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CATEGORIES:Engineering Safe AI
SUMMARY:Logical Induction: a computable approach to logica
l non-omniscience - Adrià Garriga Alonso (Universi
ty of Cambridge)
DTSTART;TZID=Europe/London:20180221T170000
DTEND;TZID=Europe/London:20180221T183000
UID:TALK101842AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/101842
DESCRIPTION:Link to slides: https://valuealignment.ml/talks/20
18-02-21-logical-induction.pdf\n\nIs P≠NP? Are the
re infinitely many twin primes? These conjectures
haven't been proven or disproven\, but we have qui
te a bit of "evidence" for them in the form of pro
ven related sentences. For example\, the differenc
e between any two consecutive primes is less than
7·10^7 (Zhang\, 2014).\n\nTo which degree should w
e believe in these logical sentences? How should w
e update our beliefs based on the related evidence
? One might turn to probability theory for answers
. However\, the veracity of the sentences is impli
ed by things we assume (the ZF/C axioms)\, rather
than any data we need to observe. Probability theo
ry thus dictates we should assign them probability
1 if they are true\, and 0 if they are false\, wh
ich is clearly impossible to do in general for a c
omputable agent (read: its program runs in a finit
e amount of time).\n\nIn this session we will talk
about Logical Induction (Garrabrant et al.\, 2016
)\, a computable algorithm for assigning probabili
ties to every logical statement in a formal langua
ge. We will examine several desirable properties o
f the algorithm. For example\, Logical Induction (
almost quoting from their abstract):\n\n(1) learns
to predict patterns of truth and falsehood in log
ical statements\, often long before having the res
ources to prove or disprove the statements\, so lo
ng as the patterns can be written in polynomial ti
me\,\n\n(2) learns to use appropriate statistical
summaries to predict sequences of statements whose
truth values appear pseudorandom\n\n(3) learns to
have accurate beliefs about its own current belie
fs\, in a manner that avoids the standard paradoxe
s of self-reference.\n\nFinally\, we will talk abo
ut its construction\, and its implications for sol
ving the value alignment problem.\n\n\nReferences:
\n\nLogical Induction (Scott Garrabrant\, Tsvi Ben
son-Tilsen\, Andrew Critch\, Nate Soares\, Jessica
Taylor): https://arxiv.org/abs/1609.03543\n\nAbri
dged version: https://intelligence.org/files/Logic
alInductionAbridged.pdf\n\nZhang\, Yitang. "Bounde
d gaps between primes." Annals of Mathematics 179.
3\n(2014): 1121-1174.\nhttp://annals.math.princeto
n.edu/wp-content/uploads/annals-v179-n3-p07-p.pdf\
n
LOCATION: Cambridge University Engineering Department\, CBL
Seminar room BE4-38. For directions see http://l
earning.eng.cam.ac.uk/Public/Directions
CONTACT:Adrià Garriga Alonso
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