Small clues amid noise: Your brain on Sudoku

Move over, crossword puzzles. Sudoku — the addictive number-placement game first popularized in Japan — has taken America by storm.

After spawning innumerable books and websites and providing hours of entertainment for stranded airline passengers, the deceptively simple game has recently attracted an academic following. If molecular biology professor John Hopfield is correct, Sudoku may provide a window into how the brain stores memories.

Hopfield, a onetime physicist who gained fame in 1982 by inventing the associative neural network, recently designed a network to solve Sudoku puzzles. The research may help scientists design computers that can solve more difficult problems by mimicking the brain.

The puzzle involves a partially filled nine-by-nine grid separated into smaller subgrids measuring three-by-three. Players must fill in each square with a number between one and nine such that no row, column or three-by-three plot repeats a number.

Solving the game requires that the players appeal to associative memory, or the ability to infer patterns from limited information. This process can be simulated by a computer program.

"I suddenly saw the connection [between programming and memory] that I wouldn't have thought about had I not done Sudoku," Hopfield said.

Hopfield was introduced to the puzzles a year ago during a sailing trip with friends. "When the wind wasn't very good, they were Sudoku fanatics," he said.

"I looked at the puzzles, but the more interesting thing is, how do we construct them? And as I thought about it, I realized you can do something like a neural network that solves a puzzle."

Describing how answers "pop out," Hopfield explained how his neural network, like human memory, can find the answers to a Sudoku puzzle from small clues amid a lot of noise.

Similar to human players, Hopfield's network places multiple possibilities in each square and then attempts several possibilities. Just as the human memory system must efficiently remember where each number can go, the neural network model judges the possibility of each answer in the attempt to solve the puzzle.

Hopfield did not publish his result in a conventional paper. Ignoring standard scientific style, he opted to write his paper in a format that is more generally accessible. He then posted the paper on an online e-print archive where anyone can contribute papers and comment.

"I could write a paper the way I wanted to," Hopfield said. "I think as a result the paper is much more friendly for a reader."

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"If I were presenting this in a scientific paper, there would be people who would tell me, 'Publish this chunk that's memory,' or 'Publish this other chunk,' " Hopfield explained. "I think what makes it interesting is leaving the chunks together and being able to talk about the connection between the two."

Regardless of the results of Hopfield's work, Sudoku players on campus say the main attraction of the game is its challenge.

"I think it's a lot of fun," Veda Sunassee '09 said. "It's a game that keeps you concentrated for a long period of time. I'd rather do that than playing other games like Warcraft."

"When you are playing it, you have to strain and bear in mind which numbers you've used. I think it does help your memory," Sunassee added.

Hopfield said he has been pleased with the outcome of his work. "I wrote [the paper] to be read," he said.

"If I can get more people interested, then I am happy."