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nengo_spa.networks¶
Basic networks that are used by NengoSPA.
These networks do not provide any information about inputs, outputs or used vocabularies and are completely independent of SPA specifics.

Compute the circular convolution of two vectors. 

An ensemble array optimized for representing the identity circular convolution vector besides random unit vectors. 

Computes the matrix product A*B. 

Compute vectorderived transformation binding (VTB). 

Compute transposed vectorderived transformation binding (TVTB). 
Selection networks

Independent accumulator (IA) winnertakeall (WTA) network. 

Array of thresholding ensembles. 

Winnertakeall (WTA) network with lateral inhibition. 

class
nengo_spa.networks.
CircularConvolution
(n_neurons, dimensions, invert_a=False, invert_b=False, input_magnitude=1.0, **kwargs)[source]¶ Compute the circular convolution of two vectors.
The circular convolution \(c\) of vectors \(a\) and \(b\) is given by
\[c[i] = \sum_j a[j] b[i  j]\]where negative indices on \(b\) wrap around to the end of the vector.
This computation can also be done in the Fourier domain,
\[c = DFT^{1} ( DFT(a) \odot DFT(b) )\]where \(DFT\) is the Discrete Fourier Transform operator, and \(DFT^{1}\) is its inverse. This network uses this method.
 Parameters
 n_neuronsint
Number of neurons to use in each product computation.
 dimensionsint
The number of dimensions of the input and output vectors.
 invert_abool, optional
Whether to reverse the order of elements in first input.
 invert_bbool, optional
Whether to reverse the order of elements in the second input. Flipping exactly one input will make the network perform circular correlation instead of circular convolution which can be treated as an approximate inverse to circular convolution.
 input_magnitudefloat, optional
The expected magnitude of the vectors to be convolved. This value is used to determine the radius of the ensembles computing the elementwise product.
 **kwargsdict
Keyword arguments to pass through to the
nengo.Network
constructor.
Notes
The network maps the input vectors \(a\) and \(b\) of length \(N\) into the Fourier domain and aligns them for complex multiplication. Letting \(F = DFT(a)\) and \(G = DFT(b)\), this is given by:
[ F[i].real ] [ G[i].real ] [ w[i] ] [ F[i].imag ] * [ G[i].imag ] = [ x[i] ] [ F[i].real ] [ G[i].imag ] [ y[i] ] [ F[i].imag ] [ G[i].real ] [ z[i] ]
where \(i\) only ranges over the lower half of the spectrum, since the upper half of the spectrum is the flipped complex conjugate of the lower half, and therefore redundant. The input transforms are used to perform the DFT on the inputs and align them correctly for complex multiplication.
The complex product \(H = F * G\) is then
\[H[i] = (w[i]  x[i]) + (y[i] + z[i]) I\]where \(I = \sqrt{1}\). We can perform this addition along with the inverse DFT \(c = DFT^{1}(H)\) in a single output transform, finding only the real part of \(c\) since the imaginary part is analytically zero.
Examples
A basic example computing the circular convolution of two 10dimensional vectors represented by ensemble arrays:
A = EnsembleArray(50, n_ensembles=10) B = EnsembleArray(50, n_ensembles=10) C = EnsembleArray(50, n_ensembles=10) cconv = nengo_spa.networks.CircularConvolution(50, dimensions=10) nengo.Connection(A.output, cconv.input_a) nengo.Connection(B.output, cconv.input_b) nengo.Connection(cconv.output, C.input)
 Attributes
 input_anengo.Node
The first vector to be convolved.
 input_bnengo.Node
The second vector to be convolved.
 productnengo.networks.Product
Network created to do the elementwise product of the \(DFT\) components.
 outputnengo.Node
The resulting convolved vector.

class
nengo_spa.networks.
IdentityEnsembleArray
(neurons_per_dimension, dimensions, subdimensions, **kwargs)[source]¶ An ensemble array optimized for representing the identity circular convolution vector besides random unit vectors.
The ensemble array will use ensembles with subdimensions dimensions, except for the first subdimensions dimensions. These will be split into a onedimensional ensemble for the first dimension and a subdimensions1 dimensional ensemble.
 Parameters
 neurons_per_dimensionint
Neurons per dimension.
 dimensionsint
Total number of dimensions. Must be a multiple of subdimensions.
 subdimensionsint
Maximum number of dimensions per ensemble.
 **kwargsdict
Keyword arguments to pass through to the
nengo.Network
constructor.
 Attributes
 inputnengo.Node
Input node.
 outputnengo.Node
Output node.

add_neuron_input
()[source]¶ Adds a node providing input to the neurons of all ensembles.
This node will be accessible through the neuron_input attribute.
 Returns
 nengo.Node
The added node.

add_neuron_output
()[source]¶ Adds a node providing neuron (nondecoded) output of all ensembles.
This node will be accessible through the neuron_output attribute.
 Returns
 nengo.Node
The added node.

add_output
(name, function, synapse=None, **conn_kwargs)[source]¶ Adds a new decoded output.
This will add the attribute named name to the object.
 Parameters
 namestr
Name of output. Must be a valid Python attribute name.
 functionfunc
Function to decode.
 synapsefloat or nengo.Lowpass
Synapse to apply to the decoded connection to the returned output node.
 conn_kwargsdict
Additional keywword arguments to apply to the decoded connection.
 Returns
 nengo.Node
Node providing the decoded output.

class
nengo_spa.networks.
MatrixMult
(n_neurons, shape_left, shape_right, **kwargs)[source]¶ Computes the matrix product A*B.
Both matrices need to be two dimensional.
See the Nengo Matrix Multiplication example for a description of the network internals.
 Parameters
 n_neuronsint
Number of neurons used per product of two scalars.
Note
If an odd number of neurons is given, one less neuron will be used per product to obtain an even number. This is due to the implementation the
Product
network. shape_lefttuple
Shape of the A input matrix.
 shape_righttuple
Shape of the B input matrix.
 **kwargsdict
Keyword arguments to pass through to the
nengo.Network
constructor.
 Attributes
 input_leftnengo.Node
The left matrix (A) to multiply.
 input_rightnengo.Node
The left matrix (A) to multiply.
 Cnengo.networks.Product
The product network doing the matrix multiplication.
 outputnengo.node
The resulting matrix result.

class
nengo_spa.networks.
TVTB
(n_neurons, dimensions, unbind_left=False, unbind_right=False, **kwargs)[source]¶ Compute transposed vectorderived transformation binding (TVTB).
VTB uses elementwise addition for superposition. The binding operation \(\mathcal{B}(x, y)\) is defined as
\[\begin{split}\mathcal{B}(x, y) := V_y^T x = \left[\begin{array}{ccc} V_y'^T & 0 & 0 \\ 0 & V_y'^T & 0 \\ 0 & 0 & V_y'^T \end{array}\right] x\end{split}\]with
\[\begin{split}V_y' = d^{\frac{1}{4}} \left[\begin{array}{cccc} y_1 & y_2 & \dots & y_{d'} \\ y_{d' + 1} & y_{d' + 2} & \dots & y_{2d'} \\ \vdots & \vdots & \ddots & \vdots \\ y_{d  d' + 1} & y_{d  d' + 2} & \dots & y_d \end{array}\right]\end{split}\]and
\[d'^2 = d.\]The approximate inverse \(y^+\) for \(y\) is permuting the elements such that \(V_{y^+} = V_y^T\).
Note that TVTB requires the vector dimensionality to be square.
The TVTB binding operation is neither associative nor commutative. In contrast to VTB, however, TVTB has twosided identities and inverses. Other properties are equivalent to VTB.
See also
 Parameters
 n_neuronsint
Number of neurons to use in each product computation.
 dimensionsint
The number of dimensions of the input and output vectors. Needs to be a square number.
 unbind_leftbool
Whether to unbind the left input vector from the right input vector.
 unbind_rightbool
Whether to unbind the right input vector from the left input vector.
 **kwargsdict
Keyword arguments to pass through to the
nengo.Network
constructor.
 Attributes
 input_leftnengo.Node
The left operand vector to be bound.
 input_rightnengo.Node
The right operand vector to be bound.
 matnengo.Node
Representation of the matrix \(V_y'\).
 vecnengo.Node
Representation of the vector \(y\).
 matmulslist
Matrix multiplication networks.
 outputnengo.Node
The resulting bound vector.

class
nengo_spa.networks.
VTB
(n_neurons, dimensions, unbind_left=False, unbind_right=False, **kwargs)[source]¶ Compute vectorderived transformation binding (VTB).
VTB uses elementwise addition for superposition. The binding operation \(\mathcal{B}(x, y)\) is defined as
\[\begin{split}\mathcal{B}(x, y) := V_y x = \left[\begin{array}{ccc} V_y' & 0 & 0 \\ 0 & V_y' & 0 \\ 0 & 0 & V_y' \end{array}\right] x\end{split}\]with
\[\begin{split}V_y' = d^{\frac{1}{4}} \left[\begin{array}{cccc} y_1 & y_2 & \dots & y_{d'} \\ y_{d' + 1} & y_{d' + 2} & \dots & y_{2d'} \\ \vdots & \vdots & \ddots & \vdots \\ y_{d  d' + 1} & y_{d  d' + 2} & \dots & y_d \end{array}\right]\end{split}\]and
\[d'^2 = d.\]The approximate inverse \(y^+\) for \(y\) is permuting the elements such that \(V_{y^+} = V_y^T\).
Note that VTB requires the vector dimensionality to be square.
The VTB binding operation is neither associative nor commutative. Furthermore, there are right inverses and identities only. By transposing the \(V_y\) matrix, the closely related
TvtbAlgebra
(Transposed VTB) algebra is obtained which does have twosided identities and inverses.Additional information about VTB can be found in
See also
 Parameters
 n_neuronsint
Number of neurons to use in each product computation.
 dimensionsint
The number of dimensions of the input and output vectors. Needs to be a square number.
 unbind_leftbool
Whether to unbind the left input vector from the right input vector.
 unbind_rightbool
Whether to unbind the right input vector from the left input vector.
 **kwargsdict
Keyword arguments to pass through to the
nengo.Network
constructor.
 Attributes
 input_leftnengo.Node
The left operand vector to be bound.
 input_rightnengo.Node
The right operand vector to be bound.
 matnengo.Node
Representation of the matrix \(V_y'\).
 vecnengo.Node
Representation of the vector \(y\).
 matmulslist
Matrix multiplication networks.
 outputnengo.Node
The resulting bound vector.
nengo_spa.networks.selection¶
Selection networks that pick one or more options among multiple choices.

class
nengo_spa.networks.selection.
IA
(n_neurons, n_ensembles, accum_threshold=0.8, accum_neuron_ratio=0.7, accum_timescale=0.2, feedback_timescale=0.005, accum_synapse=0.1, ff_synapse=0.005, intercept_width=0.15, radius=1.0, **kwargs)[source]¶ Independent accumulator (IA) winnertakeall (WTA) network.
This is a twolayered network. The first layer consists of independent accumulators (integrators), whereas the second layer does a thresholding. Once the threshold is exceeded a feedback connection will stabilize the current choice and inhibit all other choices. To switch the selection, it is necessary to provide a transient input to input_reset to reset the accumulator states.
This network is suited especially for accumulating evidence under noisy conditions and keep a stable choice selection until the processing of the choice has been finished.
Further details are to be found in [gosmann2017].
 Parameters
 n_neuronsint
Number of neurons for each choice.
 n_ensemblesint
Number of choices.
 accum_thresholdfloat, optional
Accumulation threshold that needs to be reached to produce an output.
 accum_neuron_ratio: float, optional
Portion of n_neurons that will be used for a layer 1 accumulator ensemble. The remaining neurons will be used for a layer 2 thresholding ensemble.
 accum_timescalefloat, optional
Evidence accumulation timescale.
 feedback_timescalefloat, optional
Timescale for the feedback connection from the thresholding layer to the accumulation layer.
 accum_synapseSynapse or float, optional
The synapse for connections to the accumulator ensembles.
 ff_synapseSynapse or float, optional
Synapse for feedforward connections.
 intercept_widthfloat, optional
The
nengo.presets.ThresholdingEnsembles
intercept_width parameter. radiusfloat, optional
The representational radius of the ensembles.
 **kwargsdict
Keyword arguments passed on to
nengo.Network
.
References
 gosmann2017
Jan Gosmann, Aaron R. Voelker, and Chris Eliasmith. “A spiking independent accumulator model for winnertakeall computation.” In Proceedings of the 39th Annual Conference of the Cognitive Science Society. London, UK, 2017. Cognitive Science Society.
 Attributes
 inputnengo.Node
The inputs to the network.
 input_resetnengo.Node
Input to reset the accumulators.
 outputnengo.Node
The outputs of the network.
 accumulatorsnengo.Thresholding
The layer 1 accumulators.
 thresholdingnengo.Thresholding
The layer 2 thresholding ensembles.

class
nengo_spa.networks.selection.
Thresholding
(n_neurons, n_ensembles, threshold, intercept_width=0.15, function=None, radius=1.0, **kwargs)[source]¶ Array of thresholding ensembles.
All inputs below the threshold will produce an output of 0, whereas inputs above the threshold produce an output of equal value.
 Parameters
 n_neuronsint
Number of neurons for each ensemble.
 n_ensemblesint
Number of ensembles.
 thresholdfloat
The thresholding value.
 intercept_widthfloat, optional
The
nengo.presets.ThresholdingEnsembles
intercept_width parameter. functionfunction, optional
Function to apply to the thresholded values.
 radiusfloat, optional
The representational radius of the ensembles.
 **kwargsdict
Keyword arguments passed on to
nengo.Network
.
 Attributes
 inputnengo.Node
The inputs to the network.
 outputnengo.Node
The outputs of the network.
 thresholdednengo.Node
The raw thresholded value (before applying function or correcting for the shift produced by the thresholding).

class
nengo_spa.networks.selection.
WTA
(n_neurons, n_ensembles, inhibit_scale=1.0, inhibit_synapse=0.005, **kwargs)[source]¶ Winnertakeall (WTA) network with lateral inhibition.
 Parameters
 n_neuronsint
Number of neurons for each ensemble.
 n_ensemblesint
Number of ensembles.
 inhibit_scalefloat, optional
Scaling of the lateral inhibition.
 inhibit_synapseSynapse or float, optional
Synapse on the recurrent connection for lateral inhibition.
 **kwargsdict
Keyword arguments passed on to
Thresholding
.
 Attributes
 inputnengo.Node
The inputs to the network.
 outputnengo.Node
The outputs of the network.
 thresholdednengo.Node
The raw thresholded value (before applying function or correcting for the shift produced by the thresholding).