The Elements of a Raven Matrix

by mathpunk

Experiment Huang

Huang was a man of routine.

Each day, he'd check his mailbox and then go for a walk in the forest.  He lived in a house at the end of a lane.  There were no other buildings on the lane other than the post office, which was always closed.  Each day, Huang would pass the post office on his way to the forest.  It made sense to him that the post office was closed.  He didn't mind it.  No one else lived nearby and he couldn't think of anyone he'd want to send mail to.  In fact, he couldn't even remember the last time he saw another person and so the post office (and to be fair, pretty much everything) was of no consequence to him.  His life was lonely, but his daily walks in the forest invigorated him.  Overall, he was content.  He wasn't superstitious or religious, so when he'd come across the markings during his walks, he didn't assign any special meaning to them.

One time, Huang walked into a clearing in the forest.  A circle of tall oak trees obscured the sun, and there was a dead raven in the middle of the clearing.  There were markings on the oak trees and also on the dead raven.  The markings were composed of lines, dots, shaded gradients and shapes, all formed with vivid colors and sharp contrasts and angles.  Seeing this sort of thing was usual for Huang.  In the forest, there were markings everywhere.

Huang walked around the clearing.  He studied the patterns formed by the markings.  They seemed to be a governed by an overarching logic, or geometry.  A wave of emotion washed over him and he let out aloud laugh.  Then, he crouched down next to the dead raven.  The markings on the raven's feathers looked unreal, as if they lived in the intersection of this world and some other world.  The markings were beautiful.  The colors seemed alive, and the dots and shapes and lines seemed to dance before his eyes.  Huang thought that maybe this world was a completed canvas, and an artist from that other, unknowable world had painted the markings overtop in a palimpsest.

Huang's mind began to wander.  He thought of famous paintings that had been modified after their completion.  The most famous example was perhaps the Mona Lisa.  A few decades ago, art historians used x-rays on the Mona Lisa and found that her smile and her mouth had been retouched.

Then, he thought of The Starry Night with the tall cypress tree that symbolized death.  Vincent Van Gogh would sometimes paint an entirely new piece overtop an old one.  But he didn't paint over to realize some Dadaism of art.  He just couldn't afford new canvases.  Huang felt that the most interesting example of this sort of "art upon art" was in Francis Picabia work.  After embracing the abstract, Francis Picabia went over some of his old realist pieces and either covered them entirely with his new ideas, or defaced them (sometimes just by scrawling cocks over them).  With this method, Francis Picabia could continually transform his art and keep his oeuvre fresh.

Huang walked back to his house.

The Letter

The next day, Huang began his routine.

Before his walk in the forest, he checked his mailbox as usual and then his whole life changed.  There was a letter.  It was addressed to him.  It had a London return address that he didn't recognize.  He started to panic.  Who would send him mail?  And, why would they even do that?  Huang hid the letter under a newspaper and hurried out the door.  The post office was open.  The post office had never been open before in all the years since Huang's creation.  He could see Wren through the window of the post office, seated behind the counter playing with a pen.  He didn't remember how he knew Wren, but there was no mistaking her face.  Huang ran into the forest.  There weren't any markings in the forest anymore, and soon he got bored and scared.

Huang went home and spent the rest of the week staring at the letter.  He had retrieved it out from under the newspaper and placed it at the center of his table.  He sat at the table and stared at the letter.  On the last day, he opened the letter.  Inside, there was another envelope.  It was self-addressed and already franked.  Besides that envelope, there was also a page with nine squares printed on it, organized into an array of three rows and three columns.  Each of the squares (except for the lower right one) had markings.  The lower-right square was empty, aside from a big question mark printed in the middle of it.  Below the array, there were four more squares, again all with markings on them.  These four squares were labeled "A," "B," "C," and "D," and below these four squares there was a single word: "Answer" followed by a colon.

Huang's mouth twisted into a mix between a smile and a silent scream.  What he saw on the page terrified him.  But at the same time, he hadn't seen any markings for days.  He suddenly realized how much he missed seeing the markings and how much pleasure he used to take from exploring their intricacies.  Now that he had some markings in front of him again, their perfect forms, rhythms, and tones made him feel complete.

He composed himself, but his mind started to race.  Huang thought about Sisyphus.  Sisyphus was cunning, and he defied the gods.  Sisyphus told his wife that when he died, she shouldn't give him a proper burial.  Instead, he told her to just throw his body into the street.  When he finally died, she did as she was told and Sisyphus found himself in front of Hades at the gates of Hell.  He told Hades to let him go back to the world so he could punish his wife for disrespecting his body.  Hades agreed, and said that he could go as long as he promised to come back to Hell before the end of the week.  Of course, Sisyphus had no intention of punishing his wife, nor of returning to Hell neither.  He just wanted to walk on grass again, feel a breeze on his face again, see the sunset and wade through a stream again.  The whole thing was a ruse and Sisyphus went on the lam: he defied death.

When Sisyphus didn't come back, Hades was pissed.  He told Zeus and the two of them went looking.  They couldn't find him.  So, Zeus sends Hermes, the fastest motherf*cker in Heaven, to track him down.  Hermes pops on his winged baseball cap and gets to it and that's it for Sisyphus.  And that's why Sisyphus got punished.  That's why he has to push that goddamn rock up that goddamn hill every day.  That's why he hits the drink every evening, after spending all of his goddamn might.

Lord, does his back hurt!  The rock rolls back down the hill.  Sisyphus strolls down after it and leans against it.  He pulls a flask out of the top-left pocket of his jacket and takes a swig.  Soon, he'll push that rock back up the hill.  He's good at that.  But for now, he's leaning.

Let's get back to Huang.

That's someone who never had to push a rock in his whole life.  But even so, he always felt like he was pushing something.  Doing something.  Living, existing, feeling, even if he was just kicking a can down the lane.  Here he is.  He hasn't left his house for days and he's scared and depressed as f*ck.  He looks down at the Raven matrix.  "C."  Before Huang's eyes, the elements of the matrix seem to pop and shudder under their own jazz melody.  Sure, he's scared.  But, he's excited and for a moment everything comes together.  He knows the answer and he feels like he's one-in-a-million.  The answer is "C."

He knows he's signing his own death warrant and in his heart of hearts he knows that the experiment will be over soon, but he can't help himself and he writes down "C" at the bottom of the page anyway.  He stuffs the page into the franked envelope and licks it shut.  He wants to go for one last walk in the forest, but instead he goes next door to the post office.  Even though it's night the post office is still open and Wren is still there and he hands her the franked envelope and she smiles at him and Sisyphus climbs up on top of his rock and stands on it and starts to sing, looking up at the stars.  And then, everything gets painted black.

Epilogue: An Abstract Submitted to a Conference

Recent advances in artificial general intelligence have led to human and superhuman behavior in artificial systems.

Such systems are now regularly verified by Turing tests administered by the Artificial Systems Symposium (ASS).  Definitions of intelligence, and quantification of the intelligence of artificial systems are now areas of active research.  However, the performance of artificial systems on intelligence measuring tasks such as Raven matrices do not provide a direct human comparison, as the systems must be trained on batteries of hundreds of thousands of examples before achieving human or superhuman performance.  In contrast, humans can perform these tasks given only one example (i.e., in a one-shot setting).

In this work, we instantiate artificial systems and allow them to explore simulated natural environments in an unsupervised manner.  Elements of Raven matrices are superimposed onto aspects of the simulated natural environment.  After a period of time, the artificial systems are presented with a single random Raven matrix task, and their response is recorded.

We aggregate results for one million replications, and demonstrate superhuman performance.

To our knowledge, this is the first work to provide such results in one-shot settings, showing an incremental improvement in the generalizability of intelligence in artificial systems.