nengo_spa.semantic_pointer¶

Classes

`AbsorbingElement`(n_dimensions[, vocab, …])	Absorbing element.
`Identity`(n_dimensions[, vocab, algebra, …])	Identity element.
`NegativeIdentity`(n_dimensions[, vocab, …])	Negative identity element.
`SemanticPointer`(data[, vocab, algebra, name])	A Semantic Pointer, based on Holographic Reduced Representations.
`SemanticPointerSign`(sign, *[, algebra, …])	Sign of a Semantic Pointer.
`Zero`(n_dimensions[, vocab, algebra, sidedness])	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 two-sided inversion operator. The left and right inverese can be obtained with the linv and rinv 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: AbstractAlgebra

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: SemanticPointerSign

abs()[source]¶

Return the absolute Semantic Pointer.

See AbstractAlgebra.abs for details on absolute Semantic Pointers.

copy()[source]¶: Return another semantic pointer with the same data.

length()[source]¶: Return the L2 norm of the vector.

__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: SemanticPointer

__invert__()[source]¶: Return a reorganized SemanticPointer that acts as a two-sided inverse for binding.

See also

linv, rinv

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

See also

__invert__, rinv

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

See also

__invert__, linv

bind(other)[source]¶: Return the binding of two SemanticPointers.

rbind(other)[source]¶: Return the binding of two SemanticPointers.

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).

dot(other)[source]¶: Return the dot product of the two vectors.

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.

distance(other)[source]¶

Return a distance measure between the vectors.

This is 1-cos(angle), so that it is 0 when they are identical, and the distance gets larger as the vectors are farther apart.

mse(other)[source]¶: Return the mean-squared-error between two vectors.

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: AbstractSign

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

is_positive()[source]¶: Return whether the sign is positive.

is_negative()[source]¶: Return whether the sign is negative.

is_zero()[source]¶: Return whether the sign neither positive nor negative (i.e. zero), but definite.

is_indefinite()[source]¶: Return whether the sign is neither positive nor negative nor zero.

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

to_semantic_pointer()[source]¶

Return the Semantic Pointer corresponding to the represented sign.

Returns: Semantic Pointer corresponding to the represented sign.
Return type: SemanticPointer

class nengo_spa.semantic_pointer.Identity(n_dimensions, vocab=None, algebra=None, *, sidedness=<ElementSidedness.TWO_SIDED: 'two-sided'>)[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: 'two-sided'>)[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: 'two-sided'>)[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 real-valued 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: 'two-sided'>)[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.