nengo_spa.semantic_pointer¶
Classes

Absorbing element. 

Identity element. 

Negative identity element. 

A Semantic Pointer, based on Holographic Reduced Representations. 

Sign of a Semantic Pointer. 

Zero element. 

class
nengo_spa.semantic_pointer.
SemanticPointer
(data, vocab=None, algebra=None, name=None)[source]¶ A Semantic Pointer, based on Holographic Reduced Representations.
Operators are overloaded so that
+
and
are addition,*
is circular convolution, and~
is the twosided inversion operator. The left and right inverese can be obtained with thelinv
andrinv
methods. Parameters
data (array_like) – The vector constituting the Semantic Pointer.
vocab (Vocabulary, optional) – Vocabulary that the Semantic Pointer is considered to be part of. Mutually exclusive with the algebra argument.
algebra (AbstractAlgebra, optional) – Algebra used to perform vector symbolic operations on the Semantic Pointer. Defaults to
HrrAlgebra
. Mutually exclusive with the vocab argument.name (str, optional) – A name for the Semantic Pointer.

v
¶ The vector constituting the Semantic Pointer.
 Type
array_like

algebra
¶ Algebra that defines the vector symbolic operations on this Semantic Pointer.
 Type

vocab
¶ The vocabulary the this Semantic Pointer is considered to be part of.
 Type
Vocabulary or None

name
¶ Name of the Semantic Pointer.
 Type
str or None

normalized
()[source]¶ Normalize the Semantic Pointer and return it as a new object.
If the vector length is zero, the Semantic Pointer will be returned unchanged.
The original object is not modified.

unitary
()[source]¶ Make the Semantic Pointer unitary and return it as a new object.
The original object is not modified.
A unitary Semantic Pointer has the property that it does not change the length of Semantic Pointers it is bound with.

sign
()[source]¶ Return the sign of the Semantic Pointer.
See
AbstractAlgebra.sign
for details on signs of Semantic Pointers. Returns
Sign of the Semantic Pointer.
 Return type

abs
()[source]¶ Return the absolute Semantic Pointer.
See
AbstractAlgebra.abs
for details on absolute Semantic Pointers.

__pow__
(other)[source]¶ Binding power of the Semantic Pointer.
Integer exponents are supported for any algebra. See the
binding_power
documentation of the respective algebra for details about fractional exponents. Parameters
other (float) – Exponent of the binding power.
 Returns
 Return type

__invert__
()[source]¶ Return a reorganized
SemanticPointer
that acts as a twosided inverse for binding.

linv
()[source]¶ Return a reorganized
SemanticPointer
that acts as a left inverse for binding.See also

rinv
()[source]¶ Return a reorganized
SemanticPointer
that acts as a right inverse for binding.See also

get_binding_matrix
(swap_inputs=False)[source]¶ Return the matrix that does a binding with this vector.
This should be such that
A*B == dot(A.get_binding_matrix(), B.v)
.

compare
(other)[source]¶ Return the similarity between two SemanticPointers.
This is the normalized dot product, or (equivalently), the cosine of the angle between the two vectors.

reinterpret
(vocab)[source]¶ Reinterpret the Semantic Pointer as part of vocabulary vocab.
The vocab parameter can be set to None to clear the associated vocabulary and allow the source to be interpreted as part of the vocabulary of any Semantic Pointer it is combined with.

translate
(vocab, populate=None, keys=None, solver=None)[source]¶ Translate the Semantic Pointer to vocabulary vocab.
The translation of a Semantic Pointer uses some form of projection to convert the Semantic Pointer to a Semantic Pointer of another vocabulary. By default the outer products of terms in the source and target vocabulary are used, but if solver is given, it is used to find a least squares solution for this projection.
 Parameters
vocab (Vocabulary) – Target vocabulary.
populate (bool, optional) – Whether the target vocabulary should be populated with missing keys. This is done by default, but with a warning. Set this explicitly to True or False to silence the warning or raise an error.
keys (list, optional) – All keys to translate. If None, all keys in the source vocabulary will be translated.
solver (nengo.Solver, optional) – If given, the solver will be used to solve the least squares problem to provide a better projection for the translation.

class
nengo_spa.semantic_pointer.
SemanticPointerSign
(sign, *, algebra=None, dimensions=None, vocab=None, name=None)[source]¶ Bases:
nengo_spa.algebras.base.AbstractSign
Sign of a Semantic Pointer.
This class acts as proxy to the actual sign instance of the underlying algebra. Use the sign attribute if you want to perform equality checks with other signs.
 Parameters
sign (AbstractSign) – Actual underlying sign.
algebra (AbstractAlgebra, optional) – The underlying algebra of the Semantic Pointer for which the sign is represented.
dimensions (int, optional) – Number of dimensions of the Semantic Pointer for which the sign is represented. If not given, vocab must be given.
vocab (Vocabulary, optional) – Vocabulary of the Semantic Pointer for which the sign is represented. If not given, dimensions must be given. If dimensions and vocab are given, they must agree on the dimensionality.
name (str or Node, optional) – Name of the Semantic Pointer including the invoked sign operation.

sign
¶ Actual underlying sign
 Type

algebra
¶ The underlying algebra of the Semantic Pointer for which the sign is represented.
 Type
AbstractAlgebra or None

dimensions
¶ Number of dimensions of the Semantic Pointer for which the sign is represented.
 Type
int

vocab
¶ Vocabulary of the Semantic Pointer for which the sign is represented.
 Type
Vocabulary or None

to_vector
(d)[source]¶ Return the vector in the algebra corresponding to the sign.
 Parameters
d (int) – Vector dimensionality.
 Returns
Vector corresponding to the sign.
 Return type
(d,) ndarray

class
nengo_spa.semantic_pointer.
Identity
(n_dimensions, vocab=None, algebra=None, *, sidedness=<ElementSidedness.TWO_SIDED: 'twosided'>)[source]¶ Bases:
nengo_spa.semantic_pointer.SemanticPointer
Identity element.
 Parameters
n_dimensions (int) – Dimensionality of the identity vector.
vocab (Vocabulary, optional) – Vocabulary that the Semantic Pointer is considered to be part of. Mutually exclusive with the algebra argument.
algebra (AbstractAlgebra, optional) – Algebra used to perform vector symbolic operations on the Semantic Pointer. Defaults to
HrrAlgebra
. Mutually exclusive with the vocab argument.sidedness (ElementSidedness, optional) – Side in the binding operation on which the element acts as identity.

class
nengo_spa.semantic_pointer.
NegativeIdentity
(n_dimensions, vocab=None, algebra=None, *, sidedness=<ElementSidedness.TWO_SIDED: 'twosided'>)[source]¶ Bases:
nengo_spa.semantic_pointer.SemanticPointer
Negative identity element.
 Parameters
n_dimensions (int) – Dimensionality of the negative identity vector.
vocab (Vocabulary, optional) – Vocabulary that the Semantic Pointer is considered to be part of. Mutually exclusive with the algebra argument.
algebra (AbstractAlgebra, optional) – Algebra used to perform vector symbolic operations on the Semantic Pointer. Defaults to
HrrAlgebra
. Mutually exclusive with the vocab argument.sidedness (ElementSidedness, optional) – Side in the binding operation on which the element acts as identity.

class
nengo_spa.semantic_pointer.
AbsorbingElement
(n_dimensions, vocab=None, algebra=None, *, sidedness=<ElementSidedness.TWO_SIDED: 'twosided'>)[source]¶ Bases:
nengo_spa.semantic_pointer.SemanticPointer
Absorbing element.
If \(z\) denotes the absorbing element, \(v \circledast z = c z\), where \(v\) is a Semantic Pointer and \(c\) is a realvalued scalar. Furthermore \(\z\ = 1\).
 Parameters
n_dimensions (int) – Dimensionality of the identity vector.
vocab (Vocabulary, optional) – Vocabulary that the Semantic Pointer is considered to be part of. Mutually exclusive with the algebra argument.
algebra (AbstractAlgebra, optional) – Algebra used to perform vector symbolic operations on the Semantic Pointer. Defaults to
HrrAlgebra
. Mutually exclusive with the vocab argument.sidedness (ElementSidedness, optional) – Side in the binding operation on which the element acts as absorbing element.

class
nengo_spa.semantic_pointer.
Zero
(n_dimensions, vocab=None, algebra=None, sidedness=<ElementSidedness.TWO_SIDED: 'twosided'>)[source]¶ Bases:
nengo_spa.semantic_pointer.SemanticPointer
Zero element.
 Parameters
n_dimensions (int) – Dimensionality of the identity vector.
vocab (Vocabulary, optional) – Vocabulary that the Semantic Pointer is considered to be part of. Mutually exclusive with the algebra argument.
algebra (AbstractAlgebra, optional) – Algebra used to perform vector symbolic operations on the Semantic Pointer. Defaults to
HrrAlgebra
. Mutually exclusive with the vocab argument.sidedness (ElementSidedness, optional) – Side in the binding operation on which the element acts as zero element.