informatics 1 cg: lecture 15 · summary • inductive reasoning is everywhere: • to perceive,...
TRANSCRIPT
Knowledge
Howdoweacquireknowledge?
[Thepovertyofofstimulus]
“Howcomesitthathumanbeings,whosecontactswiththeworldarebriefandpersonalandlimited,areneverthelessabletoknowasmuchastheydoknow?”
(BertrandRussell)
Knowledge
Wheredoesknowledgecomefrom?
(1) Non-experientialsources(innate)(2) Perceptionandmemory(3) Deduction(4) Induction
Knowledge
Inductivereasoning:• Reasoningaboutcasesorprinciplesthatgobeyondcurrentdata.• Couldbewrong;entailuncertaintyorambiguity.• Havingseenonlyblackravens,wemightexpectanew,hiddenraventobeblack.• Anewravencouldbewhite!
• E.g.,Hume:“instancesofwhichwehavehadnoexperiencemustresemblethoseofwhichwehavehadexperience.”
(Hume, 1777/1975)
PerceptionJubalcalledout,"Thatnewhouseonthefarhilltop- canyouseewhatcolorthey'vepaintedit?”
AnnelookedinthedirectioninwhichJubalwaspointingandanswered,"It'swhiteonthisside."ShedidnotinquirewhyJubalhadasked,normakeanycomment.
JubalwentontoJillinnormaltones."Yousee?[…]itdoesn'tevenoccurtohertoinferthattheothersideisprobablywhitetoo…[evenifshesawit]shewouldn'tassumethatitstayed[thatcolor]...becausetheymightrepaintitassoonassheturnedherback.
(Heinlein,1961)
Perception
http://web.mit.edu/persci/people/adelson/images/checkershadow/
Perception
http://web.mit.edu/persci/people/adelson/images/checkershadow/
Memory
Serialreproductionexperiments:
“Person1:Drawthis!”
(Bartlett,1932viaXu&Griffiths,2010)
Memory
Serialreproductionexperiments:
Person1drewthis.“Person2:Drawthis!”
(Bartlett,1932viaXu&Griffiths,2010)
Memory
Serialreproductionexperiments:
Person2drewthis.“Person3:Drawthis!”
(Bartlett,1932viaXu&Griffiths,2010)
Memory
Serialreproductionexperiments:
Person3drewthis.“Person4:Drawthis!”
(Bartlett,1932viaXu&Griffiths,2010)
Memory
Serialreproductionexperiments:
(Bartlett,1932viaXu&Griffiths,2010)
Deduction
Asyllogism:
1. Allhumansaremortal.
2. Ashishuman.
3. Therefore,Ashismortal.
Deduction
Asyllogism:
1. Allhumansaremortal.
2. Ashishumanakillerandroid
3. Therefore,…?
Perfectcertaintyisrareintherealworld.
(*Hyperdyne Systemsmodel 120-A/2; http://alienanthology.wikia.com/wiki/Ash)
Induction
• Wecategorise objectswe’veneverseenbefore
• Wecanmakesenseofnewandambiguoussentences:“Ioncesawadeerridingmybicycle.”
• Wecanlearnhowtousenewtoolsandtechnology
• Wemakenewscientificdiscoveries
(https://en.wikipedia.org/wiki/List_of_linguistic_example_sentences)
Induction
Howisallthispossible?
Induction
Therationalist answer:• Themindhaslotsofinnatestructure.• Knowledgecomesfromthisstructureanditsinteractionswithexperience.
Induction
Therationalist answer:• Themindhaslotsofinnatestructure.• Knowledgecomesfromthisstructureanditsinteractionswithexperience.
Theempiricistanswer:• Thestimulusisnotasimpoverishedasonemightthink.• Wecanlearnandgeneralise withminimalinnatestructure.
Inductivebiases
Consensus:• Peoplelearnsomething fromexperience.• Weneedtohavesome startingknowledge(orassumptions)togeneralise atall.
Wecancallthis“knowledge”ourinductivebiases.
Inductivebiases
Wecanthinkofmanyquestionsincognitivescienceintermof:
(1) Whatinductivebiasesshapehumanbehaviour?
(2) Wheredoourinductivebiasescomefrom?
Inductivebiases
Inductivebiasescanbeunderstoodindifferentways:
Theycanbemadeexplicit,e.g.,• Tacitknowledgeofa“universalgrammar”• Assumptionthatcategoriesaredefinedintermsofaprototype• Assumptionthatcategorieshavehierarchicalstructure
Inductivebiases
Inductivebiasescanbeunderstoodindifferentways:
Theycanarisefromalearner’sstructureoritsenvironment:• Thearchitectureofaneuralnetwork• Thekindsofexperiencesaninfanthas
Inductivebiases
Thesearen’tmutuallyexclusive.
Aperson’sinductivebiasesmight• beaccuratelycapturedbyrulesorprobabilitydistributionsand• emergefromcomplexbiologicalphenomena.
Example:Inductivebiasesofaneuralnet
Example:Inductivebiasesofaneuralnet
(https://en.wikipedia.org/wiki/DeepDream)
Example:Inductivebiasesofaneuralnet
(https://en.wikipedia.org/wiki/DeepDream)
Example:Inductivebiasesofaneuralnet
(https://en.wikipedia.org/wiki/DeepDream)
Example:Inductivebiasesofaneuralnet
(https://en.wikipedia.org/wiki/DeepDream)
Howcanwestudyinductivebiases?
Someoptions:
1. Lookatwhatpeoplefindsurprising.2. Lookatwhatpatternspeoplefindeasy/hardtolearn.3. Predictspecifichumanjudgmentsandgeneralizations.4. Lookatstatisticalregularitiesinhumanjudgments.5. Understandwhatconstraintsbiologyimposes.
Howcanwestudyinductivebiases?
1. Lookatwhatpeoplefindsurprising.
“If<X>isinnate,infantsshouldbesurprisedby<Y>.”
Howcanwestudyinductivebiases?
2.Lookatwhatpatternspeoplefindeasy/hardtolearn.
“Ifpeoplerelyonrepresentation<X>,theyshouldcommitthefollowingkindsoferrors...”
Howcanwestudyinductivebiases?3.Predictspecifichumanjudgmentsandgeneralizations.
Howcanwestudyinductivebiases?
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8 n = 9
Random4.Lookatstatisticalregularitiesinhumanjudgments.
Howcanwestudyinductivebiases?
5. Understandwhatconstraintsbiologyimposes
Neuroscience!Examples:• Multi-unitrecording• Modelsofcellsandcellpopulations• Geneticmanipulation(e.g.,knockoutsandoptogenetics)
(Forreadingsonthis,seehttp://homepages.inf.ed.ac.uk/pseries/ccn16.htm)
http://web.stanford.edu/group/dlab/optogenetics/
Summary
• Inductivereasoningiseverywhere:• Toperceive,understand,andactontheworldaroundus,wemustgeneralise,usinginformationthatisnoisy,incomplete,andambiguous.
• Generalisation isimpossiblewithoutinductivebiases.• Inductivebiasesincludeacquiredknowledgeandbiologicalconstraints.• Manybigquestionsincognitivesciencecanbeframedintermsof:• Whatareourinductivebiases?• Wheredotheycomefrom?