Cogs 202 (SP12): Cognitive Science Foundations
Computational Modeling of Cognition
Prof. Angela Yu
Department of Cognitive Science, UCSD
http://www.cogsci.ucsd.edu/~ajyu/Teaching/Cogs202_sp12/index.html
Today
Self-introductions
Introduction to cognitive modeling
Syllabus
Assignments/grading
What is cognitive modeling and why do it?
• Actually, why do we study cognitive science at all?
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To understand how the mind works
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How we process information and act on it
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How we learn and generalize, and create new ideas
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How we think, reason, and make decisions
To make predictions of how people & animals behave
in new situations
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To treat pathology in cognition
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To build intelligent artificial systems and agents
What is cognitive modeling and why do it?
• It’s possible to study the mind without modeling
• But discovering facts is only the beginning
What is cognitive modeling and why do it?
Principles of Neural Science (Kandel, Schwartz, & Jessel)
No. pages
Year of publishing
•
•
Facts ≠ understanding, description
≠ understanding
36
Our goal is to make the book shorter!
What is cognitive modeling and why do it?
• The description is long because the system is complex
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“Understanding physics is child’s play compared to understanding
child’s play” -- Albert Einstein
• A theory makes it possible to
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Explain why we (scientists) observe what we observe
Predict what would happen in a new situation
• A model is just a very explicit theory
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Forces explicitness in assumptions, logic, and predictions
Implications often defy expectations
Aids communication among scientists
Support cumulative progress
What is cognitive modeling and why do it?
“Verbally expressed statements are sometimes
flawed by internal inconsistencies, logical
contradictions, theoretical weaknesses and
gaps. A running computational model, on the
other hand, can be considered as a sufficiency
proof of the internal coherence and
completeness of the ideas it is based
upon...” (Fum, Del Misser, Stocco, 2007)
Analogy from image compression
• The goal is to have as concise a description of the
image as possible
• Doing so requires modeling the (statistical)
relationship among components of the image
(information theory)
• Minimum description length = Bayesian inference
• A concise representation not only saves storage
space, but makes it possible to create new images
Analogy from image compression
Seam Carving for Image Resizing (Re-targeting)
Having established that modeling is useful...
How does it fit into the scientific study of cognition?
Environment
Stimuli that are perceived by the
body and nervous system
Behavior
39
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
Behavior
40
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
Behavior
Theory
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
Theory
predicts
Behavior
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
describes
Theory
predicts
Behavior
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
describes
Model
predicts
Behavior
Environment
Stimuli that are perceived by the
body and nervous system
Cognitive Mechanism
(representations, processes)
implements
Model
generates
Behavior
Environment
Stimuli that are perceived by the
body and nervous system
implements
Model
Cognitive Mechanism
(representations, processes)
generates
Behavior
manipulates
observes
Experiment
refines/tests
Model Taxonomy: Levels of Analysis
David Marr (1969): Brain = Information Processor
computational
goals of computation
SPEED-ACCURACY TRADEOFF IN SEQUENTIAL IDENTIFICATION UNDER A STOCHASTIC DEADLINE
3
why things work the way theyNEGOTIATING
do
the deadline Θ, or by the successful registry of the subject’s decision, whichever occurring earlier—
“∧” denotes the minimum of the two arguments on its either side. Then by the strong law of large
numbers the long-run average reward per unit time equals ER/ET with probability one. Therefore,
the maximum reward rate problem is equivalent to solving the stochastic optimization problem
!
#
"
E 1{τ +T0 <Θ} m
rj 1{µ=j,M =j}
j=1
input/output
V := sup
,
E [(τ + T0 ) ∧ Θ]
(τ,µ)
algorithmic
representation of
how one is transformed into the other
implementational
for which we will show that an optimal solution always exists and describe how to calculate the
supremum and an admissible decision rule (τ, µ) which attains the supremum.
An important theoretical question is whether and how Bayes-risk minimization and reward-rate
maximization are related to each other. In this work, we demonstrate that reward rate maximization
for this class of problems is formally equivalent to solving the family (W (c))c>0 of Bayes-risk
minimization problems,
how is the system physically realized
W (c) := inf E
in hardware (architecture, dynamics) (τ,µ)
$
'
m
&
&
%
c (τ + T0 ) ∧ Θ) + 1{τ +T0 <Θ}
rj 1{µ=i,M =j} + 1{τ +T0 ≥Θ}
rj 1{M =j} ,
j=1
i!=j
indexed by the unit sampling (observation or time) cost c > 0, thus rendering the reward-rate
maximization problem amenable to a large array of existing analytical and computational tools in
stochastic control theory. In particular, we show that the maximum reward rate V is the unique
unit sampling cost c > 0 which makes the minimum Bayes risk W (c) equal to the maximal expected
"
reward m
j=1 rj P(M = j) under the prior distribution. Moreover,
c!V
if and only if
$
'
m
&
%
(
inf E c (τ + T0 ) ∧ Θ − 1{τ +T0 <Θ}
rj 1{µ=j,M =j} ! 0;
(τ,µ)
j=1
namely, the maximum reward rate V is the unique unit sampling cost c for which expected total
Model taxonomy: core assumptions
Studying/comparing different models sheds light
on the Big Questions in cognitive science
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Representation
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Domain-specificity and modularity
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distinct or shared mechanism/architecture across cognitive
domains
Nature vs. nurture
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•
symbolic or distributed
what and how much is innate? what are learned?
Embodiment
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to what extent are cognitive abilities determined by the “body”
and environment?
Model taxonomy: approach
• Different modeling approaches make different core
assumptions, aim at different levels of analysis, and
are applied to different aspects of cognition
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connectionist/neural network
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Bayesian/ideal-observer
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symbolic/rule-based
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dynamical systems
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cognitive architectures
Modeling approaches
• Connectionist
✦
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emphasizes distributed representations and general-purpose,
experience-dependent learning mechanisms
typically implemented as artificial neural networks (ANN)
Figure: http://en.wikipedia.org/wiki/Artificial_neural_network
Modeling approaches
!"#$%%&'()*++,"*-.$/)
• Bayesian/ideal observer
! 0*1$/&*'2)
✦
emphasizes computational-level explanations using probability
! 34+.*/&5$/)-"4+67*7&"'*%8%$9$%)$:+%*'*7&"'/)6/&'()+,";*;&%&71)
theory,
optimal behavior under uncertainty and noise
7.$",1<)"+7&4*%);$.*9&",)6'#$,)6'-$,7*&'71=)
✦
shares
techniques with statistical machine learning methods
! >.*,$/)7$-.'&?6$/)@&7.)/7*7&/7&-*%)4*-.&'$)%$*,'&'()4$7."#/=)
A&(6,$/2)>7$19$,/)*'#)B,&CC&7./<))DEEF=))
Figure: Steyvers and Griffiths, 2007
Modeling approaches
"#$%%&'()*++,"*-.$/)
• Symbolic/rule-based
,&1.2&-32$-.*'&/1&-4)
✦ emphasizes procedural steps involved in processing information
2+.*/&6$/)+,"-$#7,*%)
+/)&'8"%8$#)&')+,"-$//&'()
✦ usually in a specific domain
",2*1&"':)7/7*%%;)&')*)
$-&9&-)#"2*&'<)
1),$*%%;)*)/&'(%$)*++,"*-.)
+.&%"/"+.;:)/")2*;)>$)
2>"%&-3,7%$?>*/$#)",)
1&/1&-*%<)
@A)
)*'#)D&'1$,:))@EEF<))
Figure: Perruchet and Vinter, 1998
Modeling approaches
• Dynamical systems:
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emphasizes the dynamic interaction between agent and environment,
as well as among computational components within the agent
connections to robotics and philosophy of embodied cognition
Modeling approaches
• Cognitive architectures:
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emphasizes information flow and modularity, as well as timing. Rulebased or hybrid (rules + activation levels)
Also has a more applied bend than other approaches, e.g. how will
adding a new display to a control panel affect a pilot’s reaction time?
Figure: ACT-R, from http://act-r.psy.cmu.edu/about/
Course schedule
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04/02: Introduction
04/09: Foundational issues in cognitive modeling
04/16: Neural network and connectionist models
04/23: Information theory and ideal observer models
04/30: Bayesian/probabilistic models
05/07: Dynamical systems models
05/14: Hybrid models (Bayesian + NN, Bayesian + dynamical systems)
05/21: Cognitive architectures
05/28: (no class)
06/04: Decision theoretic and reinforcement learning models
Class format
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45 min: background (conceptual, technical)
5 min: break
30 min: paper 1
5 min: break
30 min: paper 2
5 min: break
45 min: discussion
Presenter schedule
Every student presents twice
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•
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04/02: Introduction
04/09: Foundational issues in cognitive modeling (RT, AA)
04/16: Neural network and connectionist models (DFry, MB, LE)
04/23: Information theory and ideal observer models (MR, CF)
04/30: Bayesian/probabilistic models (MB, MR, LE)
05/07: Dynamical systems models (DFry, RT, DF)
05/14: Hybrid models (Bayesian + NN, Bayesian + dynamical systems)
(CF, EJK, DF)
• 05/21: Cognitive architectures (EJK, SI)
• 05/28: (no class)
• 06/04: Decision theoretic and reinforcement learning models (SI, AA)
Grading
• 50% participation
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reading (please read assigned papers before class)
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in-class discussion
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wiki (required if cannot be in class)
• 30% discussion leading
• 20% final project (wiki page)
• No laptop, tablet, or cell phone in class, unless you
need it for presentation (get a notebook to take
notes!)
Course wiki
• Accessible from course website
• Forum for discussion, feedback, and extra
references
• Testing ground for final wiki page
• cogs202:cogs202pd