*Abstract*

The classical theory of computation rests on two fundamental assumptions: states are finite, and symbols
are atomic. Although automata built on these assumptions are extremely successful at solving many
computational tasks, the assumptions are highly implausible for human and animal cognition. First, the
signals used by the brain and other biological systems are mainly continuous, as evidenced by the
widespread use of differential equations in modeling these systems. For this reason, it makes little sense
to view mental states as countable, let alone finite. Second, there is very little reason to believe that
mental representations involve locally-stored atomic symbols. Consequently, classical pointer-based
discrete structures over such symbols, and algorithms operating on such structures, are not biologically
realistic. Experimental evidence instead favors a view in which the representations of entities, concepts,
relations, etc., are distributed over a large number of individually meaningless elements in a way that
supports similarity metrics and content-based retrieval.
Although both continuous-state computation and distributed representations have received a fair amount
of research attention, it is uncommon to see them discussed together in the unconventional-computation
literature (except, perhaps, as part of a general survey). In our presentation we argue that a biologically
plausible theory of computation will require both a continuous-state automaton component and a
distributed-memory component, much as a classical pushdown automaton uses both a finite-state
automaton and a pushdown stack. This view is supported by current research in clinical psychiatry
suggesting hemispheric differentiation for sequence processing and conceptual structure.
We show further that stack-like operations (PUSH and POP) over distributed representations can be
performed as simple vector addition and scalar multiplication, in a way reminiscent of foreground/background effects in visual processing. This possibility suggests that "higher" mental
functions like language and abstract thought might be exploiting existing neural circuitry already
available for other purposes. We conclude with a simple application example from language parsing, and
some speculation about possible new directions and guiding principles for biologically-inspired
unconventional computation.

Download the poster (large).