Emergence Berkeley presentation for devices

Emergency Berkeley

1. Emergent Functions of
Simple Systems
J. L. McClelland
Stanford University

2. Topics
Emergent probabilistic optimization in neural
networks
Relationship between competence/rational
approaches and mechanistic (including
connectionist) approaches
Some models that bring connectionist and
probabilistic approaches into proximal contact

3. Connectionist Units Calculate Posteriors
based on Priors and Evidence
Given
A unit representing hypothesis h
i, with
binary inputs j representing the state of
various elements of evidence e, where
for all j p(e
j) is assumed conditionally
independent given h
i
A bias on the unit equal to
log(prior
i/(1-prior
i))
Weights to the unit from each input
equal to log(p(e
j|h
i)/(log(p(e
j|not h
i))
If
the output of the unit is computed
from the logistic function
a
i= 1/[1+exp( bias
i+ S
ja
jw
ij)]
Then
a
i= p(h
i|e)
Unit i
Input from
unit j
w
ij

4. Choosing one of N alternatives
A collection of connectionist units representing
mutually exclusive alternative hypotheses can assign the
posterior probability to each in a similar way, using the
softmax activation function
net
i= bias
i+ S
ja
jw
ij
a
i= exp(gnet
i)/S
i’exp(gnet
i’)
If g= 1, this constitutes probability matching.
As gincreases, more and more of the activation goes to
the most likely alternative(s).

5. Emergent Outcomes from Local Computations
(Hopfield, ’82, Hinton & Sejnowski, ’83)
If w
ij= w
jiand if units are updated asynchronously,
setting
a
i= 1 if net
i>0, a
i= 0 otherwise
A network will settle to a state swhich is a local
maximum in a measure Rumelhart et al (1986) called G
G(s) =S
i<jw
ija
ia
j+ S
ia
i(bias
i+ ext
i)
If each unit sets its activation to 1 with probability
logistic(gnet
i) then
p(s) = exp(gG(s))/S
s’(exp(gG(s’))

6. A Tweaked Connectionist Model (McClelland &
Rumelhart, 1981) that is Also a Graphical Model
Each pool of units in the IA model is equivalent to
a Dirichlet variable (c.f. Dean, 2005).
This is enforced by using softmax to set one of the
a
iin each pool to 1 with probability:
p
j= e
gnet
j/S
j’e
gnet
j’
Weight arrays linking the variables are equivalent
of the ‘edges’ encoding conditional relationships
between states of these different variables.
Biases at word level encode prior p(w).
Weights are bi-directional, but encode generative
constraints (p(l|w), p(f|l)).
At equilibrium with g= 1, network’s probability of
being in state sequals p(s|I).

7. But that’s not the true PDP approach
to Perception/Cognition/etc…
We want to learn how to represent the
world and constraints among its
constituents from experience, using (to
the fullest extent possible) a domain-
general approach.
In this context, the prototypical
connectionist learning rules correspond
to probability maximization or
matching
Back Propagation Algorithm:
Treats output units (or n-way pools) as
conditionally independent given Input
Maximizes p(o
i|I) for each output unit.
I o

8. Overcoming the Independence
Assumption
The Boltzmann Machine learning algorithm learns to match probabilities of
entire output statesogiven current Input.
That is, it minimizes
∫p(o|I) log(p(o|I)/q(o|I)) do
where: p(o|I) is sampled from the environment (plus phase)
q(o|I) is net’s estimate of p(o|I) obtained by settling with the
input only (minus phase)
The algorithm is beautifully simple and local:
Dw
ij= e(a
i
+
a
j
+
-a
i
-
a
j
-
)

9. Recent Developments
Hinton’s deep belief
networks are fully distributed
learned connectionist models
that use a restricted form of
the Boltzmann machine (no
intra-layer connections) and
learn state-of-the-art models
very fast.
Generic constraints (sparsity,
locality) allow such networks
to learn efficiently and
generalize very well in
demanding task contexts.
Hinton, Osindero, and Teh (2006). A fast
learning algorithm for deep belief networks.
Neural Computation, 18, 1527-54.

10. Topics
Emergent probabilistic optimization in neural
networks
Relationship between competence/rational
approaches and mechanistic (including
connectionist) approaches
Some models that bring connectionist and
probabilistic approaches into proximal contact

11. One take on the relationship between rational
analysis and human behavior
Characterizing what’s optimal is always a great thing to do
Optimality is always relative to some framework; what that framework should
be isn’t always obvious.
It is possible to construct a way of seeing virtually anything as optimal post hoc
(c.f. Voltaire’s Candide).
Optimization is also relative to a set of constraints
Time
Memory
Processing speed
Available mechanisms
Simplifying assumptions …
The question of whether people do behave optimally (according to some
framework and constraints) in any particular situation is an empirical
question.
The question of why and how people can/do so behave in some situations
and not in others is worth understanding more thoroughly.

12. Two perspectives
People are rational, their behavior is optimal.
They seek explicit internal models of the structure
of the world, within which to reason.
Optimal structure type for each domain
Optimal structure instance within type
Resource limits and implementation constraints
are unknown, and should be ignored in
determining what is rational/optimal.
Inference is still hard, and prior domain-specific
constraints are therefore essential.
People evolved through an optimization process,
and are likely to approximate optimality/rationality
within limits.
Many aspects of natural/intuitive cognition may
depend largely on implicit knowledge.
Natural structure (e.g. language) does not exactly
correspond to any specific structure type.
Culture/School encourages us to think and reason
explicitly, and gives us tools for this; we do so
under some circumstances.

13. Same experienced structure leads to different
outcomes under different performance conditions
(Sternberg & McClelland, in prep)
Box appears…
Then one or two objects appear
Then a dot may or may not appear
RT condition: Respond as fast as
possible when dot appears
Prediction condition: Predict whether a
dot will appear, get feedback after
prediction.
Each event in box occur several times,
interleaved, with reversal of outcome
on 10% of trials.
Half of participants are instructed in
Causal Powers model, half not.
All participants learn explicit relations.
Only Instructed Prediction subjects
show Blocking and Screening.
AB+,A+
CD+,C-
EF+
GH-,G-
fillers

14. Two perspectives
People are rational, their behavior is optimal.
They seek explicit internal models of the structure
of the world, within which to reason.
Optimal structure type for each domain
Optimal structure instance within type
Resource limits and implementation constraints
are unknown, and should be ignored in
determining what is rational/optimal.
Inference is still hard, and prior domain-specific
constraints are therefore essential.
People evolved through an optimization process,
and are likely to approximate optimality/rationality
within limits.
Many aspects of natural/intuitive cognition may
depend largely on implicit knowledge.
Natural structure (e.g. language) does not exactly
correspond to any specific structure type.
Culture/School encourages us to think and reason
explicitly, and gives us tools for this; we do so
under some circumstances.
Many connectionist models do not directly
address this kind of thinking; eventually they
should be elaborated to do so.
Human behavior won’t be understood without
considering the constraints it operates under.
Determining what is optimal sansconstraints is
always useful, even so
Such an effort should not presuppose individual
humans intend to derive an explicit model.
Inference is hard, and domain specific priors can
help, but domain-general mechanisms subject to
generic constraints deserve full exploration.
In some cases such models may closely
approximate what might be the optimal explicit
model.
But that model might only be an approximation and
the domain-specific constraints might not be
necessary.

15. What is happening here?
Prediction participants have both a causal framework
and the time to reason explicitly about which objects
have the power to make the dot appear and which do
not.
Recall of (e.g.) C-during a CD prediction trial, in
conjunction with the causal powers story, licenses the
inference to D+
This inference does not occur without the boththe time
to think and the appropriate cover story.

16. The Rumelhart Sematic Attribution Model is Approximated
by a Gradually Changing Mixture of Increasingly Specific
Naïve Bayes Classifiers (Roger Grosse, 2007)
Very young
Stillyoung
Older
Correlation of network’s attributions with indicated classifier

17. Topics
Emergent probabilistic optimization in neural
networks
Relationship between competence/rational
approaches and mechanistic (including
connectionist) approaches
Some models that bring connectionist and
probabilistic approaches into proximal contact

18. Some models that bring connectionist and
probabilistic approaches into proximal contact
Graphical IA model of Context Effects in Perception
In progress; see Movellan & McClelland, 2001.
Leaky Competing Accumulator Model of Decision
Dynamics
Usher and McClelland, 2001, and the large family of related
decision making models
Models of Unsupervised Category Learning
Competitive Learning, OME, TOME (Lake et al, ICDL08).
Subjective Likelihood Model of Recognition Memory
McClelland and Chappell, 1998; c.f. REM, Steyvers and
Shiffrin, 1997), and a forthcoming variant using distributed
item representations.