Learning and auditory scene analysis in gradient frequency nonlinear oscillator networks
A method for learning connections between nonlinear oscillators in a neural network comprising the steps of providing a plurality of nonlinear oscillators, with each respective oscillator producing an oscillation distinct from the others in response to an input and detecting an input at an at least first oscillator of the plurality of nonlinear oscillators. Detecting an input at an at least a second oscillator of the plurality of nonlinear oscillators, comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time, and determining whether there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator. Changing at least one of the amplitude and phase of a connection between the at least first oscillator and the at least second least oscillator as a function coherency between the at least first oscillator and the oscillation of the at least second oscillator.
1. A method for learning connections between nonlinear oscillators in a neural network comprises the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to a common input;
detecting an input at an at least first oscillator of the plurality of nonlinear oscillators;
detecting an input at an at least a second oscillator of the plurality of the nonlinear oscillators;
comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time;
determining whether there is multi-frequency phase coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator; and
changing at least one of the amplitude and phase of a connection between the at least first oscillator and the at least second oscillator as a function of the multi-frequency phase coherency between the oscillation of the at least second oscillator and the at least first oscillator.
2. A method for learning connections between nonlinear oscillators in a neural network comprises the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to an input, the connection being represented as
c
.
ij
=
-
δ
ij
c
ij
+
k
ij
z
i
1
-
ɛ
z
i
·
z
_
j
1
-
ɛ
z
_
j
where c ij is the magnitude and phase of the connection between any two nonlinear oscillators, δ and k are parameters representing the speed of change of connection, z is the complex valued state variables of the two connected oscillators.
3. The method of claim 1 , further comprising the step of adjusting the phase of the connection to reflect the ongoing phase relationship between the at least first oscillator and the second oscillator when there is coherency between the oscillation of the at least first oscillator and the at least second oscillator.
4. The method of claim 1 , further comprising the step of:
decreasing the amplitude of connection between the at least first oscillator and the at least second oscillator when there is no coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator.
5. The method of claim 1 , further comprising the step of:
increasing the amplitude of connection between the at least first oscillator and the at least second oscillator when there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator.
6. A method for learning connections between nonlinear oscillators in a neural network comprises the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to a common input;
detecting an input at an at least first oscillator of the plurality of nonlinear oscillators;
detecting an input at an at least a second oscillator of the plurality of the nonlinear oscillators;
comparing the oscillation of the at least one oscillator to the oscillation of the at least second oscillator at a point in time;
determining whether there is multi-frequency phase coherency between the oscillation of the at least one oscillator and the oscillation of the at least second oscillator; and
decreasing the amplitude of a connection between the at least first oscillator and the at least second oscillator and the second oscillator when the oscillation of the at least one oscillator is substantially multi-frequency phase coherent with the oscillation of the at least second oscillator.
7. A method for learning connections between nonlinear oscillators in a neural network comprises the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to an input;
detecting an input at an at least first oscillator of the plurality of nonlinear oscillators;
detecting an input at an at least a second oscillator of the plurality of the nonlinear oscillators;
comparing the oscillation of the at least one oscillator to the oscillation of the at least second oscillator at a point in time;
determining whether there is coherency between the oscillation of the at least one oscillator and the oscillation of the at least second oscillator; and
decreasing the amplitude of a connection between the at least first oscillator and the at least second oscillator and the second oscillator when the oscillation of the at least one oscillator is substantially coherent with the oscillation of the at least second oscillator, the connection is being represented as
c
.
ij
=
-
δ
ij
c
ij
+
k
ij
z
i
1
-
ɛ
z
i
·
z
_
j
1
-
ɛ
z
_
j
where c ij is the magnitude and phase of the connection between any two nonlinear oscillators, δ and k are parameters representing the speed of change of connection, z is the complex valued state variables of the two connected oscillators.
8. The method of claim 6 , further comprising the step of adjusting the phase of the connection to reflect the ongoing phase relationship between the at least first oscillator and the second oscillator when there is coherency between the oscillation of the at least first oscillator and the at least second oscillator.
9. The method of claim 6 , further comprising the step of:
increasing the amplitude of connection between the at least first oscillator and the at least second oscillator when there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator.
10. A method for performing auditory scene analysis comprising the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to a common input;
detecting an input at an at least first oscillator of the plurality of nonlinear oscillators;
detecting an input at an at least a second oscillator of the plurality of the nonlinear oscillators;
comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time;
determining whether there is multi-frequency phase coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator; and
increasing the amplitude of a connection between the at least first oscillator and the at second least oscillator and the second oscillator when the oscillation of the at least first oscillator is multi-frequency phase coherent with the oscillation of the at least second oscillator.
11. A method for performing auditory scene analysis comprising the steps of:
providing a plurality of nonlinear oscillators, each respective oscillator producing an oscillation distinct from the others in response to an input;
detecting an input at an at least first oscillator of the plurality of nonlinear oscillators;
detecting an input at an at least a second oscillator of the plurality of the nonlinear oscillators;
comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time;
determining whether there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator; and
increasing the amplitude of a connection between the at least first oscillator and the at second least oscillator and the second oscillator when the oscillation of the at least first oscillator is coherent with the oscillation of the at least second oscillator, the connection being represented as
c
.
ij
=
-
δ
ij
c
ij
+
k
ij
z
i
1
-
ɛ
z
i
·
z
_
j
1
-
ɛ
z
_
j
where c ij is the magnitude and phase of the connection between any two nonlinear oscillators, δ and k are parameters representing the speed of change of connection, z is the complex valued state variables of the two connected oscillators.
12. The method of claim 10 , further comprising the step of adjusting the phase of the connection to reflect the ongoing phase relationship between the at least first oscillator and the second oscillator when there is coherency between the oscillation of the at least first oscillator and the at least second oscillator.
13. The method of claim 10 , further comprising the step of:
decreasing the amplitude of connection between the at least first oscillator and the at least second oscillator when there is no coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator.