Suggested further readings#

We’ve come to the end of today’s session, and briefly covered what is a very well researched field. There is a lot of research into Vector Symbolic Algebras, including algebras that we did not present today, and it is a field that is starting to garner more interest.

To read more about how VSAs can be used to model brains, Chris’ book is a good place to start:

If you’d like more detail about fractional binding and how SSPs are related to Grid and Place Cells the following papers from the lab cover this topic:

Dumont, Nicole, and Chris Eliasmith. “Accurate representation for spatial cognition using grid cells.” CogSci. 2020.

To learn more about probability modelling and VSAs, check out this paper:

Furlong, P. Michael, and Chris Eliasmith. “Modelling neural probabilistic computation using vector symbolic architectures.” Cognitive Neurodynamics (2023): 1-24.

You can find more papers that show the link between the Neurosymbolic representations and models of the brain at our lab’s website.

If you’d like to read more about the Holographic Reduced Representations, the algebra we used in this work, a great place to start is Tony Plate’s book, which summarizes a considerable amout of Dr.Plate’s early research:

Plate, Tony A. Holographic Reduced Representation: Distributed representation for cognitive structures. Vol. 150. Stanford: CSLI Publications, 2003.

Another excellent introductory work is from Pentti Kanerva, which is where the “What is the dollar of Mexico?” example came from:

There is also a 2-part survey about VSAs more generally that is good for those new to the field: