Information processing system

• US 3,950,733 A
• Filed: 06/06/1974
• Issued: 04/13/1976
• Est. Priority Date: 06/06/1974
• Status: Expired due to Term

• Current Assignee: Nestor, Inc.
• Original Assignee: Nestor Associates
• Inventors: Cooper, Leon N., Elbaum, Charles
• Primary Examiner(s): Dildine, Jr., R. STephen
• Application Number:
  US05/477,080
• Time in Patent Office: 677 Days
• Field of Search: 235/150, 235/150.1, 307/201, 340/146.3 T, 340/172.5, 445/1
• US Class Current: 706/26
• CPC Class Codes: G06F 18/213 Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
• CPC Class Codes: G06F 7/023 adaptive, e.g. self learning
• CPC Class Codes: G06N 3/065 Analogue means
• CPC Class Codes: G06N 3/091 Active learning

Abstract

An adaptive information processing system includes a module, called a Nestor module, having a plurality (N) of input terminals 1, 2 . . . , j . . . , N, adapted to receive N input signals s₁, s₂ . . . , s_j . . . , S_N, respectively, and a plurality (n) of output terminals 1, 2 . . . , i . . . , n, adapted to present n output responses r₁, r₂ . . . , r_i . . . , r_n, respectively. A plurality of junction elements, called mnemonders, couple various ones (or a multiplicity) of the input terminals with various ones (or a multiplicity) of the output terminals. These mnemonders provide a transfer of information from an input terminal j to an output terminal i in dependence upon the signal s_j appearing at the input terminal j and upon the mnemonder transfer function A_ij. Means are provided for modifying the transfer function A_ij of the mnemonders in dependence upon the product of at least one of the input signals and one of the output responses of the Nestor module. In a preferred embodiment of the invention, the modification to the transfer function of each mnemonder takes the form: ##EQU1## WHERE η IS A CONSTANT OF PROPORTIONALITY.

Claims

1. An information processing module comprising, in combination:

a. a plurality (N) of input terminals 1, 2 . . . , j . . . , N adapted to receive N input signals s₁, s₂ . . . , s_j . . . , s_N, respectively;

b. a plurality (n) of output terminals 1, 2 . . . , i . . . , n adapted to present n output responses r₁, r₂ . . . , r_i . . . , r_n, respectively;

c. a plurality of junction elements, called mnemonders, each mnemonder coupling one of said input terminals (input j) with one of said output terminals (output i) and providing a transfer of information from input j to output i in dependence upon the signal s_j appearing at the input j and upon the mnemonder transfer function A_ij ; and

d. means for modifying the transfer function A_ij of at least one of said mnemonders, when in a learning mode, in dependence upon the product of at least one of said input signals and one of said output responses;

whereby modifications to the transfer functions of the mnemonders, when in a learning mode, take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.1, s.sub.2 . . . , s.sub.j . . . , s.sub.N ;

r.sub.1, r.sub.2 . . . , r.sub.i . . . , r.sub.n).

2. The information processing module defined in claim 1, wherein the number of output terminals equals the number of input terminals (n = N).

3. The information processing module defined in claim 1, wherein the number of output terminals is less than the number of input terminals (n <

N).

4. The information processing module defined in claim 1, wherein the number of output terminals is greater than the number of input terminals (n >

N).

5. The information processing module defined in claim 1, wherein at least one mnemonder is coupled to each one of said input terminals.

6. The information processing module defined in claim 1, wherein each one of said output terminals is coupled to at least one mnemonder.

7. The information processing module defined in claim 1, wherein at least one mnemonder is coupled to each input terminal and wherein each output terminal is coupled to at least one mnemonder.

8. The information processing module defined in claim 1, wherein each one of said input terminals is coupled to at least one of said output terminals through a mnemonder.

9. The information processing module defined in claim 1, wherein each one of said input terminals is coupled to each one of said output terminals through a mnemonder.

10. The information processing module defined in claim 1, wherein the output s_j '"'"' of each mnemonder equals the product of its transfer function A_ij and the signal s_j applied at its input (s_j '"'"' = A_ij s_j).

11. The information processing module defined in claim 1, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each of said mnemonders.

12. The information processing module defined in claim 1, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of at least one of said mnemonders in dependence upon the input signal s_j applied thereto and the output response r_i at the output terminal to which the mnemonder is coupled;

whereby the modifications to the transfer function of at least one of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.j, r.sub.i).

13. The information processing module defined in claim 12, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each one of said mnemonders in dependence upon the input signal s_j applied thereto and the output response r_i at the output terminal to which the mnemonder is coupled;

whereby the modifications to the transfer function of each of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.j, r.sub.i).

14. The information processing module defined in claim 12, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of at least one of said mnemonders in proportion to the product of the input signal s_j applied thereto and the output response r_i at the output terminal to which the mnemonder is coupled;

whereby the modifications to the transfer function of at least one of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = η

s.sub.j r.sub.i,

where η

is the constant of proportionality.

15. The information processing module defined in claim 14, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each one of said mnemonders in proportion to the product of the input signal s_j applied thereto and the output response r_i at the output terminal to which the mnemonder is coupled;

whereby the modifications to the transfer function of each of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = η

s.sub.j r.sub.i ,

where η

is the constant of proportionality.

16. The information processing module defined in claim 1, further comprising logic element means, connected between each output terminal and the mnemonders coupled thereto, for receiving mnemonder outputs s_j '"'"' and producing an output response r_i in dependence upon said mnemonder outputs.

17. The information processing module defined in claim 16, wherein each of said logic element means produces said output response r_i in proportion to the sum of the mnemonder outputs s_j '"'"' applied thereto:

whereby said output response r_i takes the form;

##EQU34##

18. The information processing module defined in claim 1, further comprising:

a plurality (n) of threshold means T₁, T₂ . . . , T_i . . . , T_n, each connected to one of said output terminals, for producing an output signal if the output response r_i applied thereto is greater than a threshold level θ

_i (r_i >

θ

_i or |r_i | >

θ

_i).

19. The information processing module defined in claim 18, further comprising:

signal suppression means, connected to the outputs of each of said threshold means, for suppressing all of the output responses r₁, r₂ . . . , r_n except that response r_i applied as an input to the threshold means T_i which is producing an output signal.

20. The information processing module defined in claim 1, further comprising:

source means for selectively applying a specific desired output response r_iA to at least one of said output terminals;

whereby said information processing module may be caused to provide a "correct" output response r.sup.ω

during its operation.

21. An information processing system comprising, in combination:

a. at least one information processing module as defined in claim 1; and

b. means for adjusting the transfer function A_ij of each mnemonder of said module to a predetermined desired value,

whereby the system may be trained in a single operation.

22. An information processing system comprising, in combination:

a. at least one information processing module as defined in claim 1; and

b. means for selectively interrupting the operation of said modifying means of said module so that no modifications are made to the transfer function A_ij of the mnemonders (ε

A_ij =

     0),

whereby the system may be operated as a pure memory.

23. An information processing system comprising, in combination:

a. at least one information processing module as defined in claim 1;

b. buffer storage means for storing the transfer function A_ij of each mnemonder of said module; and

c. means for selectively transferring the transfer function A_ij of each mnemonder to said buffer storage means,

whereby the transfer functions may be preserved for later use after a period of training of said module.

24. An information processing system comprising, in combination:

a. at least one information processing module as defined in claim 1;

b. buffer storage means for storing a plurality of transfer functions A_ij ; and

c. means for selectively transferring a transfer function A_ij to at least one of said mnemonders of said module,

whereby said module can be trained in a single operation.

25. An information processing system as defined in claim 24, wherein said transferring means includes means for selectively transferring the transfer function A_ij of each mnemonder to said buffer storage means.

26. An information processing system comprising in combination:

a. a plurality of information processing modules as defined in claim 1;

b. means connecting the output terminals of at least one of said modules to the input terminals of at least one other of said modules,

whereby at least two modules are connected in series.

27. The information processing system defined in claim 26, wherein the connecting means (b) includes means for connecting the output terminals of at least two of said modules to the input terminals of one other module,

whereby at least two modules are connected in series to a third.

28. The information processing system defined in claim 26, wherein the connecting means (b) includes means for connecting the output terminals of one of said modules to the input terminals of at least two other modules,

whereby one module is connected in series to at least two other modules.

29. The information processing system defined in claim 26, wherein the total number of output terminals of said at least one module is greater than the total number of input terminals of said at least one other module.

30. The information processing system defined in claim 26, wherein the total number of output terminals of said at least one module is equal to the total number of input terminals of said at least one other module.

31. The information processing system defined in claim 26, wherein the total number of output terminals of said at least one module is less than the total number of input terminals of said at least one other module.

32. An information processing system comprising, in combination:

a. a plurality of information processing modules as defined in claim 1;

b. means for connecting the output terminals of one of said modules to the input terminals of another,

whereby at least two modules are connected in series.

33. The information processing system defined in claim 32, wherein said output terminals of one of said modules are connected to the input terminals of another in a random fashion.

34. The information processing system defined in claim 32, wherein the output terminals of one of said modules are connected to the input terminals of another in an ordered fashion,

whereby each one of the output terminals of said one module is connected to one of the input terminals of said other module.

35. An information processing system comprising, in combination:

a. a plurality of information processing modules as defined in claim 1;

b. means for connecting the output terminals of one of said modules to the output terminals of another,

whereby at least two modules are connected in parallel.

36. An information processing system comprising, in combination:

a. a plurality of information processing modules as defined in claim 1;

b. means for connecting the input terminals of one of said modules to the input terminals of another,

whereby at least two modules are connected in parallel.

37. The information processing module defined in claim 1, further comprising:

source means for selectively applying a specific desired output response r_iA to each one of said output terminals;

whereby said information processing module may be caused to provide a "correct" output response r.sup.ω

during its operation.

38. The information processing module defined in claim 1, wherein said modifying means includes means for reducing the value of the transfer function A_ij of at least one of said mnemonders with a decay at a predetermined rate.

39. The information processing module defined in claim 38, wherein said rate is constant, thereby to provide a uniform decay.

40. The information processing module defined in claim 1, wherein said modifying means includes means for reducing the value of the transfer function A_ij of each one of said mnemonders with a decay at a predetermined rate.

41. The information processing module defined in claim 40, wherein said rate is constant, thereby to provide a uniform decay.

42. The information processing module defined in claim 1, wherein the input signals s₁, s₂ . . . , s_j . . . , s_N and the output responses r₁, r₂ . . . , r_i . . . , r_n are represented by voltage levels.

43. The information processing module defined in claim 42, wherein each of said mnemonders includes a gain controlled amplifier, the transfer function A_ij of a mnemonder being represented by the gain of the mnemonder amplifier.

44. The information processing module defined in claim 1, wherein each mnemonder includes means for storing its transfer function A_ij.

45. The information processing module defined in claim 44, wherein said storage means comprises a device for storing an electrical charge.

46. The information processing module defined in claim 45, wherein said device is a capacitor.

47. The information processing module defined in claim 44, wherein said modifying means includes means for adding said increments ε

A_ij to the stored transfer function A_ij of a mnemonder.

48. The information processing module defined in claim 47, wherein electrical charge stored in said storage means of the ij'"'"'th mnemonder is Q_ij ;

wherein in each of said increments ε

A_ij is proportional to a respective increment ε

Q_ij ;

and wherein said means for adding increments ε

A_ij to the stored transfer function comprises, in combination;

a. means for producing a first pulse having an amplitude proportional to the input signal s_j and having a width t_i proportional to the absolute value of the output response r_i ; and

b. means, connected to said pulse producing means, for applying a second pulse to said device for storing an electrical charge, the pulse height and pulse width of said second pulse being proportional to the pulse height and pulse width of said first pulse and the polarity of said second pulse being equal to r_i /|r_i |.

49. An information processing element comprising, in combination:

a. a plurality (N) of input terminals 1, 2 . . . , j . . . , N adapted to receive N input signals s₁, s₂ . . . , s_j . . . , s_N, respectively;

b. an output terminal i adapted to present an output response r_i ;

c. a plurality (N) of junction elements, called mnemonders, each mnemonder coupling one of said input terminals (input j) to said output terminal (output i) and providing a transfer of information from input j to output i in dependence upon the signal s_j appearing at the input j and upon the mnemonder transfer function A_ij ; and

d. means for modifying the transfer function A_ij of at least one of said mnemonders, when in a learning mode, in dependence upon the product of at least one of said input signals and said output response;

whereby the modifications to the transfer function of the mnemonders, when in a learning mode, take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.1, s.sub.2 . . . , s.sub.j . . . , s.sub.N ;

r.sub.i).

50. The information processing element defined in claim 49, wherein said modifying means includes means for reducing the value of the transfer function A_ij of each one of said mnemonders with a decay at a predetermined rate.

51. The information processing element defined in claim 50, wherein said rate is constant, thereby to provide a uniform decay.

52. The information processing element defined in claim 49, wherein the output s_j '"'"' of each mnemonder equals the product of its transfer function A_ij and the signal s_j applied at its input (s_j '"'"' = A_ij s_j).

53. The information processing element defined in claim 49, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each of said mnemonders.

54. The information processing element defined in claim 49, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of at least one of said mnemonders in dependence upon the input signal s_j applied thereto and the output response r_i at the output terminal;

whereby the modifications to the transfer function of at least one of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.j, r.sub.i).

55. The information processing element defined in claim 54, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each one of said mnemonders in dependence upon the input signal s_j applied thereto and the output response r_i at the output terminal;

whereby the modifications to the transfer function of each of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = f (s.sub.j, r.sub.i).

56. The information processing element defined in claim 54, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of at least one of said mnemonders in proportion to the product of the input signal s_j applied thereto and the output response r_i at the output terminal;

whereby the modifications to the transfer function of at least one of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = η

s.sub.j r.sub.i ,

where η

is the constant of proportionality.

57. The information processing element defined in claim 56, wherein said transfer function modifying means includes means for modifying the transfer function A_ij of each one of said mnemonders in proportion to the product of the input signal s_j applied thereto and the output response r_i at the output terminal;

whereby the modifications to the transfer function of each of the mnemonders take the form;

space="preserve" listing-type="equation">ε

A.sub.ij = η

s.sub.j r.sub.i ,

where η

is the constant of proportionality.

58. The information processing element defined in claim 49, further comprising logic element means, connected between said output terminal and the mnemonders coupled thereto, for receiving mnemonder outputs s_j '"'"' and producing an output response r_i in dependence upon said mnemonder outputs.

59. The information processing element defined in claim 58, wherein said logic element means produces said output response r_i in proportion to the sum of the mnemonder outputs s_j '"'"' applied thereto;

whereby said output response r_i takes the form;

##EQU35##

60. The information processing element defined in claim 49, further comprising:

a threshold means T_i, connected to said output terminal, for producing an output signal if the output response r_i applied thereto is greater than a threshold level θ

_i (r_i >

θ

_i or |r_i | >

θ

_i).

61. The information processing element defined in claim 49, further comprising:

source means for selectively applying a specific desired output response r_iA to said output terminal;

whereby said information processing module may be caused to provide a "correct" output response r.sup.ω

during its operation.

62. The information processing element defined in claim 49, wherein said modifying means includes means for reducing the value of the transfer function A_ij of at least one of said mnemonders with a decay at a predetermined rate.

63. The information processing element defined in claim 62, wherein said rate is constant, thereby to provide a uniform decay.

64. The information processing element defined in claim 49, wherein the signals s₁, s₂ . . . , s_j . . . , s_N and r_i are represented by voltage levels.

65. The information processing element defined in claim 64, wherein each of said mnemonders includes a gain controlled amplifier, the transfer function A_ij of a mnemonder being represented by the gain of the mnemonder amplifier.

66. The information processing element defined in claim 49, wherein each mnemonder includes means for storing its transfer function A_ij.

67. The information processing element defined in claim 66, wherein said storage means comprises a device for storing an electrical charge.

68. The information processing element defined in claim 67, wherein said device is a capacitor.

69. The information processing element defined in claim 66, wherein said modifying means includes means for adding said increments ε

A_ij to the stored transfer function A_ij of a mnemonder.

70. The information processing element defined in claim 69, wherein electrical charge stored in said storage means of the ij'"'"'th mnemonder is Q_ij ;

wherein in each of said increments ε

A_ij is proportional to a respective increment ε

Q_ij ;

and wherein said means for adding increments ε

A_ij to the stored transfer function comprises, in combination;

a. means for producing a first pulse having an amplitude proportional to the input signal s_j and having a width t_i proportional to the absolute value of the output response r_i ; and

b. means, connected to said pulse producing means, for applying a second pulse to said device for storing an electrical charge, the pulse height and pulse width of said second pulse being proportional to the pulse height and pulse width of said first pulse and the polarity of said second pulse being equal to r_i /|r_i |.

71. A process of using an information processing module which comprises, in combination:

a. a plurality (N) of input terminals 1, 2 . . . , j . . . , N adapted to receive N input signals s₁, s₂ . . . , s_j . . . , s_N, respectively;

b. a plurality (n) of output terminals 1, 2 . . . , i . . . , n adapted to present n output responses r₁, r₂ . . . , r_i . . . , r_n, respectively;

c. a plurality of junction elements, each coupling one of said input terminals with one of said output terminals and providing a transfer of information from input j to output i in dependence upon the signal s_j appearing at the input j and upon the junction element transfer function A_ij, said junction elements coupling said input and output terminals in such a way that each output response r_i is a function of a plurality of transfer functions A_ij and a plurality of input signals s_j ;

said process comprising the steps of;

73. The process defined in claim 71, wherein the number of output terminals of the information processing module equals the number of input terminals thereof (n = N).

74. The process defined in claim 71, wherein the number of output terminals of the information processing module is less than the number of input terminals thereof (n <

N).

75. The process defined in claim 71, wherein the number of output terminals of the information processing module is greater than the number of input terminals thereof (n >

N).

76. The process defined in claim 71, wherein at least one junction element of the information processing module is coupled to each one of said input terminals thereof.

77. The process defined in claim 71, wherein each one of said output terminals of the information processing module is coupled to at least one junction element thereof.

78. The process defined in claim 71, wherein at least one junction element of the information processing module is coupled to each input terminal thereof and wherein each output terminal of the information processing module is coupled to at least one junction element thereof.

79. The process defined in claim 71, wherein each one of said input terminals of the information processing module is coupled to at least one of said output terminals thereof through a junction element.

80. The process defined in claim 71, wherein each one of said input terminals of the information processing module is coupled to each one of said output terminals thereof through a junction element.

81. The process defined in claim 71, wherein the output s_j '"'"' of each junction element of the information processing module equals the product of its transfer function A_ij and the signal s_j applied at its input (s_j '"'"' = A_ij s_j).

82. The process defined in claim 71, wherein the information processing module further comprises logic element means, connected between each output terminal and the junction elements coupled thereto, for receiving junction element outputs s_j '"'"' and producing an output response r_i in dependence upon said junction element outputs.

83. The process defined in claim 81, wherein each of said logic element means produces said output response r_i in proportion to the sum of the junction element outputs s_j '"'"' applied thereto;

whereby said output response r_i takes the form;

##EQU36##

85. The method defined in claim 83, wherein each intermediate signal s'"'"'_ij equals the product of the respective input signal s_j and the associated transfer function A_ij (s'"'"'_ij = A_ij s_j).

86. The method defined in claim 83, wherein said output response r_i is dependent upon all of said intermediate signals s'"'"'_ij.

87. The method defined in claim 83, wherein said output response r_i is proportional to the sum of a plurality of said intermediate signals s'"'"'_ij.

88. The method defined in claim 86, wherein said output response r_i is proportional to the sum of all of said intermediate signals s'"'"'_ij.

89. The method defined in claim 83, wherein step (d) includes the step of modifying each of said transfer functions A_ij in dependence upon the product of at least one of said input signals s_j and said output response r_i.

90. The method defined in claim 83, wherein step (d) includes the step of modifying at least one of said transfer functions A_ij in dependence upon the product of the input signal s_j, associated therewith, and said output response r_i.

91. The method defined in claim 89, wherein step (d) includes the step of modifying each of said transfer functions A_ij in dependence upon the product of the input signal s_j, associated therewith, and said output response r_i.

92. The method defined in claim 83, wherein step (d) includes the step of modifying at least one of said transfer functions A_ij in proportion to the product of the input signal s_j, associated therewith, and said output response r_i.

93. The method defined in claim 83, wherein step (d) includes the step of modifying each one of said transfer functions A_ij in proportion to the product of the input signal s_j, associated therewith, and the output response r_i.

94. The method defined in claim 83, wherein step (c) includes the step of producing a plurality of output responses r₁, r₂ . . . , r_i . . . , r_n, each response r_i of which is dependent upon at least one of said intermediate signals s'"'"'_ij, where j varies from 1 to N.

95. The method defined in claim 93, further comprising the step of setting at least one of said output responses r_i equal to a specific desired output response r_iA.

96. The method defined in claim 93, further comprising the step of setting each of said output responses r₁, r₂ . . . , r_i . . . , r_n equal, respectively, to a specific desired output response r_1A, r_2A . . . , r_iA . . . , r_nA.

97. The method defined in claim 93, further comprising the step of suppressing all the output responses r₁, r₂ . . . , r_n accept that response r_i which exceeds a prescribed threshold.

98. The method defined in claim 93, wherein step (c) includes the step of producing plurality of output responses r₁, r₂ . . . , r_i . . . , r_n, each response r_i of which is dependent upon all of said intermediate signals s'"'"'_ij, where j varies from 1 to N.

99. The method defined in claim 93, wherein step (c) includes the step of producing a plurality of output responses r₁, r₂ . . . , r_i . . . r_n, each response r_i of which is proportional to the sum of a plurality of said intermediate signals s'"'"'_ij, where j varies from 1 to N.

100. The method defined in claim 98, wherein step (c) includes the step of producing a plurality of output responses r₁, r₂ . . . , r_i . . . r_n, each response r_i of which is proportional to the sum of all of said intermediate signals s'"'"'_ij, where j varies from 1 to N.

101. The method defined in claim 83, further comprising the steps of:

1. receiving a second plurality of input signals s²₁, s²₂ . . . , s²_j . . . , s²_N ;

2. producing a second plurality of intermediate signals s'"'"'²_il, s'"'"'²_i2 . . . , s'"'"'²_ij . . . , s'"'"'²_iN, each s'"'"'²_ij of which is dependent upon a respective one of said second input signals s²_j and upon said transfer function A_ij that is associated with a respective one of the first intermediate signals s'"'"'_ij produced in step (b); and

3. producing a second output response r²_i which is dependent upon at least one of said second intermediate signals s'"'"'²_ij.

102. The method defined in claim 83, further comprising the step of storing each of said transfer functions A_ij in a storage device.

103. The method defined in claim 101, further comprising the step of transferring at least one of the stored transfer functions A_ij to another storage device.

104. The method defined in claim 101, further comprising the step of transferring each of the stored transfer functions A_ij to another storage device.

72. setting the transfer function A_ij of each junction element to a particular desired value representing stored information;

2. applying at least one of said input signals s₁, s₂ . . . , s_j . . . , s_N to the respective input terminal; and

3. receiving at least one of said output responses r₁, r₂ . . . , r_i . . . , r_n at the respective output terminal, whereby said module is utilized as a distributed memory.

84. A method of processing information comprising the steps of:

a. receiving a plurality of input signals s₁, s₂ . . . , s_j . . . , s_N ;

b. producing a plurality of intermediate signals s'"'"'_i1, s'"'"'_i2, . . . s'"'"'_ij . . . , s'"'"'_iN, each s'"'"'_ij of which is dependent upon a respective one of said input signals s_j and an associated transfer function A_ij ;

c. producing an output response r_i which is dependent upon at least one of said intermediate signals s'"'"'_ij ; and

d. modifying at least one of said transfer functions A_ij, when in a learning mode, in dependence upon the product of at least one of said input signals s_j and said output response r_i.