A comparison of Vector Symbolic Architectures

Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their representational power and ability to deal with fuzziness and ambiguity. Over the past years, several VSA implementations have been proposed. The available implementations differ in the underlying vector space and the particular implementations of the required VSA operators - with important ramifications for the properties of these architectures. For example, not every VSA is equally well suited to address each task, including complete incompatibility. This paper provides an overview of eleven available VSA implementations and discusses their commonalities and differences in the underlying vector space, bundling, and binding/unbinding operations. We create a taxonomy of available binding/unbinding operations and show an important ramification for non self-inverse binding operations using an example from analogical reasoning. A main contribution is the experimental comparison of the available implementations in order to evaluate (1) the capacity of bundles, (2) the approximation quality of non-exact unbinding operations, (3) the influence of combining binding and bundling operations on the query answering performance, and (4) the performance on two example applications: visual place and language recognition. An overall good performance is shown by the HRR VSA in the frequency domain. However, its non-self-inverse binding mechanism can negatively influence its applicability, e.g. to analogical reasoning. We expect this systematization and comparison to be relevant for development and evaluation of new VSAs, but most importantly, to support the selection of an appropriate VSA for a particular task. The implementations are available in form of a MATLAB toolbox.