top of the Network.context stack unless the stack is empty.

Attributes

connectionslist

Connection instances in this network.

ensembleslist

Ensemble instances in this network.

labelstr

Name of this network.

networkslist

Network instances in this network.

nodeslist

Node instances in this network.

probeslist

Probe instances in this network.

seedint

Random seed used by this network.

static add(obj)

Add the passed object to Network.context.

static default_config()

Constructs a Config object for setting defaults.

property all_objects

(list) All objects in this network and its subnetworks.

property all_ensembles

(list) All ensembles in this network and its subnetworks.

property all_nodes

(list) All nodes in this network and its subnetworks.

property all_networks

(list) All networks in this network and its subnetworks.

property all_connections

(list) All connections in this network and its subnetworks.

property all_probes

(list) All probes in this network and its subnetworks.

property config

(Config) Configuration for this network.

property n_neurons

(int) Number of neurons in this network, including subnetworks.

class nengo.Ensemble(*args, **kwargs)

A group of neurons that collectively represent a vector.

Parameters

n_neuronsint

The number of neurons.

dimensionsint

The number of representational dimensions.

radiusint, optional

The representational radius of the ensemble.

encodersDistribution or (n_neurons, dimensions) array_like, 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.

interceptsDistribution or (n_neurons,) array_like, 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_ratesDistribution or (n_neurons,) array_like, optional

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_pointsDistribution or (n_eval_points, dims) array_like, 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.

n_eval_pointsint, optional

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_typeNeuronType, optional

The model that simulates all neurons in the ensemble (see NeuronType).

gainDistribution or (n_neurons,) array_like

The gains associated with each neuron in the ensemble. If None, then the gain will be solved for using max_rates and intercepts.

biasDistribution or (n_neurons,) array_like

The biases associated with each neuron in the ensemble. If None, then the gain will be solved for using max_rates and intercepts.

noiseProcess, 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.

normalize_encodersbool, optional

Indicates whether the encoders should be normalized.

labelstr, optional

A name for the ensemble. Used for debugging and visualization.

seedint, optional

The seed used for random number generation.

Attributes

biasDistribution or (n_neurons,) array_like or None

The biases associated with each neuron in the ensemble.

dimensionsint

The number of representational dimensions.

encodersDistribution 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_pointsDistribution 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.

gainDistribution or (n_neurons,) array_like or None

The gains associated with each neuron in the ensemble.

interceptsDistribution 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.

labelstr or None

A name for the ensemble. Used for debugging and visualization.

max_ratesDistribution 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_pointsint 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_neuronsint or None

The number of neurons.

neuron_typeNeuronType

The model that simulates all neurons in the ensemble (see nengo.neurons).

noiseProcess 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.

radiusint

The representational radius of the ensemble.

seedint or None

The seed used for random number generation.

property neurons

A direct interface to the neurons in the ensemble.

property size_in

The dimensionality of the ensemble.

property size_out

The dimensionality of the ensemble.

class nengo.ensemble.Neurons(ensemble)

An interface for making connections directly to an ensemble’s neurons.

This should only ever be accessed through the neurons attribute of an ensemble, as a way to signal to Connection that the connection should be made directly to the neurons rather than to the ensemble’s decoded value, e.g.:

with nengo.Network():
    a = nengo.Ensemble(10, 1)
    b = nengo.Ensemble(10, 1)
    nengo.Connection(a.neurons, b.neurons)

property ensemble

(Ensemble) The ensemble these neurons are part of.

property probeable

(tuple) Signals that can be probed in the neuron population.

property size_in

(int) The number of neurons in the population.

property size_out

(int) The number of neurons in the population.

class nengo.Node(*args, **kwargs)

Provide non-neural inputs to Nengo objects and process outputs.

Nodes can accept input, and perform arbitrary computations for the purpose of controlling a Nengo simulation. Nodes are typically not part of a brain model per se, but serve to summarize the assumptions being made about sensory data or other environment variables that cannot be generated by a brain model alone.

Nodes can also be used to test models by providing specific input signals to parts of the model, and can simplify the input/output interface of a Network when used as a relay to/from its internal ensembles (see EnsembleArray for an example).

Parameters

outputcallable, array_like, or None

Function that transforms the Node inputs into outputs, a constant output value, or None to transmit signals unchanged.

size_inint, optional

The number of dimensions of the input data parameter.

size_outint, optional

The size of the output signal. If None, it will be determined based on the values of output and size_in.

labelstr, optional

A name for the node. Used for debugging and visualization.

seedint, optional

The seed used for random number generation. Note: no aspects of the node are random, so currently setting this seed has no effect.

Attributes

labelstr

The name of the node.

outputcallable, array_like, or None

The given output.

size_inint

The number of dimensions for incoming connection.

size_outint

The number of output dimensions.

class nengo.Connection(*args, **kwargs)

Connects two objects together.

The connection between the two object is unidirectional, transmitting information from the first argument, pre, to the second argument, post.

Almost any Nengo object can act as the pre or post side of a connection. Additionally, you can use Python slice syntax to access only some of the dimensions of the pre or post object.

For example, if node has size_out=2 and ensemble has size_in=1:

with nengo.Network() as net:
    node = nengo.Node(np.zeros(2))
    ensemble = nengo.Ensemble(10, 1)

We could not create the following connection:

with net:
    nengo.Connection(node, ensemble)

But, we could create either of these two connections:

with net:
    nengo.Connection(node[0], ensemble)
    nengo.Connection(node[1], ensemble)

Parameters

preEnsemble or Neurons or Node

The source Nengo object for the connection.

postEnsemble or Neurons or Node or LearningRule

The destination object for the connection.

synapseSynapse or None, optional

Synapse model to use for filtering (see Synapse). If None, no synapse will be used and information will be transmitted without any delay (if supported by the backend—some backends may introduce a single time step delay).

Note that at least one connection must have a synapse that is not None if components are connected in a cycle. Furthermore, a synaptic filter with a zero time constant is different from a None synapse as a synaptic filter will always add a delay of at least one time step.

functioncallable or (n_eval_points, size_mid) array_like, optional

Function to compute across the connection. Note that pre must be an ensemble to apply a function across the connection. If an array is passed, the function is implicitly defined by the points in the array and the provided eval_points, which have a one-to-one correspondence.

transform(size_out, size_mid) array_like, optional

Linear transform mapping the pre output to the post input. This transform is in terms of the sliced size; if either pre or post is a slice, the transform must be shaped according to the sliced dimensionality. Additionally, the function is applied before the transform, so if a function is computed across the connection, the transform must be of shape (size_out, size_mid).

solverSolver, optional

Solver instance to compute decoders or weights (see Solver). If solver.weights is True, a full connection weight matrix is computed instead of decoders.

learning_rule_typeLearningRuleType or iterable of LearningRuleType, optional

Modifies the decoders or connection weights during simulation.

eval_points(n_eval_points, size_in) array_like or int, optional

Points at which to evaluate function when computing decoders, spanning the interval (-pre.radius, pre.radius) in each dimension. If None, will use the eval_points associated with pre.

scale_eval_pointsbool, optional

Indicates whether the evaluation points should be scaled by the radius of the pre Ensemble.

labelstr, optional

A descriptive label for the connection.

seedint, optional

The seed used for random number generation.

Attributes

functioncallable

The given function.

function_sizeint

The output dimensionality of the given function. If no function is specified, function_size will be 0.

labelstr

A human-readable connection label for debugging and visualization. If not overridden, incorporates the labels of the pre and post objects.

learning_rule_typeinstance or list or dict of LearningRuleType, optional

The learning rule types.

postEnsemble or Neurons or Node or Probe or ObjView

The given post object.

post_objEnsemble or Neurons or Node or Probe

The underlying post object, even if post is an ObjView.

post_sliceslice or list or None

The slice associated with post if it is an ObjView, or None.

preEnsemble or Neurons or Node or ObjView

The given pre object.

pre_objEnsemble or Neurons or Node

The underlying pre object, even if post is an ObjView.

pre_sliceslice or list or None

The slice associated with pre if it is an ObjView, or None.

seedint

The seed used for random number generation.

solverSolver

The Solver instance that will be used to compute decoders or weights (see nengo.solvers).

synapseSynapse

The Synapse model used for filtering across the connection (see nengo.synapses).

transform(size_out, size_mid) array_like

Linear transform mapping the pre function output to the post input.

property learning_rule

(LearningRule or iterable) Connectable learning rule object(s).

property size_in

(int) The number of output dimensions of the pre object.

Also the input size of the function, if one is specified.

property size_mid

(int) The number of output dimensions of the function, if specified.

If the function is not specified, then size_in == size_mid.

property size_out

(int) The number of input dimensions of the post object.

Also the number of output dimensions of the transform.

class nengo.connection.LearningRule(connection, learning_rule_type)

An interface for making connections to a learning rule.

Connections to a learning rule are to allow elements of the network to affect the learning rule. For example, learning rules that use error information can obtain that information through a connection.

Learning rule objects should only ever be accessed through the learning_rule attribute of a connection.

property connection

(Connection) The connection modified by the learning rule.

property modifies

(str) The variable modified by the learning rule.

property probeable

(tuple) Signals that can be probed in the learning rule.

property size_out

(int) Cannot connect from learning rules, so always 0.

class nengo.Probe(*args, **kwargs)

A probe is an object that collects data from the simulation.

This is to be used in any situation where you wish to gather simulation data (spike data, represented values, neuron voltages, etc.) for analysis.

Probes do not directly affect the simulation.

All Nengo objects can be probed (except Probes themselves). Each object has different attributes that can be probed. To see what is probeable for each object, print its probeable attribute.

with nengo.Network():
    ens = nengo.Ensemble(10, 1)
print(ens.probeable)

('decoded_output', 'input', 'scaled_encoders')

Parameters

targetEnsemble, Neurons, Node, or Connection

The object to probe.

attrstr, optional

The signal to probe. Refer to the target’s probeable list for details. If None, the first element in the probeable list will be used.

sample_everyfloat, optional

Sampling period in seconds. If None, the dt of the simluation will be used.

synapseSynapse, optional

A synaptic model to filter the probed signal.

solverSolver, optional

Solver to compute decoders for probes that require them.

labelstr, optional

A name for the probe. Used for debugging and visualization.

seedint, optional

The seed used for random number generation.

Attributes

attrstr or None

The signal that will be probed. If None, the first element of the target’s probeable list will be used.

sample_everyfloat or None

Sampling period in seconds. If None, the dt of the simluation will be used.

solverSolver or None

Solver to compute decoders. Only used for probes of an ensemble’s decoded output.

synapseSynapse or None

A synaptic model to filter the probed signal.

targetEnsemble, Neurons, Node, or Connection

The object to probe.

property obj

(Nengo object) The underlying Nengo object target.

property size_in

(int) Dimensionality of the probed signal.

property size_out

(int) Cannot connect from probes, so always 0.

property slice

(slice) The slice associated with the Nengo object target.

Distributions

nengo.dists.Distribution	A base class for probability distributions.
nengo.dists.get_samples	Convenience function to sample a distribution or return samples.
nengo.dists.PDF	An arbitrary distribution from a PDF.
nengo.dists.Uniform	A uniform distribution.
nengo.dists.Gaussian	A Gaussian distribution.
nengo.dists.Exponential	An exponential distribution (optionally with high values clipped).
nengo.dists.UniformHypersphere	Uniform distribution on or in an n-dimensional unit hypersphere.
nengo.dists.QuasirandomSequence	Sequence for quasi Monte Carlo sampling the [0, 1]-cube.
nengo.dists.ScatteredHypersphere	Quasirandom distribution over the hypersphere or hyperball.
nengo.dists.Choice	Discrete distribution across a set of possible values.
nengo.dists.Samples	A set of samples.
nengo.dists.SqrtBeta	Distribution of the square root of a Beta distributed random variable.
nengo.dists.SubvectorLength	Distribution of the length of a subvectors of a unit vector.
nengo.dists.CosineSimilarity	Distribution of the cosine of the angle between two random vectors.

class nengo.dists.Distribution

A base class for probability distributions.

The only thing that a probabilities distribution need to define is a Distribution.sample method. This base class ensures that all distributions accept the same arguments for the sample function.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.DistributionParam(name, default=Unconfigurable, optional=False, readonly=None)

A Distribution.

class nengo.dists.DistOrArrayParam(name, default=Unconfigurable, sample_shape=None, sample_dtype=<class 'numpy.float64'>, optional=False, readonly=None)

Can be a Distribution or samples from a distribution.

nengo.dists.get_samples(dist_or_samples, n, d=None, rng=numpy.random)

Convenience function to sample a distribution or return samples.

Use this function in situations where you accept an argument that could be a distribution, or could be an array_like of samples.

Parameters

dist_or_samplesDistribution or (n, d) array_like

Source of the samples to be returned.

nint

Number samples to take.

dint or None, optional

The number of dimensions to return.

rngRandomState, optional

Random number generator.

Returns

samples(n, d) array_like

Examples

from nengo.dists import get_samples

rng = np.random.RandomState(seed=0)

def mean(values, n=100):
    samples = get_samples(values, n=n, rng=rng)
    print(f"{np.mean(samples):.4f}")

mean([1, 2, 3, 4])
mean(nengo.dists.Gaussian(0, 1))

2.5000
0.0598

class nengo.dists.PDF(x, p)

An arbitrary distribution from a PDF.

Parameters

xvector_like (n,)

Values of the points to sample from (interpolated).

pvector_like (n,)

Probabilities of the x points.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.Uniform(low, high, integer=False)

A uniform distribution.

It’s equally likely to get any scalar between low and high.

Note that the order of low and high doesn’t matter; if low < high this will still work, and low will still be a closed interval while high is open.

Parameters

lowNumber

The closed lower bound of the uniform distribution; samples >= low

highNumber

The open upper bound of the uniform distribution; samples < high

integerboolean, optional

If true, sample from a uniform distribution of integers. In this case, low and high should be integers.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.Gaussian(mean, std)

A Gaussian distribution.

This represents a bell-curve centred at mean and with spread represented by the standard deviation, std.

Parameters

meanNumber

The mean of the Gaussian.

stdNumber

The standard deviation of the Gaussian.

Raises

ValidationError if std is <= 0

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.Exponential(scale, shift=0.0, high=inf)

An exponential distribution (optionally with high values clipped).

If high is left to its default value of infinity, this is a standard exponential distribution. If high is set, then any sampled values at or above high will be clipped so they are slightly below high. This is useful for thresholding.

The probability distribution function (PDF) is given by:

       |  0                                 if x < shift
p(x) = | 1/scale * exp(-(x - shift)/scale)  if x >= shift and x < high
       |  n                                 if x == high - eps
       |  0                                 if x >= high

where n is such that the PDF integrates to one, and eps is an infinitesimally small number such that samples of x are strictly less than high (in practice, eps depends on floating point precision).

Parameters

scalefloat

The scale parameter (inverse of the rate parameter lambda). Larger values make the distribution narrower (sharper peak).

shiftfloat, optional

Amount to shift the distribution by. There will be no values smaller than this shift when sampling from the distribution.

highfloat, optional

All values larger than or equal to this value will be clipped to slightly less than this value.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.UniformHypersphere(surface=False, min_magnitude=0)

Uniform distribution on or in an n-dimensional unit hypersphere.

Sample points are uniformly distributed across the volume (default) or surface of an n-dimensional unit hypersphere.

Parameters

surfacebool, optional

Whether sample points should be distributed uniformly over the surface of the hyperphere (True), or within the hypersphere (False).

min_magnitudeNumber, optional

Lower bound on the returned vector magnitudes (such that they are in the range [min_magnitude, 1]). Must be in the range [0, 1). Ignored if surface is True.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.QuasirandomSequence

Sequence for quasi Monte Carlo sampling the [0, 1]-cube.

This is similar to np.random.uniform(0, 1, size=(num, d)), but with the additional property that each d-dimensional point is uniformly scattered.

While the sequence is defined deterministically, we introduce two stochastic elements to encourage heterogeneity in models using these sequences. First, we offset the start of the sequence by a random number between 0 and 1 to ensure we don’t oversample points aligned to the step size. Second, we shuffle the resulting sequence before returning to ensure we don’t introduce correlations between parameters sampled from this distribution.

This is based on the tutorial and code from 1.

See also

ScatteredHypersphere

References

1

Martin Roberts. “The Unreasonable Effectiveness of Quasirandom Sequences.” https://web.archive.org/web/20211029094035/http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/

Examples

rd = nengo.dists.QuasirandomSequence().sample(10000, 2)
plt.scatter(*rd.T, c=np.arange(len(rd)), cmap='Blues', s=7)

sample(self, n, d=1, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.ScatteredHypersphere(surface=False, min_magnitude=0, base=QuasirandomSequence(), method='sct-approx')

Quasirandom distribution over the hypersphere or hyperball.

Applies a spherical transform to the given quasirandom sequence (by default QuasirandomSequence) to obtain uniformly scattered samples.

This distribution has the nice mathematical property that the discrepancy between the empirical distribution and \(n\) samples is \(\widetilde{\mathcal{O}} (1 / n)\) as opposed to \(\mathcal{O} (1 / \sqrt{n})\) for the Monte Carlo method [1]. This means that the number of samples is effectively squared, making this useful as a means for sampling eval_points and encoders.

Parameters

surfacebool, optional

Whether sample points should be distributed uniformly over the surface of the hyperphere (True), or within the hypersphere (False).

min_magnitudeNumber, optional

Lower bound on the returned vector magnitudes (such that they are in the range [min_magnitude, 1]). Must be in the range [0, 1). Ignored if surface is True.

baseDistribution, optional

The base distribution from which to sample quasirandom numbers.

method{“sct-approx”, “sct”, “tfww”}

Method to use for mapping points to the hypersphere.

• “sct-approx”: Same as “sct”, but uses lookup table to approximate the beta distribution, making it faster with almost exactly the same result.

• “sct”: Use the exact Spherical Coordinate Transform (section 1.5.2 of [1]).

• “tfww”: Use the Tashiro-Fang-Wang-Wong method (section 4.3 of [1]). Faster than “sct” and “sct-approx”, with the same level of uniformity for larger numbers of samples (n >= 4000, approximately).

See also

UniformHypersphere

QuasirandomSequence

Notes

The QuasirandomSequence distribution is mostly deterministic. Nondeterminism comes from a random d-dimensional rotation.

References

1(1,2,3)

K.-T. Fang and Y. Wang, Number-Theoretic Methods in Statistics. Chapman & Hall, 1994.

Examples

Plot points sampled from the surface of the sphere in 3 dimensions:

from mpl_toolkits.mplot3d import Axes3D

points = nengo.dists.ScatteredHypersphere(surface=True).sample(1000, d=3)

ax = plt.subplot(111, projection="3d")
ax.scatter(*points.T, s=5)

Plot points sampled from the volume of the sphere in 2 dimensions (i.e. circle):

points = nengo.dists.ScatteredHypersphere(surface=False).sample(1000, d=2)
plt.scatter(*points.T, s=5)

classmethod spherical_transform_sct(samples, approx=False)

Map samples from the [0, 1]-cube onto the hypersphere.

Uses the SCT method described in section 1.5.3 of Fang and Wang (1994).

static spherical_transform_tfww(c_samples)

Map samples from the [0, 1]-cube onto the hypersphere surface.

Uses the TFWW method described in section 4.3 of Fang and Wang (1994).

static random_orthogonal(d, rng=numpy.random)

Returns a random orthogonal matrix.

sample(self, n, d=1, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.Choice(options, weights=None)

Discrete distribution across a set of possible values.

The same as Numpy random’s choice, except can take vector or matrix values for the choices.

Parameters

options(N, …) array_like

The options (choices) to choose between. The choice is always done along the first axis, so if options is a matrix, the options are the rows of that matrix.

weights(N,) array_like, optional

Weights controlling the probability of selecting each option. Will automatically be normalized. If None, weights be uniformly distributed.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.Samples(samples)

A set of samples.

This class is a subclass of Distribution so that it can be used in any situation that calls for a Distribution. However, the call to Distribution.sample must match the dimensions of the samples or a ValidationError will be raised.

Parameters

samples(n, d) array_like

n and d must match what is eventually passed to

Distribution.sample.

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

class nengo.dists.SqrtBeta(n, m=1)

Distribution of the square root of a Beta distributed random variable.

Given n + m dimensional random unit vectors, the length of subvectors with m elements will be distributed according to this distribution.

Parameters

n: int

Number of subvectors.

m: int, optional

Length of each subvector.

See also

nengo.dists.SubvectorLength

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

cdf(x)

Cumulative distribution function.

Note

Requires SciPy.

Parameters

xarray_like

Evaluation points in [0, 1].

Returns

cdfarray_like

Probability that X <= x.

pdf(x)

Probability distribution function.

Note

Requires SciPy.

Parameters

xarray_like

Evaluation points in [0, 1].

Returns

pdfarray_like

Probability density at x.

ppf(y)

Percent point function (inverse cumulative distribution).

Note

Requires SciPy.

Parameters

yarray_like

Cumulative probabilities in [0, 1].

Returns

ppfarray_like

Evaluation points x in [0, 1] such that P(X <= x) = y.

class nengo.dists.SubvectorLength(dimensions, subdimensions=1)

Distribution of the length of a subvectors of a unit vector.

Parameters

dimensionsint

Dimensionality of the complete unit vector.

subdimensionsint, optional

Dimensionality of the subvector.

See also

nengo.dists.SqrtBeta

class nengo.dists.CosineSimilarity(dimensions)

Distribution of the cosine of the angle between two random vectors.

The “cosine similarity” is the cosine of the angle between two vectors, which is equal to the dot product of the vectors, divided by the L2-norms of the individual vectors. When these vectors are unit length, this is then simply the distribution of their dot product.

This is also equivalent to the distribution of a single coefficient from a unit vector (a single dimension of UniformHypersphere(surface=True)). Furthermore, CosineSimilarity(d+2) is equivalent to the distribution of a single coordinate from points uniformly sampled from the d-dimensional unit ball (a single dimension of UniformHypersphere(surface=False).sample(n, d)). These relationships have been detailed in [Voelker2017].

This can be used to calculate an intercept c = ppf(1 - p) such that dot(u, v) >= c with probability p, for random unit vectors u and v. In other words, a neuron with intercept ppf(1 - p) will fire with probability p for a random unit length input.

Voelker2017

Aaron R. Voelker, Jan Gosmann, and Terrence C. Stewart. Efficiently sampling vectors and coordinates from the n-sphere and n-ball. Technical Report, Centre for Theoretical Neuroscience, Waterloo, ON, 2017

Parameters

dimensions: int

Dimensionality of the complete unit vector.

See also

nengo.dists.SqrtBeta

sample(self, n, d=None, rng=numpy.random)

Samples the distribution.

Parameters

nint

Number samples to take.

dint or None, optional

The number of dimensions to return. If this is an int, the return value will be of shape (n, d). If None, the return value will be of shape (n,).

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

samples(n,) or (n, d) array_like

Samples as a 1d or 2d array depending on d. The second dimension enumerates the dimensions of the process.

cdf(x)

Cumulative distribution function.

Note

Requires SciPy.

Parameters

xarray_like

Evaluation points in [0, 1].

Returns

cdfarray_like

Probability that X <= x.

pdf(x)

Probability distribution function.

Note

Requires SciPy.

Parameters

xarray_like

Evaluation points in [0, 1].

Returns

pdfarray_like

Probability density at x.

ppf(y)

Percent point function (inverse cumulative distribution).

Note

Requires SciPy.

Parameters

yarray_like

Cumulative probabilities in [0, 1].

Returns

ppfarray_like

Evaluation points x in [0, 1] such that P(X <= x) = y.

Learning rule types

nengo.learning_rules.LearningRuleType	Base class for all learning rule objects.
nengo.PES	Prescribed Error Sensitivity learning rule.
nengo.RLS	Recursive least-squares rule for online decoder optimization.
nengo.BCM	Bienenstock-Cooper-Munroe learning rule.
nengo.Oja	Oja learning rule.
nengo.Voja	Vector Oja learning rule.

class nengo.learning_rules.LearningRuleTypeSizeInParam(name, default=Unconfigurable, low=None, high=None, low_open=False, high_open=False, optional=False, readonly=None)

class nengo.learning_rules.LearningRuleType(learning_rate=Default<1e-06>, size_in=0)

Base class for all learning rule objects.

To use a learning rule, pass it as a learning_rule_type keyword argument to the Connection on which you want to do learning.

Each learning rule exposes two important pieces of metadata that the builder uses to determine what information should be stored.

The size_in is the dimensionality of the incoming error signal. It can either take an integer or one of the following string values:

• 'pre': vector error signal in pre-object space

• 'post': vector error signal in post-object space

• 'mid': vector error signal in the conn.size_mid space

• 'pre_state': vector error signal in pre-synaptic ensemble space

• 'post_state': vector error signal in post-synaptic ensemble space

The difference between 'post_state' and 'post' is that with the former, if a Neurons object is passed, it will use the dimensionality of the corresponding Ensemble, whereas the latter simply uses the post object size_in. Similarly with 'pre_state' and 'pre'.

The modifies attribute denotes the signal targeted by the rule. Options are:

• 'encoders'

• 'decoders'

• 'weights'

Parameters

learning_ratefloat, optional

A scalar indicating the rate at which modifies will be adjusted.

size_inint, str, optional

Dimensionality of the error signal (see above).

Attributes

learning_ratefloat

A scalar indicating the rate at which modifies will be adjusted.

size_inint, str

Dimensionality of the error signal.

modifiesstr

The signal targeted by the learning rule.

class nengo.PES(learning_rate=Default<0.0001>, pre_synapse=Default<Lowpass(tau=0.005)>)

Prescribed Error Sensitivity learning rule.

Modifies a connection’s decoders to minimize an error signal provided through a connection to the connection’s learning rule.

Parameters

learning_ratefloat, optional

A scalar indicating the rate at which weights will be adjusted.

pre_synapseSynapse, optional

Synapse model used to filter the pre-synaptic activities.

Attributes

learning_ratefloat

A scalar indicating the rate at which weights will be adjusted.

pre_synapseSynapse

Synapse model used to filter the pre-synaptic activities.

class nengo.RLS(learning_rate=Default<0.001>, pre_synapse=Default<Lowpass(tau=0.005)>)

Recursive least-squares rule for online decoder optimization.

This implements an online version of the standard least-squares solvers used to learn connection weights offline (e.g. nengo.solvers.LstsqL2). It can be applied in the same scenarios as PES, to minimize an error signal.

The cost of RLS is \(\mathcal{O}(n^2)\) extra time and memory. If possible, it is more efficient to do the learning offline using e.g. LstsqL2.

Parameters

learning_ratefloat, optional

Effective learning rate. This is better understood as \(\frac{1}{\alpha}\), where \(\alpha\) is an L2-regularization term. A large learning rate means little regularization, which implies quick over-fitting. A small learning rate means large regularization, which translates to slower learning 2.

pre_synapseSynapse, optional

Synapse model applied to the pre-synaptic neural activities.

See also

nengo.PES

nengo.solvers.LstsqL2

Notes

RLS works by maintaining the inverse neural correlation matrix, \(P = \Gamma^{-1}\), where \(\Gamma = A^T A + \alpha I\) are the regularized correlations, \(A\) is a matrix of (possibly filtered) neural activities, and \(\alpha\) is an L2-regularization term controlled by the learning_rate. \(P\) is used to project the error signal and update the weights each time-step.

References

2

Sussillo, D., & Abbott, L. F. (2009). Generating coherent patterns of activity from chaotic neural networks. Neuron, 63(4), 544-557.

Examples

Below, we compare PES against RLS, learning a feed-forward communication channel (identity function) online, starting with 100 spiking LIF neurons with decoders (weights) set to zero. A faster learning rate for PES results in over-fitting to the most recent online example, while a slower learning rate does not learn quickly enough. This is a general problem with greedy optimization. RLS performs better since it is L2-optimal.

from nengo.learning_rules import PES, RLS

tau = 0.005
learning_rules = (
    PES(learning_rate=1e-3, pre_synapse=tau),
    RLS(learning_rate=1e-3, pre_synapse=tau),
)

with nengo.Network() as model:
    u = nengo.Node(output=lambda t: np.sin(2 * np.pi * t))
    probes = []
    for lr in learning_rules:
        e = nengo.Node(size_in=1, output=lambda t, e: e if t < 1 else 0)
        x = nengo.Ensemble(100, 1, seed=0)
        y = nengo.Node(size_in=1)

        nengo.Connection(u, e, synapse=None, transform=-1)
        nengo.Connection(u, x, synapse=None)
        conn = nengo.Connection(
            x, y, synapse=None, learning_rule_type=lr, function=lambda x: 0
        )
        nengo.Connection(y, e, synapse=None)
        nengo.Connection(e, conn.learning_rule, synapse=tau)
        probes.append(nengo.Probe(y, synapse=tau))
    probes.append(nengo.Probe(u, synapse=tau))

with nengo.Simulator(model) as sim:
    sim.run(2.0)

plt.plot(sim.trange(), sim.data[probes[0]], label=str(learning_rules[0]))
plt.plot(sim.trange(), sim.data[probes[1]], label=str(learning_rules[1]))
plt.plot(sim.trange(), sim.data[probes[2]], label="Ideal", linestyle="--")
plt.vlines([1], -1, 1, label="Training -> Testing")
plt.ylim(-2, 2)
plt.legend(loc="upper right")
plt.xlabel("Time (s)")

class nengo.BCM(learning_rate=Default<1e-09>, pre_synapse=Default<Lowpass(tau=0.005)>, post_synapse=Default<None>, theta_synapse=Default<Lowpass(tau=1.0)>)

Bienenstock-Cooper-Munroe learning rule.

Modifies connection weights as a function of the presynaptic activity and the difference between the postsynaptic activity and the average postsynaptic activity.

Parameters

learning_ratefloat, optional

A scalar indicating the rate at which weights will be adjusted.

pre_synapseSynapse, optional

Synapse model used to filter the pre-synaptic activities.

post_synapseSynapse, optional

Synapse model used to filter the post-synaptic activities. If None, post_synapse will be the same as pre_synapse.

theta_synapseSynapse, optional

Synapse model used to filter the theta signal.

Notes

The BCM rule is dependent on pre and post neural activities, not decoded values, and so is not affected by changes in the size of pre and post ensembles. However, if you are decoding from the post ensemble, the BCM rule will have an increased effect on larger post ensembles because more connection weights are changing. In these cases, it may be advantageous to scale the learning rate on the BCM rule by 1 / post.n_neurons.

Attributes

learning_ratefloat

A scalar indicating the rate at which weights will be adjusted.

post_synapseSynapse

Synapse model used to filter the post-synaptic activities.

pre_synapseSynapse

Synapse model used to filter the pre-synaptic activities.

theta_synapseSynapse

Synapse model used to filter the theta signal.

class nengo.Oja(learning_rate=Default<1e-06>, pre_synapse=Default<Lowpass(tau=0.005)>, post_synapse=Default<None>, beta=Default<1.0>)

Oja learning rule.

Modifies connection weights according to the Hebbian Oja rule, which augments typically Hebbian coactivity with a “forgetting” term that is proportional to the weight of the connection and the square of the postsynaptic activity.

Parameters

learning_ratefloat, optional

A scalar indicating the rate at which weights will be adjusted.

pre_synapseSynapse, optional

Synapse model used to filter the pre-synaptic activities.

post_synapseSynapse, optional

Synapse model used to filter the post-synaptic activities. If None, post_synapse will be the same as pre_synapse.

betafloat, optional

A scalar weight on the forgetting term.

Notes

The Oja rule is dependent on pre and post neural activities, not decoded values, and so is not affected by changes in the size of pre and post ensembles. However, if you are decoding from the post ensemble, the Oja rule will have an increased effect on larger post ensembles because more connection weights are changing. In these cases, it may be advantageous to scale the learning rate on the Oja rule by 1 / post.n_neurons.

Attributes

betafloat

A scalar weight on the forgetting term.

learning_ratefloat

A scalar indicating the rate at which weights will be adjusted.

post_synapseSynapse

Synapse model used to filter the post-synaptic activities.

pre_synapseSynapse

Synapse model used to filter the pre-synaptic activities.

class nengo.Voja(learning_rate=Default<0.01>, post_synapse=Default<Lowpass(tau=0.005)>)

Vector Oja learning rule.

Modifies an ensemble’s encoders to be selective to its inputs.

A connection to the learning rule will provide a scalar weight for the learning rate, minus 1. For instance, 0 is normal learning, -1 is no learning, and less than -1 causes anti-learning or “forgetting”.

Parameters

post_taufloat, optional

Filter constant on activities of neurons in post population.

learning_ratefloat, optional

A scalar indicating the rate at which encoders will be adjusted.

post_synapseSynapse, optional

Synapse model used to filter the post-synaptic activities.

Attributes

learning_ratefloat

A scalar indicating the rate at which encoders will be adjusted.

post_synapseSynapse

Synapse model used to filter the post-synaptic activities.

class nengo.learning_rules.LearningRuleTypeParam(name, default=Unconfigurable, optional=False, readonly=None)

Neuron types

nengo.neurons.settled_firingrate	Compute firing rates (in Hz) for given vector input, x.
nengo.neurons.NeuronType	Base class for Nengo neuron models.
nengo.Direct	Signifies that an ensemble should simulate in direct mode.
nengo.RectifiedLinear	A rectified linear neuron model.
nengo.SpikingRectifiedLinear	A rectified integrate and fire neuron model.
nengo.Sigmoid	A non-spiking neuron model whose response curve is a sigmoid.
nengo.Tanh	A non-spiking neuron model whose response curve is a hyperbolic tangent.
nengo.LIFRate	Non-spiking version of the leaky integrate-and-fire (LIF) neuron model.
nengo.LIF	Spiking version of the leaky integrate-and-fire (LIF) neuron model.
nengo.AdaptiveLIFRate	Adaptive non-spiking version of the LIF neuron model.
nengo.AdaptiveLIF	Adaptive spiking version of the LIF neuron model.
nengo.Izhikevich	Izhikevich neuron model.
nengo.neurons.RatesToSpikesNeuronType	Base class for neuron types that turn rate types into spiking ones.
nengo.RegularSpiking	Turn a rate neuron type into a spiking one with regular inter-spike intervals.
nengo.StochasticSpiking	Turn a rate neuron type into a spiking one using stochastic rounding.
nengo.PoissonSpiking	Turn a rate neuron type into a spiking one with Poisson spiking statistics.

nengo.neurons.settled_firingrate(step, J, state, dt=0.001, settle_time=0.1, sim_time=1.0)

Compute firing rates (in Hz) for given vector input, x.

Unlike the default naive implementation, this approach takes into account some characteristics of spiking neurons. We start by simulating the neurons for a short amount of time, to let any initial transients settle. Then, we run the neurons for a second and find the average (which should approximate the firing rate).

Parameters

stepfunction

the step function of the neuron type

Jndarray

a vector of currents to generate firing rates from

statedict of ndarrays

additional state needed by the step function

class nengo.neurons.NeuronType(initial_state=None)

Base class for Nengo neuron models.

Parameters

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

Attributes

state{str: Distribution}

State variables held by the neuron type during simulation. Values in the dict indicate their initial values, or how to obtain those initial values. These elements can also be probed in the neuron population.

negativebool

Whether the neurons can emit negative outputs (i.e. negative spikes or rates).

current(x, gain, bias)

Compute current injected in each neuron given input, gain and bias.

Note that x is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected current for a neuron occurs when input for that neuron is 1.

Parameters

x(n_samples,) or (n_samples, n_neurons) array_like

Scalar inputs for which to calculate current.

gain(n_neurons,) array_like

Gains associated with each neuron.

bias(n_neurons,) array_like

Bias current associated with each neuron.

Returns

current(n_samples, n_neurons)

Current to be injected in each neuron.

gain_bias(max_rates, intercepts)

Compute the gain and bias needed to satisfy max_rates, intercepts.

This takes the neurons, approximates their response function, and then uses that approximation to find the gain and bias value that will give the requested intercepts and max_rates.

Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuron-specific implementation.

Parameters

max_rates(n_neurons,) array_like

Maximum firing rates of neurons.

intercepts(n_neurons,) array_like

X-intercepts of neurons.

Returns

gain(n_neurons,) array_like

Gain associated with each neuron. Sometimes denoted alpha.

bias(n_neurons,) array_like

Bias current associated with each neuron.

max_rates_intercepts(gain, bias)

Compute the max_rates and intercepts given gain and bias.

Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuron-specific implementation.

Parameters

gain(n_neurons,) array_like

Gain associated with each neuron. Sometimes denoted alpha.

bias(n_neurons,) array_like

Bias current associated with each neuron.

Returns

max_rates(n_neurons,) array_like

Maximum firing rates of neurons.

intercepts(n_neurons,) array_like

X-intercepts of neurons.

rates(x, gain, bias)

Compute firing rates (in Hz) for given input x.

This default implementation takes the naive approach of running the step function for a second. This should suffice for most rate-based neuron types; for spiking neurons it will likely fail (those models should override this function).

Note that x is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected rate for a neuron occurs when input for that neuron is 1.

Parameters

x(n_samples,) or (n_samples, n_neurons) array_like

Scalar inputs for which to calculate rates.

gain(n_neurons,) array_like

Gains associated with each neuron.

bias(n_neurons,) array_like

Bias current associated with each neuron.

Returns

rates(n_samples, n_neurons) ndarray

The firing rates at each given value of x.

step(dt, J, output, **state)

Implements the differential equation for this neuron type.

At a minimum, NeuronType subclasses must implement this method. That implementation should modify the output parameter rather than returning anything, for efficiency reasons.

Parameters

dtfloat

Simulation timestep.

J(n_neurons,) array_like

Input currents associated with each neuron.

output(n_neurons,) array_like

Output activity associated with each neuron (e.g., spikes or firing rates).

state{str: array_like}

State variables associated with the population.

class nengo.neurons.NeuronTypeParam(name, default=Unconfigurable, optional=False, readonly=None)

class nengo.Direct(initial_state=None)

Signifies that an ensemble should simulate in direct mode.

In direct mode, the ensemble represents and transforms signals perfectly, rather than through a neural approximation. Note that direct mode ensembles with recurrent connections can easily diverge; most other neuron types will instead saturate at a certain high firing rate.

gain_bias(max_rates, intercepts)

Always returns None, None.

max_rates_intercepts(gain, bias)

Always returns None, None.

rates(x, gain, bias)

Always returns x.

step(dt, J, output)

Raises an error if called.

Rather than calling this function, the simulator will detect that the ensemble is in direct mode, and bypass the neural approximation.

class nengo.RectifiedLinear(amplitude=1, initial_state=None)

A rectified linear neuron model.

Each neuron is modeled as a rectified line. That is, the neuron’s activity scales linearly with current, unless it passes below zero, at which point the neural activity will stay at zero.

Parameters

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

gain_bias(max_rates, intercepts)

Determine gain and bias by shifting and scaling the lines.

max_rates_intercepts(gain, bias)

Compute the inverse of gain_bias.

step(dt, J, output)

Implement the rectification nonlinearity.

class nengo.SpikingRectifiedLinear(amplitude=1, initial_state=None)

A rectified integrate and fire neuron model.

Each neuron is modeled as a rectified line. That is, the neuron’s activity scales linearly with current, unless the current is less than zero, at which point the neural activity will stay at zero. This is a spiking version of the RectifiedLinear neuron model.

Parameters

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

rates(x, gain, bias)

Use RectifiedLinear to determine rates.

step(dt, J, output, voltage)

Implement the integrate and fire nonlinearity.

class nengo.Sigmoid(tau_ref=0.0025, initial_state=None)

A non-spiking neuron model whose response curve is a sigmoid.

Since the tuning curves are strictly positive, the intercepts correspond to the inflection point of each sigmoid. That is, f(intercept) = 0.5 where f is the pure sigmoid function.

Parameters

tau_reffloat

The neuron refractory period, in seconds. The maximum firing rate of the neurons is 1 / tau_ref. Must be positive (i.e. tau_ref > 0).

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

gain_bias(max_rates, intercepts)

Analytically determine gain, bias.

max_rates_intercepts(gain, bias)

Compute the inverse of gain_bias.

step(dt, J, output)

Implement the sigmoid nonlinearity.

class nengo.Tanh(tau_ref=0.0025, initial_state=None)

A non-spiking neuron model whose response curve is a hyperbolic tangent.

Parameters

tau_reffloat

The neuron refractory period, in seconds. The maximum firing rate of the neurons is 1 / tau_ref. Must be positive (i.e. tau_ref > 0).

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

gain_bias(max_rates, intercepts)

Analytically determine gain, bias.

max_rates_intercepts(gain, bias)

Compute the inverse of gain_bias.

step(dt, J, output)

Implement the tanh nonlinearity.

class nengo.LIFRate(tau_rc=0.02, tau_ref=0.002, amplitude=1, initial_state=None)

Non-spiking version of the leaky integrate-and-fire (LIF) neuron model.

Parameters

tau_rcfloat

Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).

tau_reffloat

Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

gain_bias(max_rates, intercepts)

Analytically determine gain, bias.

max_rates_intercepts(gain, bias)

Compute the inverse of gain_bias.

rates(x, gain, bias)

Always use LIFRate to determine rates.

step(dt, J, output)

Implement the LIFRate nonlinearity.

class nengo.LIF(tau_rc=0.02, tau_ref=0.002, min_voltage=0, amplitude=1, initial_state=None)

Spiking version of the leaky integrate-and-fire (LIF) neuron model.

Parameters

tau_rcfloat

Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).

tau_reffloat

Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.

min_voltagefloat

Minimum value for the membrane voltage. If -np.inf, the voltage is never clipped.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

step(dt, J, output, voltage, refractory_time)

Implement the LIFRate nonlinearity.

class nengo.AdaptiveLIFRate(tau_n=1, inc_n=0.01, tau_rc=0.02, tau_ref=0.002, amplitude=1, initial_state=None)

Adaptive non-spiking version of the LIF neuron model.

Works as the LIF model, except with adapation state n, which is subtracted from the input current. Its dynamics are:

tau_n dn/dt = -n

where n is incremented by inc_n when the neuron spikes.

Parameters

tau_nfloat

Adaptation time constant. Affects how quickly the adaptation state decays to zero in the absence of spikes (larger = slower decay).

inc_nfloat

Adaptation increment. How much the adaptation state is increased after each spike.

tau_rcfloat

Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).

tau_reffloat

Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

References

1

Camera, Giancarlo La, et al. “Minimal models of adapted neuronal response to in Vivo-Like input currents.” Neural computation 16.10 (2004): 2101-2124.

step(dt, J, output, adaptation)

Implement the AdaptiveLIFRate nonlinearity.

class nengo.AdaptiveLIF(tau_n=1, inc_n=0.01, tau_rc=0.02, tau_ref=0.002, min_voltage=0, amplitude=1, initial_state=None)

Adaptive spiking version of the LIF neuron model.

Works as the LIF model, except with adapation state n, which is subtracted from the input current. Its dynamics are:

tau_n dn/dt = -n

where n is incremented by inc_n when the neuron spikes.

Parameters

tau_nfloat

Adaptation time constant. Affects how quickly the adaptation state decays to zero in the absence of spikes (larger = slower decay).

inc_nfloat

Adaptation increment. How much the adaptation state is increased after each spike.

tau_rcfloat

Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).

tau_reffloat

Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.

min_voltagefloat

Minimum value for the membrane voltage. If -np.inf, the voltage is never clipped.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

References

1

Camera, Giancarlo La, et al. “Minimal models of adapted neuronal response to in Vivo-Like input currents.” Neural computation 16.10 (2004): 2101-2124.

step(dt, J, output, voltage, refractory_time, adaptation)

Implement the AdaptiveLIF nonlinearity.

class nengo.Izhikevich(tau_recovery=0.02, coupling=0.2, reset_voltage=- 65.0, reset_recovery=8.0, initial_state=None)

Izhikevich neuron model.

This implementation is based on the original paper [1]; however, we rename some variables for clarity. What was originally ‘v’ we term ‘voltage’, which represents the membrane potential of each neuron. What was originally ‘u’ we term ‘recovery’, which represents membrane recovery, “which accounts for the activation of K+ ionic currents and inactivation of Na+ ionic currents.” The ‘a’, ‘b’, ‘c’, and ‘d’ parameters are also renamed (see the parameters below).

We use default values that correspond to regular spiking (‘RS’) neurons. For other classes of neurons, set the parameters as follows.

• Intrinsically bursting (IB): reset_voltage=-55, reset_recovery=4

• Chattering (CH): reset_voltage=-50, reset_recovery=2

• Fast spiking (FS): tau_recovery=0.1

• Low-threshold spiking (LTS): coupling=0.25

• Resonator (RZ): tau_recovery=0.1, coupling=0.26

Parameters

tau_recoveryfloat, optional

(Originally ‘a’) Time scale of the recovery variable.

couplingfloat, optional

(Originally ‘b’) How sensitive recovery is to subthreshold fluctuations of voltage.

reset_voltagefloat, optional

(Originally ‘c’) The voltage to reset to after a spike, in millivolts.

reset_recoveryfloat, optional

(Originally ‘d’) The recovery value to reset to after a spike.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

References

1

E. M. Izhikevich, “Simple model of spiking neurons.” IEEE Transactions on Neural Networks, vol. 14, no. 6, pp. 1569-1572. (http://www.izhikevich.org/publications/spikes.pdf)

rates(x, gain, bias)

Estimates steady-state firing rate given gain and bias.

step(dt, J, output, voltage, recovery)

Implement the Izhikevich nonlinearity.

class nengo.neurons.RatesToSpikesNeuronType(base_type, amplitude=1.0, initial_state=None)

Base class for neuron types that turn rate types into spiking ones.

gain_bias(max_rates, intercepts)

Compute the gain and bias needed to satisfy max_rates, intercepts.

This takes the neurons, approximates their response function, and then uses that approximation to find the gain and bias value that will give the requested intercepts and max_rates.

Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuron-specific implementation.

Parameters

max_rates(n_neurons,) array_like

Maximum firing rates of neurons.

intercepts(n_neurons,) array_like

X-intercepts of neurons.

Returns

gain(n_neurons,) array_like

Gain associated with each neuron. Sometimes denoted alpha.

bias(n_neurons,) array_like

Bias current associated with each neuron.

max_rates_intercepts(gain, bias)

Compute the max_rates and intercepts given gain and bias.

Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuron-specific implementation.

Parameters

gain(n_neurons,) array_like

Gain associated with each neuron. Sometimes denoted alpha.

bias(n_neurons,) array_like

Bias current associated with each neuron.

Returns

max_rates(n_neurons,) array_like

Maximum firing rates of neurons.

intercepts(n_neurons,) array_like

X-intercepts of neurons.

rates(x, gain, bias)

Compute firing rates (in Hz) for given input x.

This default implementation takes the naive approach of running the step function for a second. This should suffice for most rate-based neuron types; for spiking neurons it will likely fail (those models should override this function).

Note that x is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected rate for a neuron occurs when input for that neuron is 1.

Parameters

x(n_samples,) or (n_samples, n_neurons) array_like

Scalar inputs for which to calculate rates.

gain(n_neurons,) array_like

Gains associated with each neuron.

bias(n_neurons,) array_like

Bias current associated with each neuron.

Returns

rates(n_samples, n_neurons) ndarray

The firing rates at each given value of x.

step(dt, J, output, **state)

Implements the differential equation for this neuron type.

At a minimum, NeuronType subclasses must implement this method. That implementation should modify the output parameter rather than returning anything, for efficiency reasons.

Parameters

dtfloat

Simulation timestep.

J(n_neurons,) array_like

Input currents associated with each neuron.

output(n_neurons,) array_like

Output activity associated with each neuron (e.g., spikes or firing rates).

state{str: array_like}

State variables associated with the population.

class nengo.RegularSpiking(base_type, amplitude=1.0, initial_state=None)

Turn a rate neuron type into a spiking one with regular inter-spike intervals.

Spikes at regular intervals based on the rates of the base neuron type. [1]

Parameters

base_typeNeuronType

A rate-based neuron type to convert to a regularly spiking neuron.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

References

1

Voelker, A. R., Rasmussen, D., & Eliasmith, C. (2020). A Spike in Performance: Training Hybrid-Spiking Neural Networks with Quantized Activation Functions. arXiv preprint arXiv:2002.03553. (https://export.arxiv.org/abs/2002.03553)

step(dt, J, output, voltage)

Implements the differential equation for this neuron type.

At a minimum, NeuronType subclasses must implement this method. That implementation should modify the output parameter rather than returning anything, for efficiency reasons.

Parameters

dtfloat

Simulation timestep.

J(n_neurons,) array_like

Input currents associated with each neuron.

output(n_neurons,) array_like

Output activity associated with each neuron (e.g., spikes or firing rates).

state{str: array_like}

State variables associated with the population.

class nengo.StochasticSpiking(base_type, amplitude=1.0, initial_state=None)

Turn a rate neuron type into a spiking one using stochastic rounding.

The expected number of spikes per timestep e = dt * r is determined by the base type firing rate r and the timestep dt. Given the fractional part f and integer part q of e, the number of generated spikes is q with probability 1 - f and q + 1 with probability f. For e much less than one, this is very similar to Poisson statistics.

Parameters

base_typeNeuronType

A rate-based neuron type to convert to a stochastic spiking neuron.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

step(dt, J, output, rng, **base_state)

Implements the differential equation for this neuron type.

At a minimum, NeuronType subclasses must implement this method. That implementation should modify the output parameter rather than returning anything, for efficiency reasons.

Parameters

dtfloat

Simulation timestep.

J(n_neurons,) array_like

Input currents associated with each neuron.

output(n_neurons,) array_like

Output activity associated with each neuron (e.g., spikes or firing rates).

state{str: array_like}

State variables associated with the population.

class nengo.PoissonSpiking(base_type, amplitude=1.0, initial_state=None)

Turn a rate neuron type into a spiking one with Poisson spiking statistics.

Spikes with Poisson probability based on the rates of the base neuron type.

Parameters

base_typeNeuronType

A rate-based neuron type to convert to a Poisson spiking neuron.

amplitudefloat

Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.

initial_state{str: Distribution or array_like}

Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

step(dt, J, output, rng, **base_state)

Implements the differential equation for this neuron type.

At a minimum, NeuronType subclasses must implement this method. That implementation should modify the output parameter rather than returning anything, for efficiency reasons.

Parameters

dtfloat

Simulation timestep.

J(n_neurons,) array_like

Input currents associated with each neuron.

output(n_neurons,) array_like

Output activity associated with each neuron (e.g., spikes or firing rates).

state{str: array_like}

State variables associated with the population.

Processes

nengo.Process	A general system with input, output, and state.
nengo.processes.WhiteNoise	Full-spectrum white noise process.
nengo.processes.FilteredNoise	Filtered white noise process.
nengo.processes.BrownNoise	Brown noise process (aka Brownian noise, red noise, Wiener process).
nengo.processes.WhiteSignal	An ideal low-pass filtered white noise process.
nengo.processes.PresentInput	Present a series of inputs, each for the same fixed length of time.
nengo.processes.Piecewise	A piecewise function with different options for interpolation.

class nengo.processes.WhiteNoise(dist=Gaussian(mean=0, std=1), scale=True, **kwargs)

Full-spectrum white noise process.

Parameters

distDistribution, optional

The distribution from which to draw samples.

scalebool, optional

Whether to scale the white noise for integration. Integrating white noise requires using a time constant of sqrt(dt) instead of dt on the noise term [1], to ensure the magnitude of the integrated noise does not change with dt.

seedint, optional

Random number seed. Ensures noise will be the same each run.

References

1

Gillespie, D.T. (1996) Exact numerical simulation of the Ornstein- Uhlenbeck process and its integral. Phys. Rev. E 54, pp. 2084-91.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.processes.FilteredNoise(synapse=Lowpass(tau=0.005), dist=Gaussian(mean=0, std=1), scale=True, **kwargs)

Filtered white noise process.

This process takes white noise and filters it using the provided synapse.

Parameters

synapseSynapse, optional

The synapse to use to filter the noise.

distDistribution, optional

The distribution used to generate the white noise.

scalebool, optional

Whether to scale the white noise for integration, making the output signal invariant to dt.

seedint, optional

Random number seed. Ensures noise will be the same each run.

make_state(shape_in, shape_out, dt, dtype=None)

Get a dictionary of signals to represent the state of this process.

The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.

New in version 3.0.0.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

dtypenumpy.dtype

The data type requested by the builder. If None, then this function is free to choose the best type for the signals involved.

Returns

initial_state{string: numpy.ndarray}

A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in Process.make_step.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.processes.BrownNoise(dist=Gaussian(mean=0, std=1), **kwargs)

Brown noise process (aka Brownian noise, red noise, Wiener process).

This process is the integral of white noise.

Parameters

distDistribution, optional

The distribution used to generate the white noise.

seedint, optional

Random number seed. Ensures noise will be the same each run.

class nengo.processes.WhiteSignal(period, high, rms=0.5, y0=None, **kwargs)

An ideal low-pass filtered white noise process.

This signal is created in the frequency domain, and designed to have exactly equal power at all frequencies below the cut-off frequency, and no power above the cut-off.

The signal is naturally periodic, so it can be used beyond its period while still being continuous with continuous derivatives.

Parameters

periodfloat

A white noise signal with this period will be generated. Samples will repeat after this duration.

highfloat

The cut-off frequency of the low-pass filter, in Hz. Must not exceed the Nyquist frequency for the simulation timestep, which is 0.5 / dt.

rmsfloat, optional

The root mean square power of the filtered signal

y0float, optional

Align the phase of each output dimension to begin at the value that is closest (in absolute value) to y0.

seedint, optional

Random number seed. Ensures noise will be the same each run.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.processes.PresentInput(inputs, presentation_time, **kwargs)

Present a series of inputs, each for the same fixed length of time.

Parameters

inputsarray_like

Inputs to present, where each row is an input. Rows will be flattened.

presentation_timefloat

Show each input for this amount of time (in seconds).

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.processes.PiecewiseDataParam(name, default=Unconfigurable, optional=False, readonly=None)

Piecewise-specific validation for the data dictionary.

In the Piecewise data dict, the keys are points in time (float) and values are numerical constants or callables of the same dimensionality.

hashvalue(instance)

Returns a hashable value (hash can be called on the output).

class nengo.processes.Piecewise(data, interpolation='zero', **kwargs)

A piecewise function with different options for interpolation.

Given an input dictionary of {0: 0, 0.5: -1, 0.75: 0.5, 1: 0}, this process will emit the numerical values (0, -1, 0.5, 0) starting at the corresponding time points (0, 0.5, 0.75, 1).

The keys in the input dictionary must be times (float or int). The values in the dictionary can be floats, lists of floats, or numpy arrays. All lists or numpy arrays must be of the same length, as the output shape of the process will be determined by the shape of the values.

Interpolation on the data points using scipy.interpolate is also supported. The default interpolation is ‘zero’, which creates a piecewise function whose values change at the specified time points. So the above example would be shortcut for:

def function(t):
    if t < 0.5:
        return 0
    elif t < 0.75:
        return -1
    elif t < 1:
        return 0.5
    else:
        return 0

For times before the first specified time, an array of zeros (of the correct length) will be emitted. This means that the above can be simplified to:

from nengo.processes import Piecewise

Piecewise({0.5: -1, 0.75: 0.5, 1: 0})

Parameters

datadict

A dictionary mapping times to the values that should be emitted at those times. Times must be numbers (ints or floats), while values can be numbers, lists of numbers, numpy arrays of numbers, or callables that return any of those options.

interpolationstr, optional

One of ‘linear’, ‘nearest’, ‘slinear’, ‘quadratic’, ‘cubic’, or ‘zero’. Specifies how to interpolate between times with specified value. ‘zero’ creates a plain piecewise function whose values begin at corresponding time points, while all other options interpolate as described in scipy.interpolate.

Examples

from nengo.processes import Piecewise
process = Piecewise({0.5: 1, 0.75: -1, 1: 0})
with nengo.Network() as model:
    u = nengo.Node(process, size_out=process.default_size_out)
    up = nengo.Probe(u)
with nengo.Simulator(model, progress_bar=False) as sim:
    sim.run(1.5)
f = sim.data[up]
t = sim.trange()
print(f[t == 0.2])
print(f[t == 0.58])

[[ 0.]]
[[ 1.]]

Attributes

datadict

A dictionary mapping times to the values that should be emitted at those times. Times are numbers (ints or floats), while values can be numbers, lists of numbers, numpy arrays of numbers, or callables that return any of those options.

interpolationstr

One of ‘linear’, ‘nearest’, ‘slinear’, ‘quadratic’, ‘cubic’, or ‘zero’. Specifies how to interpolate between times with specified value. ‘zero’ creates a plain piecewise function whose values change at corresponding time points, while all other options interpolate as described in scipy.interpolate.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.Process(default_size_in=0, default_size_out=1, default_dt=0.001, seed=None)

A general system with input, output, and state.

For more details on how to use processes and make custom process subclasses, see Processes and how to use them.

Parameters

default_size_inint

Sets the default size in for nodes using this process.

default_size_outint

Sets the default size out for nodes running this process. Also, if d is not specified in run or run_steps, this will be used.

default_dtfloat

If dt is not specified in run, run_steps, ntrange, or trange, this will be used.

seedint, optional

Random number seed. Ensures random factors will be the same each run.

Attributes

default_dtfloat

If dt is not specified in run, run_steps, ntrange, or trange, this will be used.

default_size_inint

The default size in for nodes using this process.

default_size_outint

The default size out for nodes running this process. Also, if d is not specified in run or run_steps, this will be used.

seedint or None

Random number seed. Ensures random factors will be the same each run.

apply(self, x, d=None, dt=None, rng=numpy.random, copy=True, **kwargs)

Run process on a given input.

Keyword arguments that do not appear in the parameter list below will be passed to the make_step function of this process.

Parameters

xndarray

The input signal given to the process.

dint, optional

Output dimensionality. If None, default_size_out will be used.

dtfloat, optional

Simulation timestep. If None, default_dt will be used.

rngnumpy.random.RandomState

Random number generator used for stochstic processes.

copybool, optional

If True, a new output array will be created for output. If False, the input signal x will be overwritten.

get_rng(rng)

Get a properly seeded independent RNG for the process step.

Parameters

rngnumpy.random.RandomState

The parent random number generator to use if the seed is not set.

make_state(shape_in, shape_out, dt, dtype=None)

Get a dictionary of signals to represent the state of this process.

The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.

New in version 3.0.0.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

dtypenumpy.dtype

The data type requested by the builder. If None, then this function is free to choose the best type for the signals involved.

Returns

initial_state{string: numpy.ndarray}

A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in Process.make_step.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

run(self, t, d=None, dt=None, rng=numpy.random, **kwargs)

Run process without input for given length of time.

Keyword arguments that do not appear in the parameter list below will be passed to the make_step function of this process.

Parameters

tfloat

The length of time to run.

dint, optional

Output dimensionality. If None, default_size_out will be used.

dtfloat, optional

Simulation timestep. If None, default_dt will be used.

rngnumpy.random.RandomState

Random number generator used for stochstic processes.

run_steps(self, n_steps, d=None, dt=None, rng=numpy.random, **kwargs)

Run process without input for given number of steps.

Keyword arguments that do not appear in the parameter list below will be passed to the make_step function of this process.

Parameters

n_stepsint

The number of steps to run.

dint, optional

Output dimensionality. If None, default_size_out will be used.

dtfloat, optional

Simulation timestep. If None, default_dt will be used.

rngnumpy.random.RandomState

Random number generator used for stochstic processes.

ntrange(n_steps, dt=None)

Create time points corresponding to a given number of steps.

Parameters

n_stepsint

The given number of steps.

dtfloat, optional

Simulation timestep. If None, default_dt will be used.

trange(t, dt=None)

Create time points corresponding to a given length of time.

Parameters

tfloat

The given length of time.

dtfloat, optional

Simulation timestep. If None, default_dt will be used.

Solvers

Classes concerned with solving for decoders or full weight matrices.

nengo.solvers.Solver	Decoder or weight solver.
nengo.solvers.Lstsq	Unregularized least-squares solver.
nengo.solvers.LstsqNoise	Least-squares solver with additive Gaussian white noise.
nengo.solvers.LstsqMultNoise	Least-squares solver with multiplicative white noise.
nengo.solvers.LstsqL2	Least-squares solver with L2 regularization.
nengo.solvers.LstsqL2nz	Least-squares solver with L2 regularization on non-zero components.
nengo.solvers.LstsqL1	Least-squares solver with L1 and L2 regularization (elastic net).
nengo.solvers.LstsqDrop	Find sparser decoders/weights by dropping small values.
nengo.solvers.Nnls	Non-negative least-squares solver without regularization.
nengo.solvers.NnlsL2	Non-negative least-squares solver with L2 regularization.
nengo.solvers.NnlsL2nz	Non-negative least-squares with L2 regularization on nonzero components.
nengo.solvers.NoSolver	Manually pass in weights, bypassing the decoder solver.

class nengo.solvers.Solver(weights=False)

Decoder or weight solver.

A solver can have the weights parameter equal to True or False.

Weight solvers are used to form neuron-to-neuron weight matrices. They can be compositional or non-compositional. Non-compositional solvers must operate on the whole neuron-to-neuron weight matrix (i.e., each target is a separate postsynaptic current, without the bias term), while compositional solvers operate in the decoded state-space (i.e., each target is a dimension in state-space). Compositional solvers then combine the returned X with the transform and/or encoders to generate the full weight matrix.

For a solver to be compositional, the following property must be true:

X = solver(A, Y)  if and only if  L(X) = solver(A, L(Y))

where L is some arbitrary linear operator (i.e., the transform and/or encoders for the postsynaptic population). This property can then be leveraged by the backend for efficiency. See the solver’s compositional class attribute to determine if it is compositional.

Non-weight solvers always operate in the decoded state-space regardless of whether they are compositional or non-compositional.

class nengo.solvers.SolverParam(name, default=Unconfigurable, optional=False, readonly=None)

A parameter in which the value is a Solver instance.

class nengo.solvers.Lstsq(weights=False, rcond=0.01)

Unregularized least-squares solver.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

rcondfloat, optional

Cut-off ratio for small singular values (see numpy.linalg.lstsq).

Attributes

rcondfloat

Cut-off ratio for small singular values (see numpy.linalg.lstsq).

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqNoise(weights=False, noise=0.1, solver=Cholesky())

Least-squares solver with additive Gaussian white noise.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

noisefloat, optional

Amount of noise, as a fraction of the neuron activity.

solverLeastSquaresSolver, optional

Subsolver to use for solving the least squares problem.

Attributes

noisefloat

Amount of noise, as a fraction of the neuron activity.

solverLeastSquaresSolver

Subsolver to use for solving the least squares problem.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqMultNoise(weights=False, noise=0.1, solver=Cholesky())

Least-squares solver with multiplicative white noise.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

noisefloat, optional

Amount of noise, as a fraction of the neuron activity.

solverLeastSquaresSolver, optional

Subsolver to use for solving the least squares problem.

Attributes

noisefloat

Amount of noise, as a fraction of the neuron activity.

solverLeastSquaresSolver

Subsolver to use for solving the least squares problem.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL2(weights=False, reg=0.1, solver=Cholesky())

Least-squares solver with L2 regularization.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

regfloat, optional

Amount of regularization, as a fraction of the neuron activity.

solverLeastSquaresSolver, optional

Subsolver to use for solving the least squares problem.

Attributes

regfloat

Amount of regularization, as a fraction of the neuron activity.

solverLeastSquaresSolver

Subsolver to use for solving the least squares problem.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL2nz(weights=False, reg=0.1, solver=Cholesky())

Least-squares solver with L2 regularization on non-zero components.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

regfloat, optional

Amount of regularization, as a fraction of the neuron activity.

solverLeastSquaresSolver, optional

Subsolver to use for solving the least squares problem.

Attributes

regfloat

Amount of regularization, as a fraction of the neuron activity.

solverLeastSquaresSolver

Subsolver to use for solving the least squares problem.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL1(weights=False, l1=0.0001, l2=1e-06, max_iter=1000)

Least-squares solver with L1 and L2 regularization (elastic net).

This method is well suited for creating sparse decoders or weight matrices.

Note

Requires scikit-learn.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

l1float, optional

Amount of L1 regularization.

l2float, optional

Amount of L2 regularization.

max_iterint, optional

Maximum number of iterations for the underlying elastic net.

Attributes

l1float

Amount of L1 regularization.

l2float

Amount of L2 regularization.

weightsbool

If False, solve for decoders. If True, solve for weights.

max_iterint

Maximum number of iterations for the underlying elastic net.

class nengo.solvers.LstsqDrop(weights=False, drop=0.25, solver1=LstsqL2(reg=0.001), solver2=LstsqL2())

Find sparser decoders/weights by dropping small values.

This solver first solves for coefficients (decoders/weights) with L2 regularization, drops those nearest to zero, and retrains remaining.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

dropfloat, optional

Fraction of decoders or weights to set to zero.

solver1Solver, optional

Solver for finding the initial decoders.

solver2Solver, optional

Used for re-solving for the decoders after dropout.

Attributes

dropfloat

Fraction of decoders or weights to set to zero.

solver1Solver

Solver for finding the initial decoders.

solver2Solver

Used for re-solving for the decoders after dropout.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.Nnls(weights=False)

Non-negative least-squares solver without regularization.

Similar to Lstsq, except the output values are non-negative.

If solving for non-negative weights, it is important that the intercepts of the post-population are also non-negative, since neurons with negative intercepts will never be silent, affecting output accuracy.

Note

Requires SciPy.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

Attributes

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.NnlsL2(weights=False, reg=0.1)

Non-negative least-squares solver with L2 regularization.

Similar to LstsqL2, except the output values are non-negative.

If solving for non-negative weights, it is important that the intercepts of the post-population are also non-negative, since neurons with negative intercepts will never be silent, affecting output accuracy.

Note

Requires SciPy.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

regfloat, optional

Amount of regularization, as a fraction of the neuron activity.

Attributes

regfloat

Amount of regularization, as a fraction of the neuron activity.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.NnlsL2nz(weights=False, reg=0.1)

Non-negative least-squares with L2 regularization on nonzero components.

Similar to LstsqL2nz, except the output values are non-negative.

If solving for non-negative weights, it is important that the intercepts of the post-population are also non-negative, since neurons with negative intercepts will never be silent, affecting output accuracy.

Note

Requires SciPy.

Parameters

weightsbool, optional

If False, solve for decoders. If True, solve for weights.

regfloat, optional

Amount of regularization, as a fraction of the neuron activity.

Attributes

regfloat

Amount of regularization, as a fraction of the neuron activity.

weightsbool

If False, solve for decoders. If True, solve for weights.

class nengo.solvers.NoSolver(values=None, weights=False)

Manually pass in weights, bypassing the decoder solver.

Parameters

values(n_neurons, size_out) array_like, optional

The array of decoders to use. size_out is the dimensionality of the decoded signal (determined by the connection function). If None, which is the default, the solver will return an appropriately sized array of zeros.

weightsbool, optional

If False, connection will use factored weights (decoders from this solver, transform, and encoders). If True, connection will use a full weight matrix (created by linearly combining decoder, transform, and encoders).

Attributes

values(n_neurons, size_out) array_like, optional

The array of decoders to use. size_out is the dimensionality of the decoded signal (determined by the connection function). If None, which is the default, the solver will return an appropriately sized array of zeros.

weightsbool, optional

If False, connection will use factored weights (decoders from this solver, transform, and encoders). If True, connection will use a full weight matrix (created by linearly combining decoder, transform, and encoders).

Solver methods

These solvers are to be passed as arguments to Solver objects.

For example:

from nengo.solvers import LstsqL2
from nengo.utils.least_squares_solvers import SVD

with nengo.Network():
    ens_a = nengo.Ensemble(10, 1)
    ens_b = nengo.Ensemble(10, 1)
    nengo.Connection(ens_a, ens_b, solver=LstsqL2(solver=SVD()))

nengo.utils.least_squares_solvers.format_system	Extract data from A/Y matrices.
nengo.utils.least_squares_solvers.rmses	Returns the root-mean-squared error (RMSE) of the solution X.
nengo.utils.least_squares_solvers.LeastSquaresSolver	Linear least squares system solver.
nengo.utils.least_squares_solvers.Cholesky	Solve a least-squares system using the Cholesky decomposition.
nengo.utils.least_squares_solvers.ConjgradScipy	Solve a least-squares system using Scipy’s conjugate gradient.
nengo.utils.least_squares_solvers.LSMRScipy	Solve a least-squares system using Scipy’s LSMR.
nengo.utils.least_squares_solvers.Conjgrad	Solve a least-squares system using conjugate gradient.
nengo.utils.least_squares_solvers.BlockConjgrad	Solve a multiple-RHS least-squares system using block conj.
nengo.utils.least_squares_solvers.SVD	Solve a least-squares system using full SVD.
nengo.utils.least_squares_solvers.RandomizedSVD	Solve a least-squares system using a randomized (partial) SVD.
nengo.utils.least_squares_solvers.LeastSquaresSolverParam	A parameter where the value is a LeastSquaresSolver.

nengo.utils.least_squares_solvers.format_system(A, Y)

Extract data from A/Y matrices.

nengo.utils.least_squares_solvers.rmses(A, X, Y)

Returns the root-mean-squared error (RMSE) of the solution X.

class nengo.utils.least_squares_solvers.LeastSquaresSolver

Linear least squares system solver.

class nengo.utils.least_squares_solvers.Cholesky(transpose=None)

Solve a least-squares system using the Cholesky decomposition.

class nengo.utils.least_squares_solvers.ConjgradScipy(tol=0.0001, atol=1e-08)

Solve a least-squares system using Scipy’s conjugate gradient.

Parameters

tolfloat

Relative tolerance of the CG solver (see [1] for details).

atolfloat

Absolute tolerance of the CG solver (see [1] for details).

References

1(1,2)

scipy.sparse.linalg.cg documentation, https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.cg.html

class nengo.utils.least_squares_solvers.LSMRScipy(tol=0.0001)

Solve a least-squares system using Scipy’s LSMR.

class nengo.utils.least_squares_solvers.Conjgrad(tol=0.01, maxiters=None, X0=None)

Solve a least-squares system using conjugate gradient.

class nengo.utils.least_squares_solvers.BlockConjgrad(tol=0.01, X0=None)

Solve a multiple-RHS least-squares system using block conj. gradient.

class nengo.utils.least_squares_solvers.SVD

Solve a least-squares system using full SVD.

class nengo.utils.least_squares_solvers.RandomizedSVD(n_components=60, n_oversamples=10, n_iter=0)

Solve a least-squares system using a randomized (partial) SVD.

Useful for solving large matrices quickly, but non-optimally.

Parameters

n_componentsint, optional

The number of SVD components to compute. A small survey of activity matrices suggests that the first 60 components capture almost all the variance.

n_oversamplesint, optional

The number of additional samples on the range of A.

n_iterint, optional

The number of power iterations to perform (can help with noisy data).

See also

sklearn.utils.extmath.randomized_svd

Function used by this class

class nengo.utils.least_squares_solvers.LeastSquaresSolverParam(name, default=Unconfigurable, optional=False, readonly=None)

A parameter where the value is a LeastSquaresSolver.

Synapse models

nengo.synapses.Synapse	Abstract base class for synapse models.
nengo.LinearFilter	General linear time-invariant (LTI) system synapse.
nengo.Lowpass	Standard first-order lowpass filter synapse.
nengo.Alpha	Alpha-function filter synapse.
nengo.synapses.Triangle	Triangular finite impulse response (FIR) synapse.

class nengo.synapses.Synapse(default_size_in=1, default_size_out=None, default_dt=0.001, seed=None)

Abstract base class for synapse models.

Conceptually, a synapse model emulates a biological synapse, taking in input in the form of released neurotransmitter and opening ion channels to allow more or less current to flow into the neuron.

In Nengo, the implementation of a synapse is as a specific case of a Process in which the input and output shapes are the same. The input is the current across the synapse, and the output is the current that will be induced in the postsynaptic neuron.

Synapses also contain the Synapse.filt and Synapse.filtfilt methods, which make it easy to use Nengo’s synapse models outside of Nengo simulations.

Parameters

default_size_inint, optional

The size_in used if not specified.

default_size_outint

The size_out used if not specified. If None, will be the same as default_size_in.

default_dtfloat

The simulation timestep used if not specified.

seedint, optional

Random number seed. Ensures random factors will be the same each run.

Attributes

default_dtfloat

The simulation timestep used if not specified.

default_size_inint

The size_in used if not specified.

default_size_outint

The size_out used if not specified.

seedint, optional

Random number seed. Ensures random factors will be the same each run.

make_state(shape_in, shape_out, dt, dtype=None, y0=None)

Get a dictionary of signals to represent the state of this process.

The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.

New in version 3.0.0.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

dtypenumpy.dtype

The data type requested by the builder. If None, then this function is free to choose the best type for the signals involved.

Returns

initial_state{string: numpy.ndarray}

A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in Process.make_step.

filt(x, dt=None, axis=0, y0=0, copy=True, filtfilt=False)

Filter x with this synapse model.

Parameters

xarray_like

The signal to filter.

dtfloat, optional

The timestep of the input signal. If None, default_dt will be used.

axisint, optional

The axis along which to filter.

y0array_like, optional

The starting state of the filter output. Must be zero for unstable linear systems.

copybool, optional

Whether to copy the input data, or simply work in-place.

filtfiltbool, optional

If True, runs the process forward then backward on the signal, for zero-phase filtering (like Matlab’s filtfilt).

filtfilt(x, **kwargs)

Zero-phase filtering of x using this filter.

Equivalent to filt(x, filtfilt=True, **kwargs).

class nengo.LinearFilter(num, den, analog=True, method='zoh', **kwargs)

General linear time-invariant (LTI) system synapse.

This class can be used to implement any linear filter, given the filter’s transfer function. [1]

Parameters

numarray_like

Numerator coefficients of transfer function.

denarray_like

Denominator coefficients of transfer function.

analogboolean, optional

Whether the synapse coefficients are analog (i.e. continuous-time), or discrete. Analog coefficients will be converted to discrete for simulation using the simulator dt.

methodstring

The method to use for discretization (if analog is True). See scipy.signal.cont2discrete for information about the options.

New in version 3.0.0.

References

1

https://en.wikipedia.org/wiki/Filter_%28signal_processing%29

Attributes

analogboolean

Whether the synapse coefficients are analog (i.e. continuous-time), or discrete. Analog coefficients will be converted to discrete for simulation using the simulator dt.

denndarray

Denominator coefficients of transfer function.

numndarray

Numerator coefficients of transfer function.

methodstring

The method to use for discretization (if analog is True). See scipy.signal.cont2discrete for information about the options.

combine(obj)

Combine in series with another LinearFilter.

evaluate(frequencies)

Evaluate the transfer function at the given frequencies.

Examples

Using the evaluate function to make a Bode plot:

import matplotlib.pyplot as plt

synapse = nengo.synapses.LinearFilter([1], [0.02, 1])
f = np.logspace(-1, 3, 100)
y = synapse.evaluate(f)
plt.subplot(211); plt.semilogx(f, 20*np.log10(np.abs(y)))
plt.xlabel('frequency [Hz]'); plt.ylabel('magnitude [dB]')
plt.subplot(212); plt.semilogx(f, np.angle(y))
plt.xlabel('frequency [Hz]'); plt.ylabel('phase [radians]')

make_state(shape_in, shape_out, dt, dtype=None, y0=0)

Get a dictionary of signals to represent the state of this process.

The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.

New in version 3.0.0.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

dtypenumpy.dtype

The data type requested by the builder. If None, then this function is free to choose the best type for the signals involved.

Returns

initial_state{string: numpy.ndarray}

A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in Process.make_step.

make_step(shape_in, shape_out, dt, rng, state)

Returns a Step instance that implements the linear filter.

class Step(A, B, C, D, X)

Abstract base class for LTI filtering step functions.

classmethod check(A, B, C, D, X)

class NoX(A, B, C, D, X)

Step for system with no state, only passthrough matrix (D).

classmethod check(A, B, C, D, X)

class OneX(A, B, C, D, X)

Step for systems with one state element and no passthrough (D).

classmethod check(A, B, C, D, X)

class OneXScalar(A, B, C, D, X)

Step for systems with one state element, no passthrough, and a size-1 input.

Using the builtin float math improves performance.

classmethod check(A, B, C, D, X)

class NoD(A, B, C, D, X)

Step for systems with no passthrough matrix (D).

Implements:

x[t] = A x[t-1] + B u[t]
y[t] = C x[t]

Note how the input has been advanced one step as compared with the General system below, to remove the unnecessary delay.

classmethod check(A, B, C, D, X)

class General(A, B, C, D, X)

Step for any LTI system with at least one state element (X).

Implements:

x[t+1] = A x[t] + B u[t]
y[t] = C x[t] + D u[t]

Use NoX for systems with no state elements.

classmethod check(A, B, C, D, X)

class nengo.Lowpass(tau, **kwargs)

Standard first-order lowpass filter synapse.

The impulse-response function is given by:

f(t) = (1 / tau) * exp(-t / tau)

Parameters

taufloat

The time constant of the filter in seconds.

Attributes

taufloat

The time constant of the filter in seconds.

class nengo.Alpha(tau, **kwargs)

Alpha-function filter synapse.

The impulse-response function is given by:

alpha(t) = (t / tau**2) * exp(-t / tau)

and was found by [1] to be a good basic model for synapses.

Parameters

taufloat

The time constant of the filter in seconds.

References

1

Mainen, Z.F. and Sejnowski, T.J. (1995). Reliability of spike timing in neocortical neurons. Science (New York, NY), 268(5216):1503-6.

Attributes

taufloat

The time constant of the filter in seconds.

class nengo.synapses.Triangle(t, **kwargs)

Triangular finite impulse response (FIR) synapse.

This synapse has a triangular and finite impulse response. The length of the triangle is t seconds; thus the digital filter will have t / dt + 1 taps.

Parameters

tfloat

Length of the triangle, in seconds.

Attributes

tfloat

Length of the triangle, in seconds.

make_state(shape_in, shape_out, dt, dtype=None, y0=0)

Get a dictionary of signals to represent the state of this process.

The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.

New in version 3.0.0.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

dtypenumpy.dtype

The data type requested by the builder. If None, then this function is free to choose the best type for the signals involved.

Returns

initial_state{string: numpy.ndarray}

A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in Process.make_step.

make_step(shape_in, shape_out, dt, rng, state)

Create function that advances the process forward one time step.

This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.

Parameters

shape_intuple

The shape of the input signal.

shape_outtuple

The shape of the output signal.

dtfloat

The simulation timestep.

rngnumpy.random.RandomState

A random number generator.

state{string: numpy.ndarray}

A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by Process.make_state.

New in version 3.0.0.

class nengo.synapses.SynapseParam(name, default=Unconfigurable, optional=True, readonly=None)

Transforms

nengo.transforms.Transform	A base class for connection transforms.
nengo.Dense	A dense matrix transformation between an input and output signal.
nengo.transforms.SparseMatrix	Represents a sparse matrix.
nengo.Sparse	A sparse matrix transformation between an input and output signal.
nengo.Convolution	An N-dimensional convolutional transform.
nengo.ConvolutionTranspose	An N-dimensional transposed convolutional transform.
nengo.transforms.ChannelShape	Represents shape information with variable channel position.
nengo.transforms.NoTransform	Directly pass the signal through without any transform operations.
nengo.Conv	alias of nengo.Convolution
nengo.ConvTranspose	alias of nengo.ConvolutionTranspose

class nengo.transforms.Transform

A base class for connection transforms.

New in version 3.0.0.

sample(self, rng=numpy.random)

Returns concrete weights to implement the specified transform.

Parameters

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

array_like

Transform weights

property size_in

Expected size of input to transform.

property size_out

Expected size of output from transform.

class nengo.transforms.ChannelShapeParam(name, default=Unconfigurable, length=None, low=0, optional=False, readonly=None)

A parameter where the value must be a shape with channels.

New in version 3.0.0.

class nengo.Dense(shape, init=1.0)

A dense matrix transformation between an input and output signal.

New in version 3.0.0.

Parameters

shapetuple of int

The shape of the dense matrix: (size_out, size_in).

initDistribution or array_like, optional

A Distribution used to initialize the transform matrix, or a concrete instantiation for the matrix. If the matrix is square we also allow a scalar (equivalent to np.eye(n) * init) or a vector (equivalent to np.diag(init)) to represent the matrix more compactly.

sample(self, rng=numpy.random)

Returns concrete weights to implement the specified transform.

Parameters

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

array_like

Transform weights

property init_shape

The shape of the initial value.

property size_in

Expected size of input to transform.

property size_out

Expected size of output from transform.

class nengo.transforms.SparseInitParam(name, default=Unconfigurable, optional=False, readonly=None)

class nengo.transforms.SparseMatrix(indices, data, shape)

Represents a sparse matrix.

New in version 3.0.0.

Parameters

indicesarray_like of int

An Nx2 array of integers indicating the (row,col) coordinates for the N non-zero elements in the matrix.

dataarray_like or Distribution

An Nx1 array defining the value of the nonzero elements in the matrix (corresponding to indices), or a Distribution that will be used to initialize the nonzero elements.

shapetuple of int

Shape of the full matrix.

allocate()

Return a scipy.sparse.csr_matrix or dense matrix equivalent.

We mark this data as readonly to be consistent with how other data associated with signals are allocated. If this allocated data is to be modified, it should be copied first.

sample(self, rng=numpy.random)

Convert Distribution data to fixed array.

Parameters

rngnumpy.random.RandomState

Random number generator that will be used when sampling distribution.

Returns

matrixSparseMatrix

A new SparseMatrix instance with Distribution converted to array if self.data is a Distribution, otherwise simply returns self.

toarray()

Return the dense matrix equivalent of this matrix.

class nengo.Sparse(shape, indices=None, init=1.0)

A sparse matrix transformation between an input and output signal.

New in version 3.0.0.

Parameters

shapetuple of int

The full shape of the sparse matrix: (size_out, size_in).

indicesarray_like of int

An Nx2 array of integers indicating the (row,col) coordinates for the N non-zero elements in the matrix.

initDistribution or array_like, optional

A Distribution used to initialize the transform matrix, or a concrete instantiation for the matrix. If the matrix is square we also allow a scalar (equivalent to np.eye(n) * init) or a vector (equivalent to np.diag(init)) to represent the matrix more compactly.

sample(self, rng=numpy.random)

Returns concrete weights to implement the specified transform.

Parameters

rngnumpy.random.RandomState, optional

Random number generator state.

Returns

array_like

Transform weights

property size_in

Expected size of input to transform.

property size_out

Expected size of output from transform.

class nengo.Convolution(n_filters, input_shape, kernel_size=(3, 3), strides=(1, 1), padding='valid', channels_last=True, init=Uniform(low=- 1, high=1))

An N-dimensional convolutional transform.

The dimensionality of the convolution is determined by the input shape.

New in version 3.0.0.

Parameters

n_filtersint

The number of convolutional filters to apply.

input_shapetuple of int or ChannelShape

Shape of the input signal to the convolution; e.g., (height, width, channels) for a 2D convolution with channels_last=True.

kernel_sizetuple of int, optional

Size of the convolutional kernels (1 element for a 1D convolution, 2 for a 2D convolution, etc.).

stridestuple of int, optional

Stride of the convolution (1 element for a 1D convolution, 2 for a 2D convolution, etc.).

padding"same" or "valid", optional

Padding method for input signal. “Valid” means no padding, and convolution will only be applied to the fully-overlapping areas of the input signal (meaning the output will be smaller). “Same” means that the input signal is zero-padded so that the output is the same shape as the input.

channels_lastbool, optional

If True (default), the channels are the last dimension in the input signal (e.g., a 28x28 image with 3 channels would have shape (28, 28, 3)). False means that channels are the first dimension (e.g., (3, 28, 28)).

initDistribution or ndarray, optional

A predefined kernel with shape kernel_size + (input_channels, n_filters), or a Distribution that will be used to initialize the kernel.

Notes

As is typical in neural networks, this is technically correlation rather than convolution (because the kernel is not flipped).

property output_shape

Output shape after applying convolution to input.

class nengo.ConvolutionTranspose(n_filters, input_shape, output_shape=None, kernel_size=(3, 3), strides=(1, 1), padding='valid', channels_last=True, init=Uniform(low=- 1, high=1))

An N-dimensional transposed convolutional transform.

This performs the transpose operation of Convolution. The kernel_size, strides, and padding parameters all act as in Convolution, so this transform will be the transpose of a Convolution transform with those parameters. The n_filters and input_shape parameters are relative to this transform. The output shape is ambiguous, and can thus be specified (i.e. with Convolution, there can be more than one input shape that produces the same output shape, so here, there are multiple valid output shapes for some input shapes).

The dimensionality of the transpose convolution is determined by the input shape.

New in version 3.2.0.

Parameters

n_filtersint

The number of channels in the output of this transform.

input_shapetuple of int or ChannelShape

Shape of the input signal to this transform; e.g., (height, width, channels) for a 2D convolution with channels_last=True.

output_shapetuple of int or ChannelShape, optional

Shape of the output signal of this transform; e.g., (output_height, output_width, n_filters) for a 2D convolution with channels_last=True. Defaults to the smallest valid output shape.

kernel_sizetuple of int, optional

Size of the convolutional kernels (1 element for a 1D convolution, 2 for a 2D convolution, etc.).

stridestuple of int, optional

Stride of the convolution (1 element for a 1D convolution, 2 for a 2D convolution, etc.).

padding"same" or "valid", optional

Padding method for corresponding Convolution.

channels_lastbool, optional

If True (default), the channels are the last dimension in the input signal (e.g., a 28x28 image with 3 channels would have shape (28, 28, 3)). False means that channels are the first dimension (e.g., (3, 28, 28)).

initDistribution or ndarray, optional

A predefined kernel with shape kernel_size + (input_channels, n_filters), or a Distribution that will be used to initialize the kernel.

Notes

As is typical in neural networks, this is technically correlation rather than convolution (because the kernel is not flipped).

class nengo.transforms.ChannelShape(shape, channels_last=True)

Represents shape information with variable channel position.

New in version 3.0.0.

Parameters

shapeiterable of int

Signal shape

channels_lastbool, optional

If True (default), the last item in shape represents the channels, and the rest are spatial dimensions. Otherwise, the first item in shape is the channel dimension.

classmethod from_space_and_channels(spatial_shape, n_channels, channels_last=True)

Create a ChannelShape from a spatial shape and number of channels.

New in version 3.2.0.

Parameters

spatial_shapeiterable of int

The spatial part of the shape (not including channels).

n_channelsint

The number of channels.

channels_lastbool, optional

If True (default), the last item in shape represents the channels, and the rest are spatial dimensions. Otherwise, the first item in shape is the channel dimension.

property spatial_shape

The spatial part of the shape (omitting channels).

property size

The total number of elements in the represented signal.

property n_channels

The number of channels in the represented signal.

property dimensions

The spatial dimensionality of the represented signal.

class nengo.transforms.NoTransform(size_in)

Directly pass the signal through without any transform operations.

New in version 3.1.0.

Parameters

size_inint

Dimensionality of transform input and output.

sample(self, rng=numpy.random)

Returns concrete weights to implement the specified transform.

Parameters

rngnumpy.random.RandomState, optional

Random number generator state.

Raises

TypeError

There is nothing to sample for NoTransform, so it is an error if this is called.

property size_in

Expected size of input to transform.

property size_out

Expected size of output from transform.

nengo.Conv

alias of nengo.Convolution

nengo.ConvTranspose

alias of nengo.ConvolutionTranspose