Quantifying Machine Intelligence Mathematically
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In his document, Professor Peter Cochrane discusses the complexities of quantifying machine intelligence and highlights the differences between engineering and scientific approaches to problem-solving. He argues that the human brain's intricacies far exceed that of contemporary machines, challenging the notion of machine intelligence based on human standards. Ultimately, the document emphasizes the need for new frameworks to understand intelligence beyond traditional definitions and the limitations of current technological progress in comparison to biological evolution.
![Ic = I Ei - Eo I = I Ei ( si ) - Eo ( a[1 + m + p1 p2 + p2 m p1 ] si ) I
Where: s, p ,m, a are complex operators that cannot,
in general, be fully defined or detailed
E N G I N E E R I N G
LICENCE APPLIED
We simply neglect/ignore/hide the
time variability of all the functions
and mask it with a new formulation
Comparative
Intelligence](https://image.slidesharecdn.com/limwebsite-220405135004/85/Quantifying-Machine-Intelligence-Mathematically-45-320.jpg)
![Ic = I Ei - E[a.s ( 1 + m + p + mp ) ] I
E N G I N E E R I N G
LICENCE APPLIED
C o m b i n i n g s i m i l a r c o m p l e x
o p e r a t o r s f o r t h e e a s e o f
manipulation and explanation](https://image.slidesharecdn.com/limwebsite-220405135004/85/Quantifying-Machine-Intelligence-Mathematically-46-320.jpg)
![Finally, we have something meeting
all our practical bounds and limiters
that we can work with in practice
Ic = k log2 [1 + K.S.A (1 + P + M + P.M ) ]
System Constants
Ic ~ k log2 [1 + K.S.A (1 + P.M ) ]
For P.M >> (P + M)
C o n c e p t u a l
ENTROPIC LEAP
This resemble the Shannon-Hartley
theorem in Information Theory](https://image.slidesharecdn.com/limwebsite-220405135004/85/Quantifying-Machine-Intelligence-Mathematically-48-320.jpg)
![Ic ~ k log2[1 + K.A.S {𝜇 + P (Ms + Ml }]
The I/O elements A.S
shape our perception
of experiences at the
most fundamental and
Processing
and reflexes further
refine all perceived
activity & experience
(P + 𝜇)
Ml
Long Term Memory
provides context &
central awareness in
t i m e & s p a c e o n
relational axes of who,
what, when, where why
The Seat of Sentience ?
S O W H E R E I S
S E N T I E N C E ?
Ms
Short Term Memory
provides almost ‘unthinking’
functionality, largely free of
context, could be likened to an
auto-pilot!
For the human brain/body it appears to
be dominated by long term memory that
is distributed throughout the structure &
most influenced by sensory activity](https://image.slidesharecdn.com/limwebsite-220405135004/85/Quantifying-Machine-Intelligence-Mathematically-62-320.jpg)
Quantifying Machine Intelligence Mathematically
- 1. Quantifying Machine Intelligence Mathematically Professor Peter Cochrane OBE, DSc Sentient Systems Research London Institute for Mathematical Sciences 28 March 2022
- 2. S H O R T D e f i n i t i o n O F E N G I N E E R I N G “The appliance of Science” “Achieving more with £1 than a lay person might with £100”
- 3. D I F F E R E N C E W R I T L A R G E ( 1 ) “Whilst Scientists are free to declare that there is no solution to a problem…Engineers enjoy no such luxury - we always have to find a solution even if it is wrong” Guess Iterate Analogies Approximate Experiment Compute Consult Model Trial & Error
- 4. D I F F E R E N C E WRIT LARGE (2) “Problems are alway urgent with limited time and funding” “Problems come thick and fast - there is seldom time to ponder”
- 5. D I F F E R E N C E WRIT LARGE (3) “Engineers enjoy a supreme arrogance that says; we know that time travel and free energy are impossible, but everything else we can do given the time and resources”
- 6. AND SO IT STARTS WITH A CALL OUT O F T H E B L U E “We have 3 machines that cannot be exhaustively tested - can you come up with a means of quantifying their relative intelligences?”
- 7. STATE OF THE ART PUBLISHED Studies Incredibly broad (spanning machines and many biological lifeforms) Worryingly simple (at a macro level of memory and processing power) M .P Unbelievably complex (at a micro level of neurons, connectivity at scale) Modelling dendrites, neurons, synapse, axons +++
- 8. 26 Jun 2020 — Moravek and Kurzweil’s human brain estimates ~ 1016 Tlops = 10 PFlops UNCERTAINTY and CRUDITY Human Brain Equivalence Estimate
- 9. Human brains are clearly more complex than many realise - both analogue and digital, combining computing & memory within each neuron THE DAWN OF REALITY Human brain ~200 billion neurons linked by trillions of synapses containing ~1000 switches routing electrical impulse The ‘switching’ of neurons in influenced by > 50 different chemicals Some evidence of Quantum effects have also been reported recently
- 10. Way beyond anything conceived and built by man and in no way resembles an electronic computer - moreover, it is distributed across the entire body! HUMAN B R A I N Human brain ~1011 neurons linked by ~102 - 105 Human body ~ has yet to be charted!
- 11. ERROR BARS REPORTED on ABSOLUTE ESTIMATES Span Factor ~ 102 to 105 From an engineering perspective this renders all such results as useless unless significant improvements can be realised…which appears to be highly unlikely!
- 12. Problem AT Scale This may never fully understand This Dissection, Modelling, Experimentation So far we have a wiring map, + some models of individual functions, but full life cycle understanding remains a , mystery! ~10^11 Neurons ~300 Neurons
- 13. AXIOM This will never understand This Vis Thermodynamics This is increasingly becoming apparent, and we most likely need the help of Quantum Computers - but that is not going to happen for decades!
- 14. K i l l e r ProbleM We cannot describe, accurately quantify or measure intelligence in any form !
- 15. ABSOLUTE ESTIMATES OF ’N' INTELLIGENCES An incredibly broad span of machines and biological lifeforms From worryingly simple minded assumptions (at a macro level of memory and processing power alone) To unbelievably complex modelling (at a micro level of neurons, and large scale connectivity)
- 16. “An ability to learn from experience and to adapt/shape, selected environments” So, What about p h i l o s o p h Y ? All are of a general (descriptive) form: “A capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity critical thinking, and problem solving” + + + + From an engineering perspective all such descriptors are useless! “The faculty of rational behaviour” “The capacity to experience feelings and sensation” >1000 years of thinking & debating sees >150 intelligence definitions
- 17. Alfred Binet IQ Test 1909 ?? "Philosophers have given their moral approval to the deplorable verdict that affirms human intelligence is fixed, and cannot be augmented. We must protest against this brutal pessimism; we will try to demonstrate that it is founded on nothing" A test of a machine's ability to exhibit intelligent behaviour, equivalent to, or indistinguishable from, that of an actual human based on a natural language conversation. All participants are separated. If the judge cannot reliably tell the machine from the human, the machine is said to have passed. Alan Touring IQ Test 1950 ?? Z E R O W O R T H I R R E L E V A N T ?
- 18. M e a n i n g l e s s - I Q
- 19. T u r i n g T E S T “The good news Dave, is that the computer’s passed the Turing Test, but you have failed” GO Poker Chess Complexity Mamagrams Comp Games Protein Folding Medical Diagnosis Composing Music Drawing/Painting Circuit Design Data Analysis Transcription Chip Design ++++ Machine learning and rule creation have overtaken human programming for AI
- 20. H U M A N I S I N G I N T E R F A C E S Human-AI voice interactions now the norm and getting better by the day!
- 21. P H I L O S O P H E R S WERE VERY WRONG Their opinions did/do not stand up to scientific scrutiny big time!
- 22. C O M M O N E R R O R The attributes of physical dexterity, flexibility, mobility, communication, intelligence and evolved to meet the specific demands of given environments - many of which we (humans) cannot survive in! Our specific human capabilities and attributes were tuned by evolution to meet the physical opportunities and limitations of surface living on planet earth - not in water, air or space! “Speciated superiority is a nonsense”
- 23. F r o m N a r r o w T O G e n e r a l A I O NTO S E NT I E N CE C o m p u t i n g / I T p r o g r e s s i o n : t a s k s p e c i f i c t o g e n e r a l p u r p o s e - P C ! “ T h e s i n g l e b i g g e s t m i s t a k e t h e A I c o m m u n i t y h a v e m a d e i s t o a s s u m e h u m a n s a s s o m e g o l d s t a n d a r d r e f e r e n c e o f a b i l i t y a n d / o r p e r f o r m a n c e f u n c t i o n ” “ B u i l d i n g a n a r t i f i c i a l h u m a n b r a i n i s a n i n t e r e s t i n g t a r g e t , b u t c r e a t i n g n e w i n t e l l i g e n c e s i s a f a r m o r e i m p o r t a n t / u r g e n t o n e ”
- 24. All biological brains evolve slowly are now more or less in stasis - in comparison our technology is advancing exponentially - so equivalence is not a question of IF, but WHEN ? W H A T W E D o K N O W -100M -1M 1940 1990 2040 -103 -106 -109 -1012 -1015 -1018 FLOPS Biological intelligence has now ‘flat-lined’ Tech induced intelligence has only recently reached a critical growth stage and is exponential
- 25. “As a species our dependence on AI is now total - and societies can no longer function without this core technology” W H A T W E D o K N O W
- 26. Transformation OF THE C o m p l e x to S i m p l e ( R ) “Estimating the comparative intelligences of similar ‘animals’ might just be a lot easier, far more accurate, and far more useful given the stated problem set !” Note: For the same starting conditions (biology or technology) the error bars are generally negated, or greatly reduced for dissimilar entities for a given ratio calculation! Concatenation to Division of Error Bars!
- 27. A R R O G A N C E I S N O T UNIQUE TO ENGINEERS Samuel Johnson 1709 -1784 English critic, biographer, essayist, poet, and lexicographer, compiled/published the first English Dictionary SO, I started by ‘doing a Dr Johnson’ and defined intelligence! “Intelligence is the way I define it and not what others consider it to be” My misquote!
- 28. A L L P h y s i c a l & M e ta p h y s i c a l E X P E R I E N C E S Life introduces physical order into a system Intelligence transforms information in systems Both introduce Positive Entropy into systems Ergo; Life and Intelligence are strongly related
- 29. H Y P O T H E S I S C O N C AT E N AT E D Life => an emergent property of Complexity Intelligence => an emergent property of Life Sentience => an emergent property of Intelligence Complexity => an emergent property of Clustering in Chaos Complexity & Chaos => the ground state of our non-linear universe
- 30. H Y P O T H E S I S C O N C AT E N AT E D This is suggested, and increasingly, supported by a growing body of evidence Life => an emergent property of Complexity Intelligence => an emergent property of Life Sentience => an emergent property of Intelligence Complexity => an emergent property of Clustering in Chaos Complexity & Chaos => the ground state of our non-linear universe
- 31. Nature v Man/Machine Mother Nature: Chance action - no intelligence required! Mankind: Purposeful intelligence applied! Machine: Mankind /AI application of intelligence and mechanisms!
- 32. C o n c i s e d e f i n i t i o n Intelligence = Directed (or Forced) System Entropy I later realised Efficacy to be related to some IQ measure, whilst at the same time recognising that IQ is actually worthless as a measure :-(
- 33. A P O I N T O F C L A R I T Y Intelligence = I = IEi - EoI As intelligences can both increase or decrease the system Entropy; we redefine in terms of the Modular value… At this point we had something that might just work! NOTE: Entropy E = The information required to exactly define the state of the system
- 34. A P r o c e s s i o n o f o r g a n i c a n a l o g u e s n o w f o l l o w e d i n o r d e r o f i n c r e a s i n g c o m p l e x i t y …
- 35. Actuator A System Environs Sensor S T h e s i m p l e s T S ta r t i n g P o i n t A single and simple biological cell or slime mould A thermostat or light sensitive switch No signal/state processing or memory
- 36. C O U N T E r C A N D I T I O N No signal/state processing life form with hunting and complex problem solving capabilities - simple elements combining to create complex/intelligent organisms
- 37. Actuator A System Environs Sensor S A D D I T I O N O F M E M O R Y Memory M Venus Fly Trap + many other carnivorous plants A programmable thermostat It is not exactly clear if any signal processing is necessary as a discreet function but this ‘hic-up’ conveniently turns out to be unimportant !
- 38. Processor P1 Memory M Processor P2 System Environs Sensor S Actuator A Many species of very simple insects Artificial Ant - a colony of which is capable of solving the Travelling Salesman Problem PROCESSING & M E M O R Y In Nature processing and memory are combined in the synapses - only We make them discrete in our Silicon world
- 39. I M P O R T A N T R E VE L AT I O N Long term comatosed hospital patients appear brain dead due to a lack of I/O - ie Sensors and Actuators Clinically Dead - No eye movement - No reflex action - No bodily responses
- 40. I M P O R T A N T C O N D I T I O N A L S These are really helpful/vital in setting the bounds on the form of our final solution and our analysis direction Intelligence = 0 Iff P + M S + A = 0 Intelligence ≠ 0 If = 0 Without any I/O - Sensory/Actuator faculty no intelligence is evident Without any Processing or Memory intelligence is still possible
- 41. System Environs Memory ShortTerm Processor 1 Actuators Sensors Memory LongTerm Processor 2 scope for ever more complexity
- 42. Actuator A1 Actuator System Environs Memory Mlocal Actuator Memory Mshort Memory Mlong Processor P21 Processor P11 Sensors Easy to conjure unviable configs w r t a n a l y s i s
- 43. Actuator Processor P1 System Environs Memory M Processor P2 Sensors S cHoice of Viable S ta r t i n g P o i n t
- 44. Where: s, p ,m, a are complex temporal operators that cannot in general be fully defined or detailed Actuator A Processor P1 System Environs Processor P2 si i o p1 si (1 + m) p1 si Sensors S . Memory M A s s u m i n g A Nomenclature a(1 + m + p1 p2 + p2 m p1 ) si
- 45. Ic = I Ei - Eo I = I Ei ( si ) - Eo ( a[1 + m + p1 p2 + p2 m p1 ] si ) I Where: s, p ,m, a are complex operators that cannot, in general, be fully defined or detailed E N G I N E E R I N G LICENCE APPLIED We simply neglect/ignore/hide the time variability of all the functions and mask it with a new formulation Comparative Intelligence
- 46. Ic = I Ei - E[a.s ( 1 + m + p + mp ) ] I E N G I N E E R I N G LICENCE APPLIED C o m b i n i n g s i m i l a r c o m p l e x o p e r a t o r s f o r t h e e a s e o f manipulation and explanation
- 47. A P O I N T O F C L A R I T Y Intelligence = I = IEi - EoI As intelligences can both increase or decrease the system Entropy; we redefine in terms of the Modular value… At this point we had something that might just work! NOTE: Entropy E = The information required to exactly define the state of the system
- 48. Finally, we have something meeting all our practical bounds and limiters that we can work with in practice Ic = k log2 [1 + K.S.A (1 + P + M + P.M ) ] System Constants Ic ~ k log2 [1 + K.S.A (1 + P.M ) ] For P.M >> (P + M) C o n c e p t u a l ENTROPIC LEAP This resemble the Shannon-Hartley theorem in Information Theory
- 49. A P R I M A R Y IMPLICATION We are not racing toward a singularity as fast as people have previously projected Increasing S. P. M. A by a factor of 1000 would only see intelligence grow 10 fold due to the logarithmic nature of intelligence !
- 50. EXPONENTIAL V logarithmic Estimated Entropic Growth of AI capabilities
- 51. Computing Power 1960 70 80 90 2000 10 MIP/s A Wider Set of AI Estimates EXPONENTIAL V logarithmic 20 Intelligence Level
- 52. i n < 4 0 Y e a r s ~ 1,000,000,000 x chip capacity Processing Memory Sensors MacBook Pro >50Bn transistors iPhone = ~15Bn transistors IBM > 30Bn transistors/chip Feature size now ~ 5nm
- 53. i n < 4 0 Y e a r s ~ 1,000,000,000 x chip capacity Processing Memory Sensors Adapta bility Softwa re Compl exity Auton omy AI Processing Memory Sensors Manipulators Communication Networking MacBook Pro >50Bn transistors iPhone = ~15Bn transistors IBM > 30Bn transistors/chip Feature size now ~ 5nm
- 54. i n < 4 0 Y e a r s ~ 1,000,000,000 x chip capacity ~Dog Brain ~Mouse Brain ~Human Brain There is far more to intelligence than a very crude analogy to transistor - neuron equivalence and count, but this serves to indicate one reason why AI has been along time coming ! Processing Memory Sensors Adapta bility Softwa re Compl exity Auton omy AI Processing Memory Sensors Manipulators Communication Networking MacBook Pro >50Bn transistors iPhone = ~15Bn transistors IBM > 30Bn transistors/chip Feature size now ~ 5nm
- 55. G A M E C H A N G E R 2 0 1 2 Considered to be impossible by philosophers Medicine today I B M W a t s o n
- 56. G A M E C H A N G E R 2 0 1 4 Considered to be impossible by philosophers
- 57. HYPER-LEARNING Human ex perience 5 - 20k opera tion s in a lifetime Ne two rked AI - Robot >20k opera tion s per day
- 58. T hinkin g the right way People fear, & complain, overlook the big gains V i v e L a d i f f e r e n c e
- 59. Exemplar N e w C r e a t i v i t y
- 60. Exemplar N e w C r e a t i v i t y Criticism It is just copying and aping what human composers have done ! Retort 1 You mean exactly like human composers do ? Retort 2 AI has only just got into this game that humans have be at for well over 3M years
- 61. SPOT THE A I S y t e m
- 62. Ic ~ k log2[1 + K.A.S {𝜇 + P (Ms + Ml }] The I/O elements A.S shape our perception of experiences at the most fundamental and Processing and reflexes further refine all perceived activity & experience (P + 𝜇) Ml Long Term Memory provides context & central awareness in t i m e & s p a c e o n relational axes of who, what, when, where why The Seat of Sentience ? S O W H E R E I S S E N T I E N C E ? Ms Short Term Memory provides almost ‘unthinking’ functionality, largely free of context, could be likened to an auto-pilot! For the human brain/body it appears to be dominated by long term memory that is distributed throughout the structure & most influenced by sensory activity
- 63. S O W H E R E I S S E N T I E N C E ? F U R T H E R A N A L Y S I S The mathematical framework sufficient to tackle the stochastic complexity in the round may not yet exist/may be impossible…
- 64. T h a n k Y o u www.petercochrane.com