The Bongard Problems | Hacker News Reader

The Bongard Problems

foundalis.com

30 pointsvardhanw16 comments

This is very neat. Besides this site and these results (updated till 2006):

http://www.foundalis.com/res/solvprog.htm

Anyone know if since then, say using deep learning or other newer methods, these problems are solvable easier?

I like the idea behind this, perhaps being able to solve these would be a stepping stone before solving the Turing test. And I think this kind of stuff points to developing a general AI.

The background of this is very interesting. The author of this research has stopped working on the problem for ethical reasons:

http://www.foundalis.com/soc/why_no_more_Bongard.html

"If this is achieved, eventually intelligent weapons of mass destruction will be built, without doubt. That’s what I would like to explain below."

I don't want to comment on that or qualify it in any way (I do have some thoughts about it, but would rather not share them). Will just say it was an interesting find.

Also learned about Mikhail Bongard, a Soviet machine learning researcher from the 60s-70s -- http://www.foundalis.com/res/Mikhail_Moiseevich_Bongard.html for some reason I imagined that part of the world simply did not have any background or interest in that discipline at that time, so it is interesting to learn something new there too.

The OP is about the authors research into the BPs as a means to reason about cognition. Originated by the russian scientist in 1967 and used and expanded by D. Hofstaedter in GEB. Here's [1] an index to all the BPs till now, and here's [2] the authors ideas on cognition which were developed in his research. Interesting that the research was abandoned [3] earlier based on ethical concerns of the possible misuse of AI. There is also a programmatic implementation of a BP solver.

[Edit]* this comment was not posted for a while, there is already another one with similar and more details now.

[1] http://www.foundalis.com/res/bps/bpidx.htm

[2] http://www.foundalis.com/res/poc/PrinciplesOfCognition.htm

[3] http://www.foundalis.com/soc/why_no_more_Bongard.html

Boy does this make me feel stupid. Pattern puzzles in IQ tests are always the hardest for me. The first, "trivial" example stumped me...

It's easier than you think -- the problem is to find a characteristic or rule that all of the lefthand objects conform to, and that all of the righthand objects do not.

The problem is not (as is sometimes the case for similar-looking IQ test problems) to find a rule that transforms the left side of each pair into the right side, or that generates the whole sequence of six iteratively. That might have been what you were searching for; I tried to do so in vain before reassessing the problem!

Technically, the "first" Bongard problem is much simpler: http://www.foundalis.com/res/bps/bongard/p001.htm

Since this was hard to find, here's the full index: http://www.foundalis.com/res/bps/bpidx.htm

Haha, I felt smart for a second because I got the "non-trivial" example immediately, but then realized my browser history for the past month consists of research on convex vs non-convex optimization problems, so I feel I had a bit of an unfair advantage there.

Is the "hard" one that the shapes on the left all have >=50% of their sides as single, straight lines? I've never die these types of problems before so totally unsure if I stumbled on an answer quickly, or don't understand what defines a solution.

No, since the bottom left example has 7 sides of which only 3 are single straight lines and the top right counterexample has 7 sides of which 4 are single straight lines.

The rule is that the shapes on the left all have exactly three sides as single straight lines. (Similarly, the shapes on the right have exactly three "unusual" sides.)

That said, though I've referred to "the rule" and the post author also refers to "the solution" to a Bongard problem, they don't and can't have authoritative solutions, just as sequence completion problems can't. When we talk about "correct" answers to this style of question, what we mean is "what tends to occur to smart people".

That's my issue with this kind of problem. There are usually a bunch of viable solutions with little if anything to differentiate them.

They're not tests of intelligence so much as tests of how similar your pattern matching is to that of the test authors.

> They're not tests of intelligence so much as tests of how similar your pattern matching is to that of the test authors.

Well... they are tests of intelligence. A valid test of intelligence is one that lets you determine ("predict") the intelligence of a testee from their answers. For that, you need intelligent and unintelligent people to have measurably different answer patterns, but there is no requirement that the intelligent answer patterns be objectively correct. You could have a test that was entirely subjective ("Who was the better artist, Michelangelo or Jackson Pollock?") and still use it to predict intelligence[1].

[1] That's an invented example; I'm not claiming that the particular question of Michelangelo vs. Jackson Pollock is actually predictive of intelligence, just pointing out that it could be.

But how do you select 'intelligent' people to generate your 'intelligent' answers? If it's not at some point tied back to some kind of objective performance (generating correct answers) then you're not measuring intelligence.

That's wrong. If your subjective test agrees in result with your objective test, they're measuring the same thing. That we can't begin the study of intelligence tests with a fully subjective test wouldn't mean we can't end there (and in fact, we can begin that way, because we start off with the idea that someone is smart if other people are inclined to describe them that way, not that someone is smart if they do well on a math test).

These are not intelligence tests, they're cognition tests. The goal is not to seek the correct answer, but a correct answer.

Seeking a correct answer is trivially easy, though; you can always find the rule "any of the six shapes on the left", just as you can always fit a function to any arbitrary sequence.

Right, but the context is that these problems comprise an evaluation suite for artificial intelligences. Even simply textually describing the shapes on the left and the right, is an accomplishment.

A better test suite would likely provide an oracle capable of generating new images belonging to the left or right and asking the program to judge which side it belongs to.

Interesting tidbit: The author's PhD advisor is the author of the celebrated text "Godel, Escher, Bach".

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