Nengo Modelling API¶

Nengo Objects¶

class nengo.Network(label=None, seed=None, add_to_container=None)[source]¶

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(nengo.LIF(100), dimensions=2)
    with nengo.Network(label="Motor"):
        sma = nengo.Ensemble(nengo.LIF(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(nengo.LIF(100), dimensions=2)

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

Parameters:

label : str, optional (Default: None)

Name of the network.

seed : int, optional (Default: None)

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

add_to_container : bool, optional (Default: None)

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

connections	(list) `Connection` instances in this network.
ensembles	(list) `Ensemble` instances in this network.
label	(str) Name of this network.
networks	(list) `Network` instances in this network.
nodes	(list) `Node` instances in this network.
probes	(list) `Probe` instances in this network.
seed	(int) Random seed used by this network.

static add(obj)[source]¶: Add the passed object to Network.context.

static default_config()[source]¶: Constructs a Config object for setting defaults.

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

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

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

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

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

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

config¶: (Config) Configuration for this network.

class nengo.Ensemble(n_neurons, dimensions, radius=Default, encoders=Default, intercepts=Default, max_rates=Default, eval_points=Default, n_eval_points=Default, neuron_type=Default, gain=Default, bias=Default, noise=Default, label=Default, seed=Default)[source]¶

A group of neurons that collectively represent a vector.

Parameters:

n_neurons : int

The number of neurons.

dimensions : int

The number of representational dimensions.

radius : int, optional (Default: 1.0)

The representational radius of the ensemble.

encoders : Distribution or (n_neurons, dimensions) array_like, optional (Default: UniformHypersphere(surface=True))

The encoders used to transform from representational space to neuron space. Each row is a neuron’s encoder; each column is a representational dimension.

intercepts : Distribution or (n_neurons,) array_like, optional (Default: nengo.dists.Uniform(-1.0, 1.0))

The point along each neuron’s encoder where its activity is zero. If e is the neuron’s encoder, then the activity will be zero when dot(x, e) <= c, where c is the given intercept.

max_rates : Distribution or (n_neurons,) array_like, optional (Default: nengo.dists.Uniform(200, 400))

The activity of each neuron when the input signal x is magnitude 1 and aligned with that neuron’s encoder e; i.e., when dot(x, e) = 1.

eval_points : Distribution or (n_eval_points, dims) array_like, optional (Default: nengo.dists.UniformHypersphere(surface=True))

The evaluation points used for decoder solving, spanning the interval (-radius, radius) in each dimension, or a distribution from which to choose evaluation points.

n_eval_points : int, optional (Default: None)

The number of evaluation points to be drawn from the eval_points distribution. If None, then a heuristic is used to determine the number of evaluation points.

neuron_type : NeuronType, optional (Default: nengo.LIF())

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

gain : Distribution or (n_neurons,) array_like (Default: None)

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

bias : Distribution or (n_neurons,) array_like (Default: None)

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

noise : Process, optional (Default: None)

Random noise injected directly into each neuron in the ensemble as current. A sample is drawn for each individual neuron on every simulation step.

label : str, optional (Default: None)

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

seed : int, optional (Default: None)

The seed used for random number generation.

Attributes

bias	(Distribution or (n_neurons,) array_like or None) The biases associated with each neuron in the ensemble.
dimensions	(int) The number of representational dimensions.
encoders	(Distribution or (n_neurons, dimensions) array_like) The encoders, used to transform from representational space to neuron space. Each row is a neuron’s encoder, each column is a representational dimension.
eval_points	(Distribution or (n_eval_points, dims) array_like) The evaluation points used for decoder solving, spanning the interval (-radius, radius) in each dimension, or a distribution from which to choose evaluation points.
gain	(Distribution or (n_neurons,) array_like or None) The gains associated with each neuron in the ensemble.
intercepts	(Distribution or (n_neurons) array_like or None) The point along each neuron’s encoder where its activity is zero. If `e` is the neuron’s encoder, then the activity will be zero when `dot(x, e) <= c`, where `c` is the given intercept.
label	(str or None) A name for the ensemble. Used for debugging and visualization.
max_rates	(Distribution or (n_neurons,) array_like or None) The activity of each neuron when `dot(x, e) = 1`, where `e` is the neuron’s encoder.
n_eval_points	(int or None) The number of evaluation points to be drawn from the `eval_points` distribution. If None, then a heuristic is used to determine the number of evaluation points.
n_neurons	(int or None) The number of neurons.
neuron_type	(NeuronType) The model that simulates all neurons in the ensemble (see `nengo.neurons`).
noise	(Process or None) Random noise injected directly into each neuron in the ensemble as current. A sample is drawn for each individual neuron on every simulation step.
radius	(int) The representational radius of the ensemble.
seed	(int or None) The seed used for random number generation.

neurons¶: A direct interface to the neurons in the ensemble.

probeable¶: (tuple) Signals that can be probed on an ensemble.

size_in¶: The dimensionality of the ensemble.

size_out¶: The dimensionality of the ensemble.

class nengo.ensemble.Neurons(ensemble)[source]¶

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.

ensemble¶: (Ensemble) The ensemble these neurons are part of.

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

size_in¶: (int) The number of neurons in the population.

size_out¶: (int) The number of neurons in the population.

class nengo.Node(output=Default, size_in=Default, size_out=Default, label=Default, seed=Default)[source]¶

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:

output : callable, array_like, or None

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

size_in : int, optional (Default: 0)

The number of dimensions of the input data parameter.

size_out : int, optional (Default: None)

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

label : str, optional (Default: None)

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

seed : int, optional (Default: None)

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

Attributes

label	(str) The name of the node.
output	(callable, array_like, or None) The given output.
size_in	(int) The number of dimensions for incoming connection.
size_out	(int) The number of output dimensions.

probeable¶: (tuple) Signals that can be probed on a node.

class nengo.Connection(pre, post, synapse=Default, function=Default, transform=Default, solver=Default, learning_rule_type=Default, eval_points=Default, scale_eval_points=Default, label=Default, seed=Default, modulatory=Unconfigurable)[source]¶

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, we could not create the following connection:

nengo.Connection(node, ensemble)

But, we could create either of these two connections:

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

Parameters:

pre : Ensemble or Neurons or Node

The source Nengo object for the connection.

post : Ensemble or Neurons or Node or Probe

The destination object for the connection.

synapse : Synapse, optional (Default: nengo.synapses.Lowpass(tau=0.005))

Synapse model to use for filtering (see Synapse).

function : callable, optional (Default: None)

Function to compute across the connection. Note that pre must be an ensemble to apply a function across the connection.

transform : (post.size_in, pre.size_out) array_like, optional (Default: np.array(1.0))

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 (len(function(np.zeros(post.size_in))), pre.size_out).

solver : Solver, optional (Default: nengo.solvers.LstsqL2())

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_type : LearningRuleType or iterable of LearningRuleType, optional (Default: None)

Modifies the decoders or connection weights during simulation.

eval_points : (n_eval_points, pre.size_out) array_like or int, optional (Default: None)

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_points : bool, optional (Default: True)

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

label : str, optional (Default: None)

A descriptive label for the connection.

seed : int, optional (Default: None)

The seed used for random number generation.

Attributes

is_decoded	(bool) True if and only if the connection is decoded. This will not occur when `solver.weights` is True or both pre and post are `Neurons`.
function	(callable) The given function.
function_size	(int) The output dimensionality of the given function. If no function is specified, function_size will be 0.
label	(str) A human-readable connection label for debugging and visualization. If not overridden, incorporates the labels of the pre and post objects.
learning_rule_type	(instance or list or dict of LearningRuleType, optional) The learning rule types.
post	(Ensemble or Neurons or Node or Probe or ObjView) The given post object.
post_obj	(Ensemble or Neurons or Node or Probe) The underlying post object, even if `post` is an `ObjView`.
post_slice	(slice or list or None) The slice associated with `post` if it is an ObjView, or None.
pre	(Ensemble or Neurons or Node or ObjView) The given pre object.
pre_obj	(Ensemble or Neurons or Node) The underlying pre object, even if `post` is an `ObjView`.
pre_slice	(slice or list or None) The slice associated with `pre` if it is an ObjView, or None.
seed	(int) The seed used for random number generation.
solver	(Solver) The Solver instance that will be used to compute decoders or weights (see `nengo.solvers`).
synapse	(Synapse) The Synapse model used for filtering across the connection (see `nengo.synapses`).
transform	((size_mid, size_out) array_like) Linear transform mapping the pre function output to the post input.

learning_rule¶: (LearningRule or iterable) Connectable learning rule object(s).

size_in¶

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

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

size_mid¶

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

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

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)[source]¶

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.

connection¶: (Connection) The connection modified by the learning rule.

error_type¶: (str) The type of information expected by the learning rule.

modifies¶: (str) The quantity modified by the learning rule.

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

size_in¶: (int) Dimensionality of the signal expected by the learning rule.

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

class nengo.Probe(target, attr=None, sample_every=Default, synapse=Default, solver=Default, label=Default, seed=Default)[source]¶

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')

Parameters:

target : Ensemble, Neurons, Node, or Connection

The object to probe.

attr : str, optional (Default: None)

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_every : float, optional (Default: None)

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

synapse : Synapse, optional (Default: None)

A synaptic model to filtering the probed signal.

solver : Solver, optional (Default: ConnectionDefault)

Solver to compute decoders for probes that require them.

label : str, optional (Default: None)

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

seed : int, optional (Default: None)

The seed used for random number generation.

Attributes

attr	(str or None) The signal that will be probed. If None, the first element of the target’s `probeable` list will be used.
sample_every	(float or None) Sampling period in seconds. If None, the `dt` of the simluation will be used.
solver	(Solver or None) `Solver` to compute decoders. Only used for probes of an ensemble’s decoded output.
synapse	(Synapse or None) A synaptic model to filtering the probed signal.
target	(Ensemble, Neurons, Node, or Connection) The object to probe.

obj¶: (Nengo object) The underlying Nengo object target.

size_in¶: (int) Dimensionality of the probed signal.

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

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

Neuron types¶

class nengo.neurons.NeuronType[source]¶

Base class for Nengo neuron models.

Attributes

probeable

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

gain_bias(max_rates, intercepts)[source]¶

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 : ndarray(dtype=float64)

Maximum firing rates of neurons.

intercepts : ndarray(dtype=float64)

X-intercepts of neurons.

Returns:

gain : ndarray(dtype=float64)

Gain associated with each neuron. Sometimes denoted alpha.

bias : ndarray(dtype=float64)

Bias current associated with each neuron.

rates(x, gain, bias)[source]¶

Compute firing rates (in Hz) for given vector 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.

Parameters:

x : ndarray(dtype=float64)

Vector-space input.

gain : ndarray(dtype=float64)

Gains associated with each neuron.

bias : ndarray(dtype=float64)

Bias current associated with each neuron.

step_math(dt, J, output)[source]¶

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:

dt : float

Simulation timestep.

J : ndarray(dtype=float64)

Input currents associated with each neuron.

output : ndarray(dtype=float64)

Output activities associated with each neuron.

class nengo.Direct[source]¶

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)[source]¶: Always returns None, None.

rates(x, gain, bias)[source]¶: Always returns x.

step_math(dt, J, output)[source]¶

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[source]¶

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.

gain_bias(max_rates, intercepts)[source]¶: Determine gain and bias by shifting and scaling the lines.

step_math(dt, J, output)[source]¶: Implement the rectification nonlinearity.

class nengo.Sigmoid(tau_ref=0.002)[source]¶

A neuron model whose response curve is a sigmoid.

gain_bias(max_rates, intercepts)[source]¶: Analytically determine gain, bias.

step_math(dt, J, output)[source]¶: Implement the sigmoid nonlinearity.

class nengo.LIF(tau_rc=0.02, tau_ref=0.002, min_voltage=0)[source]¶

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

Parameters:

tau_rc : float

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

tau_ref : float

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

min_voltage : float

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

step_math(dt, J, spiked, voltage, refractory_time)[source]¶: Implement the LIF nonlinearity.

class nengo.LIFRate(tau_rc=0.02, tau_ref=0.002)[source]¶

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

Parameters:

tau_rc : float

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

tau_ref : float

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

gain_bias(max_rates, intercepts)[source]¶: Analytically determine gain, bias.

rates(x, gain, bias)[source]¶: Always use LIFRate to determine rates.

step_math(dt, J, output)[source]¶: Implement the LIFRate nonlinearity.

class nengo.AdaptiveLIF(tau_n=1, inc_n=0.01, **lif_args)[source]¶

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_n : float

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

inc_n : float

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

tau_rc : float

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

tau_ref : float

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

References

[R1]	Koch, Christof. Biophysics of Computation: Information Processing in Single Neurons. Oxford University Press, 1999. p. 339

step_math(dt, J, output, voltage, ref, adaptation)[source]¶: Implement the AdaptiveLIF nonlinearity.

class nengo.AdaptiveLIFRate(tau_n=1, inc_n=0.01, **lif_args)[source]¶

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_n : float

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

inc_n : float

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

tau_rc : float

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

tau_ref : float

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

References

[R2]	Koch, Christof. Biophysics of Computation: Information Processing in Single Neurons. Oxford University Press, 1999. p. 339

step_math(dt, J, output, adaptation)[source]¶: Implement the AdaptiveLIFRate nonlinearity.

class nengo.Izhikevich(tau_recovery=0.02, coupling=0.2, reset_voltage=-65.0, reset_recovery=8.0)[source]¶

Izhikevich neuron model.

This implementation is based on the original paper [R3]; 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_recovery : float, optional (Default: 0.02)

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

coupling : float, optional (Default: 0.2)

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

reset_voltage : float, optional (Default: -65.)

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

reset_recovery : float, optional (Default: 8.)

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

References

[R3]	(1, 2) 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)[source]¶

Estimates steady-state firing rate given gain and bias.

Uses the nengo.utils.neurons.settled_firingrate helper function.

step_math(dt, J, spiked, voltage, recovery)[source]¶: Implement the Izhikevich nonlinearity.

Learning rule types¶

class nengo.learning_rules.LearningRuleType(learning_rate=1e-06)[source]¶

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 error_type is the type of the incoming error signal. Options are:

'none': no error signal
'scalar': scalar error signal
'decoded': vector error signal in decoded space
'neuron': vector error signal in neuron space

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

'encoders'
'decoders'
'weights'

Parameters:

learning_rate : float, optional (Default: 1e-6)

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

Attributes

error_type	(str) The type of the incoming error signal. This also determines the dimensionality of the error signal.
learning_rate	(float) A scalar indicating the rate at which `modifies` will be adjusted.
modifies	(str) The signal targeted by the learning rule.

class nengo.PES(learning_rate=0.0001, pre_tau=0.005)[source]¶

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_rate : float, optional (Default: 1e-4)

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

pre_tau : float, optional (Default: 0.005)

Filter constant on activities of neurons in pre population.

Attributes

learning_rate	(float) A scalar indicating the rate at which weights will be adjusted.
pre_tau	(float) Filter constant on activities of neurons in pre population.

class nengo.BCM(pre_tau=0.005, post_tau=None, theta_tau=1.0, learning_rate=1e-09)[source]¶

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:

theta_tau : float, optional (Default: 1.0)

A scalar indicating the time constant for theta integration.

pre_tau : float, optional (Default: 0.005)

Filter constant on activities of neurons in pre population.

post_tau : float, optional (Default: None)

Filter constant on activities of neurons in post population. If None, post_tau will be the same as pre_tau.

learning_rate : float, optional (Default: 1e-9)

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

Attributes

learning_rate	(float) A scalar indicating the rate at which weights will be adjusted.
post_tau	(float) Filter constant on activities of neurons in post population.
pre_tau	(float) Filter constant on activities of neurons in pre population.
theta_tau	(float) A scalar indicating the time constant for theta integration.

class nengo.Oja(pre_tau=0.005, post_tau=None, beta=1.0, learning_rate=1e-06)[source]¶

Oja learning rule.

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

Parameters:

pre_tau : float, optional (Default: 0.005)

Filter constant on activities of neurons in pre population.

post_tau : float, optional (Default: None)

Filter constant on activities of neurons in post population. If None, post_tau will be the same as pre_tau.

beta : float, optional (Default: 1.0)

A scalar weight on the forgetting term.

learning_rate : float, optional (Default: 1e-6)

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

Attributes

beta	(float) A scalar weight on the forgetting term.
learning_rate	(float) A scalar indicating the rate at which weights will be adjusted.
post_tau	(float) Filter constant on activities of neurons in post population.
pre_tau	(float) Filter constant on activities of neurons in pre population.

class nengo.Voja(post_tau=0.005, learning_rate=0.01)[source]¶

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_tau : float, optional (Default: 0.005)

Filter constant on activities of neurons in post population.

learning_rate : float, optional (Default: 1e-2)

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

Attributes

learning_rate	(float) A scalar indicating the rate at which encoders will be adjusted.
post_tau	(float) Filter constant on activities of neurons in post population.

Synapse models¶

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

Abstract base class for synapse model.

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 isthe current that will be imparted 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_in : int, optional (Default: 1)

The size_in used if not specified.

default_size_out : int (Default: None)

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

default_dt : float (Default: 0.001 (1 millisecond))

The simulation timestep used if not specified.

seed : int, optional (Default: None)

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

Attributes

default_dt	(float (Default: 0.001 (1 millisecond))) The simulation timestep used if not specified.
default_size_in	(int (Default: 0)) The size_in used if not specified.
default_size_out	(int (Default: 1)) The size_out used if not specified.
seed	(int, optional (Deafult: None)) Random number seed. Ensures random factors will be the same each run.

filt(x, dt=None, axis=0, y0=None, copy=True, filtfilt=False)[source]¶

Filter x with this synapse model.

Parameters:

x : array_like

The signal to filter.

dt : float, optional (Default: None)

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

axis : int, optional (Default: 0)

The axis along which to filter.

y0 : array_like, optional (Default: None)

The starting state of the filter output. If None, the initial value of the input signal along the axis filtered will be used.

copy : bool, optional (Default: True)

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

filtfilt : bool, optional (Default: False)

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

filtfilt(x, **kwargs)[source]¶

Zero-phase filtering of x using this filter.

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

make_step(shape_in, shape_out, dt, rng, y0=None, dtype=<type 'numpy.float64'>)[source]¶

Create function to advance the synapse forward one time step.

At a minimum, Synapse subclasses must implement this method. That implementation should return a callable that will perform the synaptic filtering operation.

Parameters:

shape_in : tuple

Shape of the input signal to be filtered.

shape_out : tuple

Shape of the output filtered signal.

dt : float

The timestep of the simulation.

rng : numpy.random.RandomState

Random number generator.

y0 : array_like, optional (Default: None)

The starting state of the filter output. If None, each dimension of the state will start at zero.

dtype : numpy.dtype (Default: np.float64)

Type of data used by the synapse model. This is important for ensuring that certain synapses avoid or force integer division.

nengo.synapses.filt(signal, synapse, dt, axis=0, x0=None, copy=True)[source]¶: Filter signal with synapse.

Note

Deprecated in Nengo 2.1.0. Use Synapse.filt method instead.

nengo.synapses.filtfilt(signal, synapse, dt, axis=0, x0=None, copy=True)[source]¶: Zero-phase filtering of signal using the synapse filter.

Note

Deprecated in Nengo 2.1.0. Use Synapse.filtfilt method instead.

class nengo.LinearFilter(num, den, analog=True, **kwargs)[source]¶

General linear time-invariant (LTI) system synapse.

This class can be used to implement any linear filter, given the filter’s transfer function. [R4]

Parameters:

num : array_like

Numerator coefficients of transfer function.

den : array_like

Denominator coefficients of transfer function.

analog : boolean, optional (Default: True)

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.

References

[R4]	(1, 2) http://en.wikipedia.org/wiki/Filter_%28signal_processing%29

Attributes

analog	(boolean) 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`.
den	(ndarray) Denominator coefficients of transfer function.
num	(ndarray) Numerator coefficients of transfer function.

evaluate(frequencies)[source]¶

Evaluate the transfer function at the given frequencies.

Examples

Using the evaluate function to make a Bode plot:

synapse = nengo.synapses.LinearFilter([1], [0.02, 1])
f = numpy.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_step(shape_in, shape_out, dt, rng, y0=None, dtype=<type 'numpy.float64'>, method='zoh')[source]¶: Returns a Step instance that implements the linear filter.

class Step(num, den, output)[source]¶: Abstract base class for LTI filtering step functions.

class LinearFilter.NoDen(num, den, output)[source]¶

An LTI step function for transfer functions with no denominator.

This step function should be much faster than the equivalent general step function.

class LinearFilter.Simple(num, den, output, y0=None)[source]¶

An LTI step function for transfer functions with one num and den.

This step function should be much faster than the equivalent general step function.

class LinearFilter.General(num, den, output, y0=None)[source]¶

An LTI step function for any given transfer function.

Implements a discrete-time LTI system using the difference equation [R5] for the given transfer function (num, den).

References

[R5]	(1, 2) http://en.wikipedia.org/wiki/Digital_filter#Difference_equation

class nengo.Lowpass(tau, **kwargs)[source]¶

Standard first-order lowpass filter synapse.

Parameters:

tau : float

The time constant of the filter in seconds.

Attributes

tau	(float) The time constant of the filter in seconds.

make_step(shape_in, shape_out, dt, rng, y0=None, dtype=<type 'numpy.float64'>, **kwargs)[source]¶: Returns an optimized LinearFilter.Step subclass.

class nengo.Alpha(tau, **kwargs)[source]¶

Alpha-function filter synapse.

The impulse-response function is given by:

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

and was found by [R6] to be a good basic model for synapses.

Parameters:

tau : float

The time constant of the filter in seconds.

References

[R6]	(1, 2) Mainen, Z.F. and Sejnowski, T.J. (1995). Reliability of spike timing in neocortical neurons. Science (New York, NY), 268(5216):1503-6.

Attributes

tau	(float) The time constant of the filter in seconds.

make_step(shape_in, shape_out, dt, rng, y0=None, dtype=<type 'numpy.float64'>, **kwargs)[source]¶: Returns an optimized LinearFilter.Step subclass.

class nengo.synapses.Triangle(t, **kwargs)[source]¶

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:

t : float

Length of the triangle, in seconds.

Attributes

t	(float) Length of the triangle, in seconds.

make_step(shape_in, shape_out, dt, rng, y0=None, dtype=<type 'numpy.float64'>)[source]¶: Returns a custom step function.

Decoder and connection weight solvers¶

class nengo.solvers.Solver[source]¶

Decoder or weight solver.

__call__(A, Y, rng=None, E=None)[source]¶

Call the solver.

Parameters:

A : (n_eval_points, n_neurons) array_like

Matrix of the neurons’ activities at the evaluation points

Y : (n_eval_points, dimensions) array_like

Matrix of the target decoded values for each of the D dimensions, at each of the evaluation points.

rng : numpy.random.RandomState, optional (Default: None)

A random number generator to use as required. If None, the numpy.random module functions will be used.

E : (dimensions, post.n_neurons) array_like, optional (Default: None)

Array of post-population encoders. Providing this tells the solver to return an array of connection weights rather than decoders.

Returns:

X : (n_neurons, dimensions) or (n_neurons, post.n_neurons) ndarray

(n_neurons, dimensions) array of decoders (if solver.weights is False) or (n_neurons, post.n_neurons) array of weights (if 'solver.weights is True).

info : dict

A dictionary of information about the solver. All dictionaries have an 'rmses' key that contains RMS errors of the solve. Other keys are unique to particular solvers.

mul_encoders(Y, E, copy=False)[source]¶

Helper function that projects signal Y onto encoders E.

Parameters:

Y : ndarray

The signal of interest.

E : (dimensions, n_neurons) array_like or None

Array of encoders. If None, Y will be returned unchanged.

copy : bool, optional (Default: False)

Whether a copy of Y should be returned if E is None.

class nengo.solvers.Lstsq[source]¶

Unregularized least-squares solver.

Parameters:

weights : bool, optional (Default: False)

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

rcond : float, optional (Default: 0.01)

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

Attributes

rcond	(float) Cut-off ratio for small singular values (see `numpy.linalg.lstsq`).
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqNoise(weights=False, noise=0.1, solver=<nengo.utils.least_squares_solvers.Cholesky object>)[source]¶

Least-squares solver with additive Gaussian white noise.

Parameters:

weights : bool, optional (Default: False)

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

noise : float, optional (Default: 0.1)

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

solver : LeastSquaresSolver, optional (Default: Cholesky())

Subsolver to use for solving the least squares problem.

Attributes

noise	(float) Amount of noise, as a fraction of the neuron activity.
solver	(`LeastSquaresSolver`) Subsolver to use for solving the least squares problem.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqMultNoise(weights=False, noise=0.1, solver=<nengo.utils.least_squares_solvers.Cholesky object>)[source]¶

Least-squares solver with multiplicative white noise.

Parameters:

weights : bool, optional (Default: False)

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

noise : float, optional (Default: 0.1)

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

solver : LeastSquaresSolver, optional (Default: Cholesky())

Subsolver to use for solving the least squares problem.

Attributes

noise	(float) Amount of noise, as a fraction of the neuron activity.
solver	(`LeastSquaresSolver`) Subsolver to use for solving the least squares problem.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL2(weights=False, reg=0.1, solver=<nengo.utils.least_squares_solvers.Cholesky object>)[source]¶

Least-squares solver with L2 regularization.

Parameters:

weights : bool, optional (Default: False)

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

reg : float, optional (Default: 0.1)

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

solver : LeastSquaresSolver, optional (Default: Cholesky())

Subsolver to use for solving the least squares problem.

Attributes

reg	(float) Amount of regularization, as a fraction of the neuron activity.
solver	(`LeastSquaresSolver`) Subsolver to use for solving the least squares problem.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL2nz(weights=False, reg=0.1, solver=<nengo.utils.least_squares_solvers.Cholesky object>)[source]¶

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

Parameters:

weights : bool, optional (Default: False)

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

reg : float, optional (Default: 0.1)

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

solver : LeastSquaresSolver, optional (Default: Cholesky())

Subsolver to use for solving the least squares problem.

Attributes

reg	(float) Amount of regularization, as a fraction of the neuron activity.
solver	(`LeastSquaresSolver`) Subsolver to use for solving the least squares problem.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqL1(weights=False, l1=0.0001, l2=1e-06)[source]¶

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:

weights : bool, optional (Default: False)

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

l1 : float, optional (Default: 1e-4)

Amount of L1 regularization.

l2 : float, optional (Default: 1e-6)

Amount of L2 regularization.

Attributes

l1	(float) Amount of L1 regularization.
l2	(float) Amount of L2 regularization.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.LstsqDrop(weights=False, drop=0.25, solver1=<nengo.solvers.LstsqL2nz object>, solver2=<nengo.solvers.LstsqL2nz object>)[source]¶

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:

weights : bool, optional (Default: False)

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

drop : float, optional (Default: 0.25)

Fraction of decoders or weights to set to zero.

solver1 : Solver, optional (Default: LstsqL2nz(reg=0.1))

Solver for finding the initial decoders.

solver2 : Solver, optional (Default: LstsqL2nz(reg=0.01))

Used for re-solving for the decoders after dropout.

Attributes

drop	(float) Fraction of decoders or weights to set to zero.
solver1	(Solver) Solver for finding the initial decoders.
solver2	(Solver) Used for re-solving for the decoders after dropout.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.Nnls(weights=False)[source]¶

Non-negative least-squares solver without regularization.

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

Note

Requires SciPy.

Parameters:

weights : bool, optional (Default: False)

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

Attributes

weights

(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.NnlsL2(weights=False, reg=0.1)[source]¶

Non-negative least-squares solver with L2 regularization.

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

Note

Requires SciPy.

Parameters:

weights : bool, optional (Default: False)

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

reg : float, optional (Default: 0.1)

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

Attributes

reg	(float) Amount of regularization, as a fraction of the neuron activity.
weights	(bool) If False, solve for decoders. If True, solve for weights.

class nengo.solvers.NnlsL2nz(weights=False, reg=0.1)[source]¶

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

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

Note

Requires SciPy.

Parameters:

weights : bool, optional (Default: False)

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

reg : float, optional (Default: 0.1)

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

Attributes

reg	(float) Amount of regularization, as a fraction of the neuron activity.
weights	(bool) If False, solve for decoders. If True, solve for weights.