How to make computers work like the brain

Transcription

1 How to make computers work like the brain (without really solving the brain) Dileep George

2 a single special machine can be made to do the work of all. It could in fact be made to work as a model of any other machine. Alan Turing 1937

3 Mathematics Databases Communications Video Imaging Audio Gaming - etc. - a single special machine can be made to do the work of all. It could in fact be made to work as a model of any other machine. Alan Turing 1937

4 a single special machine can be made to do the work of all. It could in fact be made to work as a model of any other machine. Alan Turing 1937 Mathematics Databases Communications Video Imaging Audio Gaming - etc. - Visual perception Auditory perception Somatosensory perception Languages Adaptive behavior Planning, thinking,

5 Intelligence paradigms

6 Intelligence paradigms Early AI (1940s to 1970s)

7 Intelligence paradigms Early AI (1940s to 1970s) Program Intelligence

8 Intelligence paradigms Early AI (1940s to 1970s) Program Intelligence Ignore what the brain does

9 Intelligence paradigms Early AI (1940s to 1970s) Program Intelligence Ignore what the brain does Airplanes were not made by...

10 Intelligence paradigms Early AI (1940s to 1970s) Program Intelligence Ignore what the brain does Airplanes were not made by... No learning

11 Intelligence paradigms Early AI (1940s to 1970s) Program Intelligence Ignore what the brain does Airplanes were not made by... No learning Commonsense problem

12 Intelligence Paradigms

13 Intelligence Paradigms Neural Networks (1980s and 1990s)

14 Intelligence Paradigms Neural Networks (1980s and 1990s) Back-propagation algorithmf or multi-layer networks

15 Intelligence Paradigms Neural Networks (1980s and 1990s) Back-propagation algorithmf or multi-layer networks Universal learning machines..can fit any function

16 Intelligence Paradigms Neural Networks (1980s and 1990s) Back-propagation algorithmf or multi-layer networks Universal learning machines..can fit any function The problem of scale

17 Story of chess..

18 Sample complexity of learning Face Non-face 256^1024

19 Sample complexity of learning Face Non-face 256^1024 P(Face) ^1024

20 256^1024=

21 256^1024=

22 256^1024= Number of seconds in a human s life:

23 Origins of Language.. Ramachandran and Hubbard, 2001

24 Bouba Kiki

25

26 Laminar structure

27 Common cortical algorithm: Supporting evidence Seeing in the Sound Zone," by Michael Merzenich, Nature, Vol. 404, April 20, 2000, pp "Induction of visual orientation modules in auditory cortex," by Jitendra Sharma, Alessandra Angelucci and Mriganka Sur, Nature, Vol. 404, April 20, 2000, pp

28 sensory substitution

29 sensory substitution A sensorimotor account of vision and visual consciousness, Kevin O Regan and Alva Noe. Photograph courtesy: P Bach-y-Rita

30 Neocortex Assume that: Neocortex uses the same algorithm to learn different modalities Neocortex learns efficiently

31 The No Free Lunch Theorem

32 The No Free Lunch Theorem No learning algorithm has an inherent superiority over other learning algorithms for all problems. (Wolpert, 1995)

33 The No Free Lunch Theorem No learning algorithm has an inherent superiority over other learning algorithms for all problems. (Wolpert, 1995) An algorithm s superiority comes from the assumptions that it makes about the problem

34 Neocortex Assume that: Neocortex uses the same algorithm to learn different modalities Neocortex learns efficiently

35 Neocortex Assume that: Neocortex uses the same algorithm to learn different modalities Neocortex learns efficiently => Data from different modalities must have the same underlying statistical structure

36 The right question to ask.. Are there assumptions we can make about the world that are 1. General enough to be applied to be a large number of problems 2. Specific enough to make learning possible??

37 High-level properties of the neocortex Hierarchical organization Spatial and temporal Using time as a supervisor Ability to make predictions Sparse Distributed Representations Feed-forward and feedback connections Sensori-motor

38 Abstraction levels Consciousness Cognitive models Perception Connections High-level anatomical structure Micro-circuit structure Neuron models Dendrites Learning rules Synapses Ion channels Proteins Glia

39 Neocortex Source of assumptions and constraints World s Data (Visual/Auditory etc...) To find correspondence with Neocortex properties Computational Principles (Machine Learning/Graphical Models etc..) To understand why brain does what it does in that particular way

40 If you are not computationally grounded, looking into biology is like looking into a religious text. You will always find what you are looking for.

41 Temporal learning example Suppose A-C-D and B-C-E are frequent in the data A C D B C E

42 Temporal learning example Suppose A-C-D and B-C-E are frequent in the data A C D B C E First-order model A C D B E

43 Temporal Models t t t-2 t-1 t-1 N^2, but can initialize from data to create a sparse model Not a scalable way to build higher order models

44 Variable order sequences t A B C D t-1 (kn)^2

45 State-splitting model First order model A C D B E

46 State-splitting model First order model A C D B E Model with replicated A C D states B C E

47 State-splitting model First order model A C D B E Model with replicated A C D states B C E Model after further A C D learning B C E

48 State-splitting model Learn first order model Replicate potential higher-order states Learn temporal statistics on the new model

49 State-splitting model Learn first order model Replicate potential higher-order states Learn temporal statistics on the new model

50 Start with replicated states Should be online Should still be sparse and efficient

51 t t+1 Which cell in this column do we connect to?

52

53 Connection to HMM c1 c2 c3 c4 c5

54 HMM and Forward-Backward Forward-backward algorithm On the restricted HMM, works very well in finding the higher-order states Can be made online by making reducing the lookahead One step look-ahead works quite well Zero look-ahead (pure Hebbian learning) doesn t work well.

55 t t+1 t+2 Which cell in this column do we connect to?

56 Biological implication A B C Can A know whether B was successful in firing C? The answer is YES

57

58

59 The idea of replicated states for learning higher order Neocortex Source of assumptions and constraints HMM model. Why one-step look-ahead is required. Predicted a computational property of neurons Nature of higher-order sequences World s Data (Visual/Auditory etc...) To find correspondence with Neocortex properties Computational Principles (Machine Learning/Graphical Models etc..) To understand why brain does what it does in that particular way

60 Recipe for building brain-like computers Accept the broad biological constraints Hierarchy, time as supervisor, sparse distributed representations, sensori-motor interactions... Have a biological circuit model for the learned system Put in biological details you can computationally justify Get to the biological circuit model using the most expedient learning algorithm Need not be biological. In fact, being biological can be a disadvantage. Work on a real problem

61 On to the paper...

62

63 Can we come to a set of mathematical equations that model cortical function?

64 Can we come to a set of mathematical equations that model cortical function? Something like Maxwell s equations for electromagnetic waves

65 Can we come to a set of mathematical equations that model cortical function? Something like Maxwell s equations for electromagnetic waves Assigns functions/equations for laminar circuits

66 Can we come to a set of mathematical equations that model cortical function? Something like Maxwell s equations for electromagnetic waves Assigns functions/equations for laminar circuits

67 Hierarchical Temporal Memory Mathematical Expression of Theory +

68 Hierarchical Temporal Memory Mathematical Expression of Theory Biological Data Constraints on connectivity, placement +

69 Hierarchical Temporal Memory Mathematical Expression of Theory Biological Data Constraints on connectivity, placement + Laminar Cortical Circuit Model

70

71

72

73 Markov chains (sequences) Coincidence patterns

74 Largel Spatial Scales/ Slow temporal scales. Small Spatial Scales/ Fast temporal scales.

75 Largel Spatial Scales/ Slow temporal scales. Small Spatial Scales/ Fast temporal scales.

76

77 1. Mathematical expression of HTM inference

78 1. Mathematical expression of HTM inference 2. Abstract neural implementation of equations

79 1. Mathematical expression of HTM inference 2. Abstract neural implementation of equations 3. Map the abstract neural implementation to laminar circuits using biological data

80 1. Mathematical expression of HTM inference 2. Abstract neural implementation of equations 3. Map the abstract neural implementation to laminar circuits using biological data

81

82

83 Markov chains (sequences) Coincidence patterns

84 2 Calculate likelihood of Markov chains 3 Calculate belief of coincidence patterns 1 Calculate likelihood of coincidence 4 Calculate probability of Markov chains

85 (1) Coincidence likelihood (2) Markov chain likelihood (3) Coincidence Belief (4) Feedback messages

86 y t (i) =P ( e t c i (t)) M j=1 λ m j t (r m j i )

87 α t (c i,g r )=P ( e t c i (t)) c j (t 1) C k P (c i (t) c j (t 1),g r )α t 1 (c j,g r ) D D D D D D D

88 2 Calculate likelihood of Markov chains 3 Calculate belief of coincidence patterns 1 Calculate likelihood of coincidence 4 Calculate probability of Markov chains

89 2 3 D D D D D D D D D D D D D D 1 4 Belief

90 1. Mathematical expression of HTM inference 2. Abstract neural implementation of equations 3. Map the abstract neural implementation to laminar circuits using biological data

91

92 Alex M. Thomson and A. Peter Bannister. Interlaminar connections in the neocortex. Cerebral cortex (New York, N.Y. : 1991), 13(1):5 14, Bannister 2003

93 D D D D D D D D D D D D D D Belief

94 D D D D D D D D D D D D D D Belief

95

96 Why Layer 4? Thalamo-cortical inputs go to layer 4

97

98

99

100

101

102 I II/III IV V VI

103

104

105 Lee and Mumford, J.Opt. Soc. America. July 2003

106 (a) (b)

107

108

109

110

111

112

113 Thank You Papers, thesis etc.