The surprising usefulness of sloppy arithmetic
Ask a computer to add 100 and 100, and its answer will be 200. But what if it sometimes answered 202, and sometimes 199, or any other number within about 1 percent of the correct answer?
Arithmetic circuits that returned such imprecise answers would be much smaller than those in today鈥檚 computers. They would consume less power, and many more of them could fit on a single chip, greatly increasing the number of calculations it could perform at once. The question is how useful those imprecise calculations would be.
If early results of a research project at MIT are any indication, the answer is, surprisingly useful. About a year ago, Joseph Bates, an adjunct professor of computer science at Carnegie Mellon University, was giving a presentation at MIT and found himself talking to Deb Roy, a researcher at MIT鈥檚 Media Lab. Three years earlier, before the birth of his son, Roy had outfitted his home with 11 video cameras and 14 microphones, intending to flesh out what he calls the 鈥渟urprisingly incomplete and biased observational data鈥� about human speech acquisition. Data about a child鈥檚 interactions with both its caregivers and its environment could help confirm or refute a number of competing theories in developmental psychology. But combing through more than 100,000 hours of video for, say, every instance in which either a child or its caregivers says 鈥渂all,鈥� together with all the child鈥檚 interactions with actual balls, is a daunting task for human researchers and artificial-intelligence systems alike. Bates had designed a chip that could perform tens of thousands of simultaneous calculations using sloppy arithmetic and was looking for applications that leant themselves to it.
Roy and Bates knew that algorithms for processing visual data are often fairly error-prone: A system that identifies objects in static images, for instance, is considered good if it鈥檚 right about half the time. Increasing a video-processing algorithm鈥檚 margin of error ever so slightly, the researchers reasoned, probably wouldn鈥檛 compromise its performance too badly. And if the payoff was the ability to do thousands of computations in parallel, Roy and his colleagues might be able to perform analyses of video data that they hadn鈥檛 dreamt of before.
High tolerance
So in May 2010, with funding from the U.S. Office of Naval Research, Bates came to MIT as a visiting professor, working with Roy鈥檚 group to determine whether video algorithms could be retooled to tolerate sloppy arithmetic. George Shaw, a graduate student in Roy鈥檚 group, began by evaluating an algorithm, commonly used in object-recognition systems, that distinguishes foreground and background elements in frames of video.
To simulate the effects of a chip with imprecise arithmetic circuits, Shaw rewrote the algorithm so that the results of all its numerical calculations were either raised or lowered by a randomly generated factor of between 0 and 1 percent. Then he compared its performance to that of the standard implementation of the algorithm. 鈥淭he difference between the low-precision and the standard arithmetic was trivial,鈥� Shaw says. 鈥淚t was about 14 pixels out of a million, averaged over many, many frames of video.鈥� 鈥淣o human could see any of that,鈥� Bates adds.
Of course, a really useful algorithm would have to do more than simply separate foregrounds and backgrounds in frames of video, and the researchers are exploring what tasks to tackle next. But Bates鈥� chip design looks to be particularly compatible with image and video processing. Although he hasn鈥檛 had the chip manufactured yet, Bates has used standard design software to verify that it will work as anticipated. Where current commercial computer chips often have four or even eight 鈥渃ores,鈥� or separate processing units, Bates鈥� chip has a thousand; since they don鈥檛 have to provide perfectly precise results, they鈥檙e much smaller than conventional cores.
But the chip has another notable idiosyncrasy. In most commercial chips, and even in many experimental chips with dozens of cores, any core can communicate with any other. But sending data across the breadth of a chip consumes much more time and energy than sending it locally. So in Bates鈥� chip, each core can communicate only with its immediate neighbors. That makes it much more efficient 鈥� a chip with 1,000 cores would really be 1,000 times faster than a conventional chip 鈥� but it also limits its use. Any computation that runs on the chip has to be easily divided into subtasks whose results have consequences mainly for small clusters of related subtasks 鈥� those running on the adjacent cores.
On the grid
Fortunately, video processing seems to fit the bill. Digital images are just big blocks of pixels, which can be split into smaller blocks of pixels, each of which is assigned its own core. If the task is to, say, determine whether the image changes from frame to frame, each core need report only on its own block. The core associated with the top left corner of the image doesn鈥檛 need to know what鈥檚 happening in the bottom right corner.
Bates has identified a few other problems that his chip also handles well. One is a standard problem in computer science called 鈥渘earest-neighbor search,鈥� in which you have a set of objects that can each be described by hundreds or thousands of criteria, and you want to find the one that best matches some sample. Another is computer analysis of protein folding, in which you need to calculate all the different ways in which the different parts of a long biological molecule could interact with each other.
Bob Colwell, who was the chief architect on several of Intel鈥檚 Pentium processors and has been a private consultant since 2000, thinks that the most promising application of Bates鈥� chip could be in human-computer interactions. 鈥淭here鈥檚 a lot of places where the machine does a lot of work on your behalf just to get information in and out of the machine suitable for a human being,鈥� Colwell says. 鈥淚f you put your hand on a mouse, and you move it a little bit, it really doesn鈥檛 matter where exactly the mouse is, because you鈥檙e in the loop. If you don鈥檛 like where the cursor goes, you鈥檒l move it a little more. Real accuracy in the input is really not necessary.鈥� A system that can tolerate inaccuracy in the input, Colwell, argues can also tolerate (some) inaccuracy in its calculations. The type of graphics processors found in most modern computers are another example, Colwell says, since they work furiously hard to produce 3-D images that probably don鈥檛 need to be rendered perfectly.
Bates stresses that his chip would work in conjunction with a standard processor, shouldering a few targeted but labor-intensive tasks, and Colwell says that, depending on how Bates鈥� chip is constructed, there could be some difficulty in integrating it with existing technologies. But he doesn鈥檛 see any of the technical problems as insurmountable. But 鈥渢here鈥檚 going to be a fair amount of people out in the world that as soon as you tell them I鈥檝e got a facility in my new chip that gives sort-of wrong answers, that鈥檚 what they鈥檙e going to hear no matter how you describe it,鈥� he adds. 鈥淭hat鈥檚 kind of a non-technical barrier, but it鈥檚 real nonetheless.鈥�
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