We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, canemploy selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles)of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitudecodes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitudeinformation; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules anddirect the flow of computation (attention) to effect transitions betweentwo subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitude codes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules and direct the flow of computation (attention) to effect transitions between two subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

We have designed an architecture to span the gap between biophysics andcognitive science to address and explore issues of how a discrete symbol processing system can arise from the continuum, and how complex dynamics like oscillation and synchronization can then be employed in its operation and affect its learning. We show how a discrete-time recurrent "Elman" network architecture can be constructed from recurrently connected oscillatory associative memory modules described by continuous nonlinear ordinary differential equations.The modules can learn connection weights between themselves which will cause the system to evolve under a clocked "machine cycle" by a sequence of transitions of attractors within the modules, much as a digital computer evolves by transitions ofits binary flip-flop attractors. The architecture thus employs theprinciple of "computing with attractors" used by macroscopic systemsfor reliable computation in the presence of noise. We have specifically constructed a system which functions as a finite state automaton that recognizes or generates the infinite set of six symbol strings that are defined by a Reber grammar. It is a symbol processing system, but with analog input and oscillatory subsymbolic representations.The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter.This holds input and "context" modules clamped at their attractors while'hidden and output modules change state, then clamps hidden and output states while context modules are released to load those states as the new context for the next cycle of input. Superior noise immunity has been demonstrated for systems with dynamic attractors over systems with static attractors, and synchronization ("binding") between coupled oscillatory attractors in different modules has been shown to be important for effecting reliable transitions.

We have designed an architecture to span the gap between biophysics and cognitive science to address and explore issues of how a discrete symbol processing system can arise from the continuum, and how complex dynamics like oscillation and synchronization can then be employed in its operation and affect its learning. We show how a discrete-time recurrent "Elman" network architecture can be constructed from recurrently connected oscillatory associative memory modules described by continuous nonlinear ordinary differential equations. The modules can learn connection weights between themselves which will cause the system to evolve under a clocked "machine cycle" by a sequence of transitions of attractors within the modules, much as a digital computer evolves by transitions of its binary flip-flop attractors. The architecture thus employs the principle of "computing with attractors" used by macroscopic systems for reliable computation in the presence of noise. We have specifically constructed a system which functions as a finite state automaton that recognizes or generates the infinite set of six symbol strings that are defined by a Reber grammar. It is a symbol processing system, but with analog input and oscillatory subsymbolic representations. The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. This holds input and "context" modules clamped at their attractors while'hidden and output modules change state, then clamps hidden and output states while context modules are released to load those states as the new context for the next cycle of input. Superior noise immunity has been demonstrated for systems with dynamic attractors over systems with static attractors, and synchronization ("binding") between coupled oscillatory attractors in different modules has been shown to be important for effecting reliable transitions.