Teaching Recurrent NN to be Dynamical Systems

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Presentation transcript:

Teaching Recurrent NN to be Dynamical Systems

Homogeneous Linear Systems (no inputs) Example:

Discrete time recurrent networks External Input Weights V Inputs u Outputs Recurrent Weights W f y1 y2 yn

Non-Linear sin wave generator example Teacher y1 y2 w12 w11 w22 b2 b1 w21 Limit cycle attractor

t(n) u(n) y1(n) y2(n) t(n - k) y1(n - k) y2(n - k) u(n - k) t(2) y1(2) u(2) y2(2) t(1) y1(1) u(1) y2(1) t(0) y1(0) y2(0)

Parenthesis balancing Turing Machine A before B A B OUT input input Parenthesis balancing Turing Machine …( ( ) ( ) ) )… FSM Tape

Recurrent NN model of active memory Load-in Info-in Info-in Load-in 1 2 n … Load-in Info-in Out

Testing Spiking Info-in load-in Hidden-1 Hidden-2 Hidden-3 Hidden-4 Out

{ { Color match to sample Recorded in IT Red Neuron 1 Green Red 19 1 Sample Delay Match