# A Dynamical Systems Reformulation of the Normalized Recurrence Algorithm

- Bo Pedersen,
*Rosetta Stone Labs*

## Abstract

The Normalized Recurrence Algorithm is a kind of localist
attractor network describing the temporal dynamics in continuous and recurrent
information integration emerging in experimental psychology data (The Continuity
of Mind, Michael Spivey, 2007). Despite the fact that this algorithm successfully
models time series data, it is somewhat unsatisfactory to deal with an algorithm
within a dynamical systems context and furthermore it is difficult to prove
conjectures, so we suggest this description: E(t+1)=E(t)+E(t)xC*E(t), where t is
time, E is all the different activity vectors pooled together and C is a
connectivity matrix (x and * is the matrix and hadamard product respectively).
The normalization is performed post hoc only, and with this reformulation we can
now prove the set size/convergence linearity hypothesis (p220), and reject the
indirect crosstalk hypothesis (p103), and more importantly open up this model to
comparisons within the field of dynamical systems where it truly belongs.

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