Tensor product representations
Tensor product representations have constituent structure but are distributed and context sensitive in a nonclassical way; thereby, avoiding the dilemma (see detailed text).
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).

Artificial Intelligence »Artificial Intelligence
Can computers think? [1] »Can computers think? [1]
Yes: connectionist networks can think [5a] »Yes: connectionist networks can think [5a]
The Connectionist Dilemma »The Connectionist Dilemma
Connectionist representations avoid the dilemma »Connectionist representations avoid the dilemma
Tensor product representations
Constituents lack causal powers »Constituents lack causal powers
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