Operators

Kongming provides two core algebraic operations on hypervectors.

Bind

Binding ($\otimes$) combines two vectors into a result that is dissimilar to both inputs. It is the multiplicative operation in the HDC 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, which is derived from bind, as the equivalent of division, as opposed to multiplication.

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

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 — the result is similar to all inputs. It is the additive operation within VSA algebra.

Mathematically

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

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

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

Check out original paper for details on bundle operator.

Check out code snippets from the API reference.