Word of advice. You're creating your own artificial world here with its own
artificial rules.
AGI is about real vision of real objects in the real world. The two do not
relate - or compute.
It's a pity - it's good that you keep testing yourself, it's bad that they
aren't realistic tests. Subject yourself to reality - it'll feel better every
which way.
From: David Jones
Sent: Sunday, June 27, 2010 6:31 AM
To: agi
Subject: [agi] Huge Progress on the Core of AGI
A method for comparing hypotheses in explanatory-based reasoning:
We prefer the hypothesis or explanation that *expects* more observations. If
both explanations expect the same observations, then the simpler of the two is
preferred (because the unnecessary terms of the more complicated explanation do
not add to the predictive power).
Why are expected events so important? They are a measure of 1) explanatory
power and 2) predictive power. The more predictive and the more explanatory a
hypothesis is, the more likely the hypothesis is when compared to a competing
hypothesis.
Here are two case studies I've been analyzing from sensory perception of
simplified visual input:
The goal of the case studies is to answer the following: How do you generate
the most likely motion hypothesis in a way that is general and applicable to
AGI?
Case Study 1) Here is a link to an example: animated gif of two black squares
move from left to right. Description: Two black squares are moving in unison
from left to right across a white screen. In each frame the black squares shift
to the right so that square 1 steals square 2's original position and square
two moves an equal distance to the right.
Case Study 2) Here is a link to an example: the interrupted square.
Description: A single square is moving from left to right. Suddenly in the
third frame, a single black square is added in the middle of the expected path
of the original black square. This second square just stays there. So, what
happened? Did the square moving from left to right keep moving? Or did it stop
and then another square suddenly appeared and moved from left to right?
Here is a simplified version of how we solve case study 1:
The important hypotheses to consider are:
1) the square from frame 1 of the video that has a very close position to the
square from frame 2 should be matched (we hypothesize that they are the same
square and that any difference in position is motion). So, what happens is
that in each two frames of the video, we only match one square. The other
square goes unmatched.
2) We do the same thing as in hypothesis #1, but this time we also match the
remaining squares and hypothesize motion as follows: the first square jumps
over the second square from left to right. We hypothesize that this happens
over and over in each frame of the video. Square 2 stops and square 1 jumps
over it.... over and over again.
3) We hypothesize that both squares move to the right in unison. This is the
correct hypothesis.
So, why should we prefer the correct hypothesis, #3 over the other two?
Well, first of all, #3 is correct because it has the most explanatory power of
the three and is the simplest of the three. Simpler is better because, with the
given evidence and information, there is no reason to desire a more complicated
hypothesis such as #2.
So, the answer to the question is because explanation #3 expects the most
observations, such as:
1) the consistent relative positions of the squares in each frame are expected.
2) It also expects their new positions in each from based on velocity
calculations.
3) It expects both squares to occur in each frame.
Explanation 1 ignores 1 square from each frame of the video, because it can't
match it. Hypothesis #1 doesn't have a reason for why the a new square appears
in each frame and why one disappears. It doesn't expect these observations. In
fact, explanation 1 doesn't expect anything that happens because something new
happens in each frame, which doesn't give it a chance to confirm its hypotheses
in subsequent frames.
The power of this method is immediately clear. It is general and it solves the
problem very cleanly.
Here is a simplified version of how we solve case study 2:
We expect the original square to move at a similar velocity from left to right
because we hypothesized that it did move from left to right and we calculated
its velocity. If this expectation is confirmed, then it is more likely than
saying that the square suddenly stopped and another started moving. Such a
change would be unexpected and such a conclusion would be unjustifiable.
I also believe that explanations which generate fewer incorrect expectations
should be preferred over those that more incorrect expectations.
The idea I came up with earlier this month regarding high frame rates to reduce
uncertainty is still applicable. It is important that all generated hypotheses
have as low uncertainty as possible given our constraints and resources
available.
I thought I'd share my progress with you all. I'll be testing the ideas on test
cases such as the ones I mentioned in the coming days and weeks.
Dave
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