Operators

kongming provides two core algebraic operations on sparse binary hypervectors.

Bind

Binding ($\otimes$) combines two vectors into a result that is dissimilar to both inputs. It is the multiplicative operation in the VSA algebra.

Mathematically

$$A\otimes B=B\otimes A\text{(commutative)}$$

$$(A\otimes B)\otimes C=A\otimes (B\otimes C)\text{(associative)}$$

$$A\otimes I=A\text{(where I is an identity vector)}$$

$$A\otimes A^{-1}=I\text{(inverse)}$$

$$O(A\otimes B,A)\approx O(A\otimes B,B)\approx \text{noise}\text{(dissimilarity)}$$

Implementation: segment-wise offset addition modulo segment size.

Check out original paper for details.

Check out code snippets from the API reference.

Release

Occasionally we use release, as the equivalent of division.

$$A\oslash B=A\otimes B^{-1}$$

Note that release is anti-commutative: $$(A\oslash B{)}^{-1}=B\oslash A$$

Check out code snippets from the API reference.

Bundle

Bundling ($\oplus$) creates a superposition of vectors, which is similar to all inputs. It is the additive operation in the VSA algebra.

$$S=\sum _{i,\oplus }{A}_i$$

Mathematically

$$O(S,A_i)\gg O_{\text{random}}\text{(similarity to each member)}$$

$$O(S,X)\approx O_{\text{random}}\text{for }X\notin \{A_i\}\text{(dissimilarity to non-members)}$$

Check out original paper for details on bundle operator.

Check out code snippets from the API reference.