Vectors representing roles (e.g. subject or object) and fillers (e.g. John, Mary, loves, etc) can be bound together by a network that takes the tensor product of the two vectors. The vectors that result are then added together to produce complex representations.

Paul Smolensky (1988a).


Tensor Product Representations

In a tensor product representation, vectors representing roles (e.g. subject and verb) are combined with vectors representing role fillers (e.g. John and Mary) by taking their tensor product.

A tensor product is the vector that results from multiplying each element of one vector by each element of the other.

In a connectionist network, this can be implemented by feeding the role and filler vectors into separate input layers that connect at a set of multiplicative joints.

Once a filler has been combined with a role it may be combined with other role or filler products by vector addition (with corresponding elements are simply added together).