Cognition, Information and Subjective Computation

Cognition, Information & Subjective Computation

Hector Zenil

[email protected]

Unit of Computational Medicine, KI

Invited TalkRepresentation of Reality: Humans, Animals and Machines @ AISB50

Study of Artificial Intelligence and Simulation of BehaviourGoldsmiths, University of London, 1-4 April, London, UK

Hector Zenil Cognition, Information & Subjective Computation 1 / 28

Introduction Outline

Outline

Intelligence, understanding and internal experience

The information network approach to consciousness

A measure of subjective computation and programmability

Clinical application and Information Biology


Intelligence vs. conscience tests A behavioural approach to machine intelligence

A behavioural approach to intelligence

The Turing test (TT) is a reformulation of a question of non-factual characterinto a measurable one: something is intelligent if it behaves in an intelligentfashion.

Figure : The classic Turing-test to decide intelligent behaviour



Turing test-like approaches are far from death

(Cronin, Krasnogor, et al, Nature Biotechnology 2006)(Maier et al., A Turing test for artificial expression data, Bioinformatics (2013) 29 (20):

2603-2609, 2013).

[Zenil in Computing Nature, & SAPERE Series, Springer (2013)]



intelligence , consciousness

Figure : Searle’s Chinese room argument (CRA): The person inside the roomunderstands nothing but replies in an “intelligent” fashion (meaning it would pass theTuring test under optimal conditions).



Passing the Turing test is trivially achievable (inprinciple)

By a CRA-type thought experiment!

Number of (comprehensible) sentences is finiteTime of conversations is finite

Write a lookup table with all possible conversations.

Passing the TT is trivially attainable in finite amount of time and space bybrute force: just a combinatorial problem.

Lookup tables run in O(1) time! (by exchange of time for space) but the size ofthe lookup table for a machine to pass the TT would grow exponentially forlinearly growing conversations.



Program efficiency and program size matters

Scott Aaronson rightly points out that, in light of the theoretical triviality ofpassing the Turing test, one has to ask about resources.

Personally, I find this response to Searle extremely interesting [his attack to rulebased systems] since if correct, it suggests that the distinction between polynomialand exponential complexity has metaphysical significance. According to thisresponse, an exponential-sized [computer program] lookup table that passed theTuring Test would not be sentient (or conscious, intelligent, self-aware, etc.), but apolynomially-bounded program with exactly the same input/output behavior wouldbe sentient. Furthermore, the latter program would be sentient because it waspolynomially-bounded.

–S Aaronson

(emphasis and brackets added)

[S. Aaronson, Why Philosophers Should Care About Computational Complexity, 2011.arXiv:1108.1791 [cs.CC]]



Constraints or metaphysics

Machine (or human) understanding for Searle cannot be achieved by lookup table bruteforce.

TT objections can be:

of metaphysical type or

adhere to Searle and introduce resource constraints or

some other option not covered here

Either:

the mind has some metaphysical properties that cannot be represented andreproduced by science, or

the TT can only make sense if resources are taken into account. That is, passingTT with certain amount of space and in certain amount of time, or

the question of machine intelligence is independent of the TT (and of computing)

understanding is a form of rule/data compression and decompression time (answerefficiency)? Searle is right in that the brain is unlikely to have such an enormouslookup table (although one cannot completely rule it out, i.e. the mind is like a Chineseroom!) Compression is comprehension [G. Chaitin].



Lookup tables, rules and computer programs

In summary:Searle’s CRA and soft AI seem to suggest that a program that does notgrow with the size of the input is not subject to CRA-type objections(perhaps because we don’t longer understand those programs? at thelowest level they are not different to pure rule-based).

The TT test, Searle’s CRA and Aaronson argument, seem to imply a rolefor program-size and efficiency in the concept of intelligence a la Searle(i.e. understanding, internal experience, consciousness!)

This is compatible with the fact that Searle does not oppose himself to theidea that human minds may be soft AI, he opposes lookup table type ofprograms epitomized by the CRA, but CRA is not an instance of allcomputer programs, hence Searle is not metaphysical (he agrees on this).

This is again deeply related to computation, more precisely questions ofcomputational and algorithmic (program-size) complexity!



Integrated Information TheoryThe phenomenology of internal experience, the unity and integration of thenotion of consciousness have been taken as axioms for a integrated informationtheory (Tononi).

The higher the φ, the more conscious the entity. Panpsychism can preventedby a threshold.

[From FQXi Tononi’s presentation]Hector Zenil Cognition, Information & Subjective Computation 10 / 28


Dreams, Zombies and Anesthesia

[From FQXi Tononi’s presentation]



A feedforward networkA feedforward network resembles a lookup table (modulo the encoding of theinterconnections)

Figure : Highly hierarchical, layers are disconnected beyond distance 1. φ = 0 network(no consciousness).

[From FQXi Tononi’s presentation]Hector Zenil Cognition, Information & Subjective Computation 12 / 28


What is Computation?

One of the most important contending theories deeply connects consciousnessto information theory.We keep connecting mind properties to computation:

Turing connected human intelligence to computationSearle indirectly connects understanding (and consciousness) to programcomplexity (soft AI).Tononi’s connects consciousness to computation and information

Can understanding computation shed light on intelligence and consciousness?

What is computation?

I aim at finding a (grading and weakly observer dependent) metric ofcomputation.



Cellular automata as case study

[Wolfram, (1994)]



Long run of rule 30

[Wolfram, (1994)]



Behavioural richness (sorted by K complexity)



Towards a metric based on uncompressibility

Which string looks more random?

(a) 1111111111111111111111111111111111111111(b) 0011010011010010110111010010100010111010(c) 0101010101010101010101010101010101010101

Definition

KU(s) = min{|p|,U(p) = s} (1)

CompressibilityA string with low Kolmogorov complexity is c-compressible if |p| + c = |s|. Astring is random if K(s) ≈ |s|. K takes advantage of any patterns and compressthe object.

[Kolmogorov (1965); Chaitin (1966)]Hector Zenil Cognition, Information & Subjective Computation 17 / 28


Rule 22 dual behaviour

[Zenil and Villarreal, Bifurcation and Chaos, (2013)]Hector Zenil Cognition, Information & Subjective Computation 18 / 28


Rule 22 dual behaviour detection

[Zenil and Villarreal, Bifurcation and Chaos, (2013)]Hector Zenil Cognition, Information & Subjective Computation 19 / 28


Measuring asymptotic qualitative behaviour

Compressed evolutions over time:

[Zenil, Complex Systems (2010)]Hector Zenil Cognition, Information & Subjective Computation 20 / 28


Capturing behaviour (sensitivity, variability andefficiency)

Histograms of asymptotic behaviour of compression ratios (space saving) ofECAs evolutions over time for different initial conditions (see rules 22, 30, 54):



A behavioural approach to computation

A Turing-test like test strategy to the question of life (instead of Turing’soriginal question of artificial intelligence):

[Zenil, Philosophy & Technology and SAPERE, (2013)]Hector Zenil Cognition, Information & Subjective Computation 22 / 28


Programmability measureLet the characteristic exponent ct

n be defined as the mean of the absolute values of thedifferences between the compressed lengths of the outputs of a system M running overthe initial segment of initial conditions ij with j = {1, . . . ,n} following a Gray-code, andrunning for t steps in intervals of n. Formally,

ctn =|C(Mt(i1)) − C(Mt(i2))| + . . . + |C(Mt(in−1)) − C(Mt(in))|

t(n − 1)(2)

Let C denote the transition coefficient defined as C(U) = f ′(Sc), the derivative of theline that fits the sequence Sc by finding the least-squares with Sc = S(cn

t ) for a chosensample frequency n and running time t. The value Ct

n(U) (simply C until the discussionof definitions in the next section), based on the phase transition coefficient, will be anindicator of the degree of programmability of a system U relative to its external stimuli(input). The larger the derivative, the greater the change.

[Zenil, Complex Systems (2011)]Hector Zenil Cognition, Information & Subjective Computation 23 / 28


Chalmer’s rock multirealizability objection tofunctionalism

Figure : Sieve-like behaviour of ECA R4 has a low Ctn value for any n and t (it doesn’t

react to external stimuli) hence behaviourally this is not a computer.

[Zenil, Philosophy & Technology, (2013)]Hector Zenil Cognition, Information & Subjective Computation 24 / 28


Turing universality

Figure : ECA R110 has large asymptotic coefficient Ctn value for large enough choices

of t and n, which is compatible with the fact that it is Turing universal (for particularsemi-periodic initial configurations).



A hierarchical view of computing byprogrammability

Programmability of physical and biological entities sorted by variabilityversus controllability:

The diagonal determines the degree of programmability (there is acorrespondence to intelligence).

[Zenil, Ball, Tegner, ECAL MIT Press Proceedings, (2013)]Hector Zenil Cognition, Information & Subjective Computation 26 / 28


Properties of CC is:

Similar to the Turing test in that it is behavioral in nature (Turing)Observer relative (Searle)Is a graded numerical metric of computation (as Tononi’s φ)Sensitive to resources complexity (Aaronson)

Strength sources:

uncomputability introduces inevitable subjectivity (what you see withthe resources you are given)links to Kolmogorov complexity, the theory of mathematical randomness,towards optimal pattern detection.

Possible caveats:

It is likely not a distance (no triangle inequality holds, not yet proven)A related, independent, idea to mine was recently pointed out to me: J. Hernandez-Orallo, andD.L. Dowe. Measuring Universal Intelligence: Towards an Anytime Intelligence Test ArtificialIntelligence, 2010.

[Zenil, Philosophy & Technology, Springer (2013)]Hector Zenil Cognition, Information & Subjective Computation 27 / 28


Algorithmic information theory in the clinic!



H. Zenil, Compression-based Investigation of the Dynamical Properties ofCellular Automata and Other Systems, Complex Systems, Vol. 19, No. 1, pages1-28, 2010.

H. Zenil, What is Nature-like Computation? A Behavioural Approach and aNotion of Programmability, Philosophy & Technology (special issue on Historyand Philosophy of Computing), 2013.

H. Zenil, On the Dynamic Qualitative Behavior of Universal ComputationComplex Systems, vol. 20, No. 3, pp. 265-278, 2012.

G. Terrazas, H. Zenil and N. Krasnogor, Exploring Programmable Self-Assemblyin Non DNA-based Computing, Natural Computing, vol 12(4): 499–515, 2013.DOI: 10.1007/s11047-013-9397-2.

H. Zenil and E. Villarreal-Zapata, Asymptotic Behaviour and Ratios of Complexityin Cellular Automata Rule Spaces, Journal of Bifurcation and Chaos (in press).

H. Zenil, G. Ball and J. Tegner, Testing Biological Models for Non-linearSensitivity with a Programmability Test. In P. Lio, O. Miglino, G. Nicosia, S. Nolfiand M. Pavone (eds), Advances in Artificial Intelligence, ECAL 2013, pp.1222-1223, MIT Press, 2013.

H. Zenil, A Turing Test-Inspired Approach to Natural Computation. In G.Primiero and L. De Mol (eds.), Turing in Context II (Brussels, 10-12 October 2012),



Historical and Contemporary Research in Logic, Computing Machinery andArtificial Intelligence, Proceedings published by the Royal Flemish Academy ofBelgium for Science and Arts, 2013.

A Behavioural Foundation for Natural Computing and a Programmability Test. InG. Dodig-Crnkovic and R. Giovagnoli (eds), Computing Nature: Turing CentenaryPerspective, SAPERE Series vol. 7, Springer, 2013.

H. Zenil, Turing Patterns with Turing Machines: Emergence and Low-levelStructure Formation, Natural Computing, 12(2): 291-303 (2013), 2013.

J.-P. Delahaye and H. Zenil, Numerical Evaluation of the Complexity of ShortStrings: A Glance Into the Innermost Structure of Algorithmic Randomness,Applied Mathematics and Computation 219, pp. 63-77, 2012.


Cognition, Information and Subjective Computation

Education

behavioural approach

tt test

turing test tt

uk hector zenil cognition

information network

classic turingtest

metaphysics machine

tt objections