Learning “The Hard Way”:
Negative Thinking in Context Spaces
Robert Burke,
March 2000
David
and Helen are going to the Symphony on a Friday night. David has never been to the Symphony before
and isn’t sure what he should wear. He
decides to dress only somewhat formally.
When he arrives at the performance, he feels comfortable. But when he meets Helen, he finds she is
much more formally dressed than he is, and this makes him feel uncomfortable.
On
countless occasions, David has searched through his wardrobe for something to
wear. But this evening, the context in
which he made his decision was unique.
To help make the decision, David remembered past experiences that took
place in similar contexts. In the
future, when he finds himself facing a similar decision, he should also draw
upon what he learned tonight at the Symphony.
As
Dr Minsky points out in section 2-1 of The
Emotion Machine, this process of learning and re-membering is rather
complex. David will need to “file”
information about his experience -- both positive and negative -- in such a way
that it can be readily recalled the next time he makes a similar decision. Retrieving this information will require
David to partition and search through the set of all possible contexts in which
a question like “what should I wear?” can be posed.
In
The Dimensions of Context-Space, Doug
Lenat proposes classifying contexts along twelve dimensions: time, type of
time, geographic location, type of place, culture, sophistication, topic,
granularity, modality/disposition, argument-preference, justification, and
domain assumptions. Lenat is considering context as a building block needed to
construct a knowledge base, which is
precisely what David’s mind is doing: building an efficient, but adaptive and
thorough, compilation of knowledge.
When
we begin thinking about a twelve-dimensional context space, it becomes
immediately (and perhaps painfully!) clear why David’s mind faces such hard
problems. In this paper, we’ll discuss
some of those problems -- like hypothesis forming, generalizing and searching
in a context space. What we’ll find,
once again, is the power of negative thinking.
By maintaining both negative and positive hypotheses, and taking
advantage of the Corrector, Suppressor, and Censor mechanisms Dr Minsky
describes in section 3-4 of The Emotion
Machine, we can avoid brute-force searches through context space and turn
it into a manageable habitat for ideas.
Generalization and Learning
Years
ago, David went to a highschool semi-formal in jeans and a T-shirt and was
teased by his peers. At the time, some
of these peers were among David’s imprimers, and their mockery was a formative
experience. His mind formed hypotheses
about what he should learn from the experience. One student he respected told him he should wear a tie in the
future. Another told him he shouldn’t
wear jeans. But David didn’t interpret
this to mean he should always wear a
tie or never wear jeans. Instead, David subconsciously (or, perhaps
consciously) solved the so-called credit assignment problem in his mind,
figuring out which aspects of the context were most salient.
In
terms of Lenat’s context space dimensions, David might have considered the type of place, type of time and culture dimensions
to be particularly salient. Then,
around a particular point in context space, he generalized by carving out a
subspace that contained all the contexts he thought this new information might
apply to. For example, “type of place”
might have been generalized to include all semi-formal public gatherings, and
not just high-school dances.
As
David grows up, he assembles an increasingly intricate map of the context
space, which serves as a sort of address book for the kinds of decisions he
should -- and shouldn’t -- make in various contexts.
Decision Making: Searching the
Context Space
In
making his decision to wear formal clothes to the Symphony, David first decided
which elements of the context were most salient. It’s probably not important that it’s the 23rd of March as
opposed to the 22nd, but it is likely
important that David will be attending a cultural event, with someone he
respects and wants to impress, on a Friday evening in a New England
climate. This brings him to a much
narrower locale in context space.
The
fact that the Symphony is a cultural event seems to be the most salient of
these parameters, for reasons which could fill another paper in and of
themselves. Quickly, one might
hypothesize that the fact it is a cultural event is the most salient
information for David because, for him, it is the aspect of the event that is
most out of the ordinary. Indeed, it is
so far out of the ordinary that David has never been to the Symphony
before. He won’t find a perfect,
specific event from his past to draw knowledge from; instead, he will have to
generalize from past knowledge and form a new hypothesis.
Decision Making: Hypothesis
Forming
Even
before David begins to think and form a hypothesis, we see how Censors, as
postulated by Freud, can help cull off a vast array of absurd
possibilities. It simply won’t occur to
David to wear a bathing suit, or attend the Symphony in the nude. It might be possible that our mind, in order
to save time, discards these silly possibilities as a first step before really
considering the context space.
The
context space has been filling up with two types of knowledge. The first consists of positive examples of
things that can potentially form hypotheses:
“In another semi-formal situation on a
Friday night, I impressed someone by dressing formally.”
“Someone I respect told me to wear a tie to
formal gatherings.”
“I have heard that educated people are
comfortable wearing dressy clothes to the Symphony.”
The
others are negative examples that are woven into Suppressors and Correctors:
“I once intimidated someone by being too
formally dressed.”
“I once embarrassed myself by wearing jeans
and a T-shirt to a semi-formal occasion.”
“A mentor once told me never to wear poorly
creased pants at a public gathering.”
All
of these thoughts need not be stored in explicit detail; rather, the relation
of each thought to other knowledge in the context space provides us with
implicit information. Perhaps even more
importantly, these relationships provide us with a built-in mechanism that
facilitates arbitrary levels of generalization. After this trip to the Symphony, for example, David will still be
careful not to intimidate people by overdressing. However, he might build in a new, more specific suppressor that
suggests, “Helen can be very well dressed, and not matching her level of
formality can be embarrassing.” That
way, David might dress the same way the next time he attends the Symphony,
unless he’s planning on meeting Helen there.
Sometimes,
our search through context space will reveal a perfect or near-perfect match to
a past situation which serves as a positive example of how we might
proceed. How far should we stray from a
positive example of something that worked in the past? We certainly don’t always make the same
decisions, although some people are more adventurous than others. If we never tried new options in old
contexts, we wouldn’t learn very much.
We each strike a unique balance between experimentation with new
options, and exploitation of knowledge gained from old successes (and, indirectly,
failures). Maintaining this
experimentation-versus-exploitation balance allows us to refine our notions of
how we partition context space, while at the same time taking advantage of
knowledge that we’ve acquired.
More on Learning the Hard Way
What
would happen if we ignored negative thinking, and didn’t maintain negative as
well as positive hypotheses in our context spaces? We would still tend to reinforce positive experience. However, during experimentation, we would be
more likely to stumble back on old mistakes.
If David hadn’t maintained a suppressor that reminded him not to wear
jeans at a formal occasion, his mind might have decided this Symphony trip was
a good chance to experiment with jeans as potential formal attire.
Perhaps
the strongest argument for negative thinking arises from the complexity of the
context space. Each of the twelve
dimensions Lenat mentions, like “type of place” and “culture,” are themselves
highly intricate and multidimensional spaces.
In the paper, Lenat suggests that there were originally over 100
dimensions considered for their system.
If we consider the many sub-dimensions of the dozen “uber-dimensions”
Lenat arrived at, we will likely be back to at least 100 dimensions again.
If
we are rewarded for an action (our expectations are met or exceeded, we are
praised by an imprimer, etc.) we will want to form hypotheses which suggest
potential contexts in which a similar action might also be rewarded. (In essence, this is exactly what David did
once when he dressed formally for a semi-formal situation and impressed the
people he respected. He hypothesized
that wearing formal attire again in a similar situation would result in a
similar positive reaction.) There are a
near-infinite number of such potential hypotheses, varying both in terms of
generality, and in which dimensionalities of the context are considered most
salient. It is likely that these
hypotheses will accumulate quickly. In
any case, hypotheses will “fade” or “be culled” if they aren’t confirmed or
tested within a reasonable timeframe.
Instead of creating a vast number of positive hypotheses -- most of
which will eventually be discarded as false -- the mind can keep track of
salient negative hypotheses as well.
Thus,
in addition to preventing us from revisiting negative experience, negative
hypotheses let us effectively probe a high-dimensional context space. Very few people want to subject themselves
to suffering. But there’s much to be
said about the importance of learning things “the hard way.”