70 4 Brief Survey of Cognitive Architectures
application of supervised learning algorithms such as recurrent neural networks. These cluster- ing and prediction processes occur separately in each node, but the nodes are linked together via bidirectional dynamics: each node feeds input to its parents, and receives "advice" from its parents that is used to condition its probability calculations in a contextual way.
These processes are executed formally by the following basic belief update rule, which governs the learning process and is identical for every node in the architecture. The belief state is a probability mass function over the sequences of stimuli that the nodes learns to represent. Consequently, each node is allocated a predefined number of state variables each denoting a dynamic pattern, or sequence, that is autonomously learned. The DeSTIN update rule maps the current observation (o), belief state (b), and the belief state of a higher-layer node or context (c), to a new (updated) belief state (0’), such that
Pr(s’MN on bne) Pr(onbne)
b’ (s’) = Pr (s’|o, b,c) = ; (4.1)
alternatively expressed as
_ Pr(ols’, b, c) Pr (s'|6, c) Pr (6, c)
(8) = Pr (06, ce) Pr (6, c} (4.2)
Under the assumption that observations depend only on the true state, or Pr(ols’, b,c) = Pr(o|s’), we can further simplify the expression such that
__ Pr(o|s’) Pr (s’|b, c)
/ i = A, u (s) = Pe (43) where Pr (s‘|b,c) = >> Pr (s‘|s,c)b(s), yielding the belief update rule ses Pr (o|s’) $> Pr (s'|s, c) 6(s)
Pf oh ses 0) = Prop") Pre sco) Ad)
sles ses
where S denotes the sequence set (i.e. belief dimension) such that the denominator term is a normalization factor.
One interpretation of eq. (4.4) would be that the static pattern similarity metric, Pr (o|s’), is modulated by a construct that reflects the system dynamics, Pr (s’|s,c). As such, the belief state inherently captures both spatial and temporal information. In our implementation, the belief state of the parent node, c, is chosen using the selection rule
c= argmaxb,(s), 4.5 Op
where 6, is the belief distribution of the parent node.
A close look at eq. (4.4) reveals that there are two core constructs to be learned, Pr(o|s’) and Pr(s‘|s,c). In the current DeSTIN design, the former is learned via online clustering while the latter is learned based on experience by inductively learning a rule that predicts the next state s’ given the prior state s and c.
The overall result is a robust framework that autonomously (i.e. with no human engineered pre-processing of any type) learns to represent complex data patterns, and thus serves the
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