2
The Theory
of how people
figure out stuff from data
humanoids seminar 1, fall ‘09
Tuesday, September 6, 2011
what it’s going to be about: what people (or other agents) need in order to make sense of the
world
but first: a little motivation
why we should care:
Tuesday, September 6, 2011
programming an intelligent humanoid is the same problem as programming an intelligent human
(that is, like evolution, we have to figure out how to make sense of the world in order to act in it)
The primary goal of this reading group to identify the research topics in cognitive science that help us make sense of how to make sense of the world.
These goals relate strongly to our goals in humanoid robotics. Research in robotics shares a lot of fundamental ideas with various topics in psychology, particularly
developmental work, and some of the most notable advances in the field have drawn heavily from concepts which originated in psychology.
In psych there has been a huge amount of empirical and theoretical work on {what mechanisms underly human mental machinery, what the prereqs are for cognitive
development, what the developmental arc is for acquiring these skills, even theories of how inference and decision are computed}
and so i’d say that psych is more mature as a science than the fluffy descriptive field as labeled by its detractors. If science matures through an arc over descriptive,
empirical, and theoretical phases, then what is robotics? Really, the 4th phase - application. In considering problems we want humanoid robots to solve, we're clearly a bit
out of our depth on the theory. not surprisingly, many of the famous research domains in robotics were originally motivated by theories of mind: notably subsumption
architecture from society of mind, and social robotics from theory of mind. why we should care:
=
Tuesday, September 6, 2011
programming an intelligent humanoid is the same problem as programming an intelligent human
(that is, like evolution, we have to figure out how to make sense of the world in order to act in it)
The primary goal of this reading group to identify the research topics in cognitive science that help us make sense of how to make sense of the world.
These goals relate strongly to our goals in humanoid robotics. Research in robotics shares a lot of fundamental ideas with various topics in psychology, particularly
developmental work, and some of the most notable advances in the field have drawn heavily from concepts which originated in psychology.
In psych there has been a huge amount of empirical and theoretical work on {what mechanisms underly human mental machinery, what the prereqs are for cognitive
development, what the developmental arc is for acquiring these skills, even theories of how inference and decision are computed}
and so i’d say that psych is more mature as a science than the fluffy descriptive field as labeled by its detractors. If science matures through an arc over descriptive,
empirical, and theoretical phases, then what is robotics? Really, the 4th phase - application. In considering problems we want humanoid robots to solve, we're clearly a bit
out of our depth on the theory. not surprisingly, many of the famous research domains in robotics were originally motivated by theories of mind: notably subsumption
architecture from society of mind, and social robotics from theory of mind. just a few examples of
borrowed concepts...
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
• the shape bias in object recognition
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
• the shape bias in object recognition
• object permanence
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
• the shape bias in object recognition
• object permanence
• causal interaction
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
• the shape bias in object recognition
• object permanence
• causal interaction
• gaze detection
Tuesday, September 6, 2011
just a few examples of
borrowed concepts...
• social learning and theory of mind
• the shape bias in object recognition
• object permanence
• causal interaction
• gaze detection
• behavioral modularity
Tuesday, September 6, 2011
and considering what
we take for granted:
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
and considering what
we take for granted:
•
represent what other agents know, what they mean,
and what they want
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
and considering what
we take for granted:
•
represent what other agents know, what they mean,
and what they want
•
understand structured relationships between things
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
and considering what
we take for granted:
•
represent what other agents know, what they mean,
and what they want
•
understand structured relationships between things
•
can learn to recognize novel types based on small,
high-dimensional data
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
and considering what
we take for granted:
•
represent what other agents know, what they mean,
and what they want
•
understand structured relationships between things
•
•
can learn to recognize novel types based on small,
high-dimensional data
reason about causes and effects in the physical world
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
and considering what
we take for granted:
•
represent what other agents know, what they mean,
and what they want
•
understand structured relationships between things
•
•
can learn to recognize novel types based on small,
high-dimensional data
reason about causes and effects in the physical world
•
can use tools to extend your physical capabilities
we have a lot to learn from ourselves
Tuesday, September 6, 2011
structure: (tree: taxonomy, continuum: political spectrum, cycles: seasons, relational:
"better", "older", "taller" etc. (e.g. understanding of transitive property not understood till age
7)
types: (e.g. distinguish horses from non-horses after just a few examples as a child)
causality: (e.g. hands push blocks, not the other way around. )
The Theory Theory
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Theory Theory
• An account of how we know
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Theory Theory
• An account of how we know
• nativism vs. empiricism
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Theory Theory
• An account of how we know
• nativism vs. empiricism
• theory is empiricist
2
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Theory Theory
• An account of how we know
• nativism vs. empiricism
• theory is empiricist
• “an alternative to the innateness
2
hypothesis”
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Theory Theory
• An account of how we know
• nativism vs. empiricism
• theory is empiricist
• “an alternative to the innateness
2
hypothesis”
• Chomsky says: you can’t learn anything
without knowing something
Tuesday, September 6, 2011
read highlight on p2
now, her paper is an argument which you either read or you didn’t. I’m just going to
summarize the theory
The Innate Hypothesis
Tuesday, September 6, 2011
2: can only formulate a small set of the possible representations and rules
The Innate Hypothesis
• One specific nativist hypothesis
Tuesday, September 6, 2011
2: can only formulate a small set of the possible representations and rules
The Innate Hypothesis
• One specific nativist hypothesis
• Proposed that human minds are highly
constrained innately
Tuesday, September 6, 2011
2: can only formulate a small set of the possible representations and rules
The Innate Hypothesis
• One specific nativist hypothesis
• Proposed that human minds are highly
constrained innately
• Information from outside can trigger
enrichment of representation, but not
different constraints
Tuesday, September 6, 2011
2: can only formulate a small set of the possible representations and rules
Why such a radical
theory?
Tuesday, September 6, 2011
Why such a radical
theory?
• Poverty of the stimulus
Tuesday, September 6, 2011
Why such a radical
theory?
• Poverty of the stimulus
• Ancient philosophical argument:
Tuesday, September 6, 2011
Why such a radical
theory?
• Poverty of the stimulus
• Ancient philosophical argument:
• all known learning mechanisms are too
weak to explain human learning
Tuesday, September 6, 2011
Why such a radical
theory?
• Poverty of the stimulus
• Ancient philosophical argument:
• all known learning mechanisms are too
weak to explain human learning
• Evidence for Chomsky came from
language (proposed “universal grammar”)
Tuesday, September 6, 2011
2
The Theory
Tuesday, September 6, 2011
take
2
The Theory
•
Tuesday, September 6, 2011
take
Fine, but how do you explain science (or other
forms of human learning through data and
experimentation)??
2
The Theory
take
•
Fine, but how do you explain science (or other
forms of human learning through data and
experimentation)??
•
Instead: an empiricist alternative
Tuesday, September 6, 2011
2
The Theory
take
•
Fine, but how do you explain science (or other
forms of human learning through data and
experimentation)??
•
•
Instead: an empiricist alternative
Tuesday, September 6, 2011
Gopnik says:
2
The Theory
take
•
Fine, but how do you explain science (or other
forms of human learning through data and
experimentation)??
•
•
Instead: an empiricist alternative
Tuesday, September 6, 2011
Gopnik says:
•
1) humans DO have the ability to discover new
systems of representation (theories)
2
The Theory
take
•
Fine, but how do you explain science (or other
forms of human learning through data and
experimentation)??
•
•
Instead: an empiricist alternative
Tuesday, September 6, 2011
Gopnik says:
•
1) humans DO have the ability to discover new
systems of representation (theories)
•
2) these mechanisms explain human development
What exactly is a
“theory”
Tuesday, September 6, 2011
...in the way a perceptual system assigns representations to visual input or the syntactic
system assigns representations to phonological input.
read the “Neurath’s metaphor on sailboat”, p5
What exactly is a
“theory”
• “ a particular kind of system that assigns
representations to inputs...”
Tuesday, September 6, 2011
...in the way a perceptual system assigns representations to visual input or the syntactic
system assigns representations to phonological input.
read the “Neurath’s metaphor on sailboat”, p5
What exactly is a
“theory”
• “ a particular kind of system that assigns
representations to inputs...”
• key difference w/ Chomskyan grammar:
Tuesday, September 6, 2011
...in the way a perceptual system assigns representations to visual input or the syntactic
system assigns representations to phonological input.
read the “Neurath’s metaphor on sailboat”, p5
What exactly is a
“theory”
• “ a particular kind of system that assigns
representations to inputs...”
• key difference w/ Chomskyan grammar:
• the patterns of representation that occur
can alter the nature of the representation
system itself (yes neil, we know lisp does
that)
Tuesday, September 6, 2011
...in the way a perceptual system assigns representations to visual input or the syntactic
system assigns representations to phonological input.
read the “Neurath’s metaphor on sailboat”, p5
Possible empiricist
alternatives?
Tuesday, September 6, 2011
Possible empiricist
alternatives?
• Behaviorism
Tuesday, September 6, 2011
Possible empiricist
alternatives?
• Behaviorism
• Championed most by Skinner (innateness was
largely a reaction against this)
Tuesday, September 6, 2011
Possible empiricist
alternatives?
• Behaviorism
• Championed most by Skinner (innateness was
largely a reaction against this)
• Connectionism (McClelland & Rummelhart)
Tuesday, September 6, 2011
Possible empiricist
alternatives?
• Behaviorism
• Championed most by Skinner (innateness was
largely a reaction against this)
• Connectionism (McClelland & Rummelhart)
• Modern alternative
Tuesday, September 6, 2011
Possible empiricist
alternatives?
• Behaviorism
• Championed most by Skinner (innateness was
largely a reaction against this)
• Connectionism (McClelland & Rummelhart)
• Modern alternative
• proposes neural mechanisms for
abstraction
Tuesday, September 6, 2011
What’s wrong with
these?
Tuesday, September 6, 2011
•
Tuesday, September 6, 2011
What’s wrong with
these?
Both resort to a “scaling up” argument:
•
Tuesday, September 6, 2011
What’s wrong with
these?
Both resort to a “scaling up” argument:
•
Given some learning mechanism which can produce a
representation that is at least somewhat more abstract or
structured than the input, all that’s left is ‘scaling it up’ by
enriching input or adding connections and *poof* we get
human cognition
•
•
Tuesday, September 6, 2011
What’s wrong with
these?
Both resort to a “scaling up” argument:
•
Given some learning mechanism which can produce a
representation that is at least somewhat more abstract or
structured than the input, all that’s left is ‘scaling it up’ by
enriching input or adding connections and *poof* we get
human cognition
Problem: has never really worked
•
•
Tuesday, September 6, 2011
What’s wrong with
these?
Both resort to a “scaling up” argument:
•
Given some learning mechanism which can produce a
representation that is at least somewhat more abstract or
structured than the input, all that’s left is ‘scaling it up’ by
enriching input or adding connections and *poof* we get
human cognition
Problem: has never really worked
•
Output is never as complex or structured as
the phenomena that we’re trying to explain
So then how does it get
started?
Tuesday, September 6, 2011
So then how does it get
started?
• Starting-State Nativism (Gopnik)
Tuesday, September 6, 2011
So then how does it get
started?
• Starting-State Nativism (Gopnik)
• A set of innate constraints to guide
theory formation
Tuesday, September 6, 2011
So then how does it get
started?
• Starting-State Nativism (Gopnik)
• A set of innate constraints to guide
theory formation
• But isn’t that like Chomsky?
Tuesday, September 6, 2011
So then how does it get
started?
• Starting-State Nativism (Gopnik)
• A set of innate constraints to guide
theory formation
• But isn’t that like Chomsky?
• No, in this version the representation is
subject to revision
Tuesday, September 6, 2011
Thanks, but an example
would be great...
Tuesday, September 6, 2011
Thanks, but an example
would be great...
• Sorry, but there still isn’t a fully elaborated
“theory making machine”
Tuesday, September 6, 2011
Thanks, but an example
would be great...
• Sorry, but there still isn’t a fully elaborated
“theory making machine”
• But! There have been advances in learning
theory (spurred by ML), that directly
support the Theory2
Tuesday, September 6, 2011
Thanks, but an example
would be great...
• Sorry, but there still isn’t a fully elaborated
“theory making machine”
• But! There have been advances in learning
theory (spurred by ML), that directly
support the Theory2
•
Tuesday, September 6, 2011
The skeleton of a
theory
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
The skeleton of a
theory
• Remember: the goal is to define a system that can
incorporate new data in an analogous fashion that
scientists do
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
The skeleton of a
theory
• Remember: the goal is to define a system that can
incorporate new data in an analogous fashion that
scientists do
• So, what do scientists do?
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
The skeleton of a
theory
• Remember: the goal is to define a system that can
incorporate new data in an analogous fashion that
scientists do
• So, what do scientists do?
• Reason about cause and effect
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
The skeleton of a
theory
• Remember: the goal is to define a system that can
incorporate new data in an analogous fashion that
scientists do
• So, what do scientists do?
• Reason about cause and effect
• We need a system that builds representations of
causal relationships from experience in the
world
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
The skeleton of a
theory
• Remember: the goal is to define a system that can
incorporate new data in an analogous fashion that
scientists do
• So, what do scientists do?
• Reason about cause and effect
• We need a system that builds representations of
causal relationships from experience in the
world
•
note: this is really an introduction to the TICS paper, entitled “Mechanisms of theory
formation in young children”, so keep that in mind as we go...
Tuesday, September 6, 2011
* science is just a rational, institutionalized version of the theory2
Representing Cause
and effect
Tuesday, September 6, 2011
Representing Cause
and effect
• Core idea: capture it all in a bayes net
Tuesday, September 6, 2011
Representing Cause
and effect
• Core idea: capture it all in a bayes net
• Edges reflect conditional dependence
(conditional independence implied by lack
of edge)
Tuesday, September 6, 2011
Mechanisms of theory
formation in young children
Tuesday, September 6, 2011
Learning about
conditional probabilities
Tuesday, September 6, 2011
Learning about
conditional probabilities
•
Tuesday, September 6, 2011
Paradigm: which object caused the sound?
Learning about
conditional probabilities
•
Tuesday, September 6, 2011
Paradigm: which object caused the sound?
•
Children see various combinations of objects placed
on a machine
Learning about
conditional probabilities
•
Tuesday, September 6, 2011
Paradigm: which object caused the sound?
•
Children see various combinations of objects placed
on a machine
•
sometimes machine generates light & noise when
block is placed on it
Learning about
conditional probabilities
•
Tuesday, September 6, 2011
Paradigm: which object caused the sound?
•
Children see various combinations of objects placed
on a machine
•
sometimes machine generates light & noise when
block is placed on it
•
Children are told “blickets make the machine go”,
and then asked to point out the blicket
Experiment 1: conditional
independence asymmetry
• P(E,B|A) = 2/3
• P(E,A|B) = 2/3
• P(E|A)P(B|A) = 2/3
• P(E|B)P(A|B) = 1/3
Tuesday, September 6, 2011
kids say A not B
Experiment II: conditional
independence symmetry
P(E,B|A) = 0
P(E,A|B) = 0
P(E|A)P(B|A) = 0
P(E|B)P(A|B) = 0
Tuesday, September 6, 2011
kids equally likely to say A as B
Experiment III: inference
condition
• P(E|B)=1
• P(E|A) = 1/2
• B fully explains activation of machine
Tuesday, September 6, 2011
kids answer B
Experiment IV: ambiguous
condition
• P(E|A) = 1
• P(E|B) = 1
Tuesday, September 6, 2011
Kids answer equally, or are unsure