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.
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