麻豆传媒

KRISHNA PALEM鈥橲 computers won鈥檛 win any awards for accuracy. Most of the time they can鈥檛 even add up correctly. For them, 2 + 2 might as well be 5. But don鈥檛 be fooled by the wobbly arithmetic. Palem is making machines that could represent a new dawn for computing.

Inaccuracy is not something we typically associate with computers. Since Alan Turing laid down their ground rules in the 1930s, computers have been sticklers for precision, built on the principle of following step-by-step instructions in an exact and reproducible manner. They should not make errors.

But maybe we should cut them some slack. Letting computers make mistakes could be the best way to unlock the next wave of smart devices and prevent high-performance computing hitting a wall. It would allow us to run complex simulations that are beyond today鈥檚 supercomputers 鈥� models that better predict climate change, help us design more efficient cars and aircraft, and reveal the secrets of galaxy formation. They may even unlock the biggest mystery of all, by letting us simulate the human brain.

Until now, we have had to accept a trade-off between performance and energy efficiency: a computer can be either fast or low-powered, but not both. This not only means that more powerful smartphones need better batteries, but also that supercomputers are energy guzzlers. Next-generation 鈥渆xaflop鈥� machines, which are capable of 10¹⁸ operations a second, could consume as much as 100 megawatts, the output of a small power station. So the race is on to make computers do more with less.

One way is simply to reduce the amount of time spent executing code 鈥� the less time taken, the less power used. For programmers, this means looking for ways to get the desired result more quickly. Take the classic travelling-salesman problem of finding the shortest route around a group of cities. It鈥檚 notoriously tough to solve, given that the number of possible routes shoots up exponentially with the number of cities. Palem, a computer scientist at Rice University in Houston, Texas, says that coders often settle for a route that they estimate to be about half as good as the best, because to do better would use up too much computer time. A more recent version of this approach is to use a machine-learning algorithm to arrive at an approximate result for a given piece of code. This rough answer 鈥� like a back-of-the-envelope calculation 鈥� can then be used each time the program runs instead of executing the original section of code itself.

But saving energy by cutting corners in software only goes so far. To really save power, you need to change the way the hardware works. Computers can save vast amounts of energy simply by not operating all their transistors at full power all the time, but as we鈥檒l soon see, this means sacrificing accuracy. Palem鈥檚 team is hobbling computers so that they get their sums wrong in an acceptable way. 鈥淲hat we are proposing is to alter the computer itself to give you cheaper but slightly less accurate answers,鈥� says Palem. Take any algorithm that you think does a good job, and he will solve it inexactly with a different physical system under the hood.

Standard computer chips use a sliver of silicon called a channel to act as a switch that can flip between on (1) and off (0). The switching is controlled by a gate that stops a current flowing through the channel until you apply a voltage. Then the gate opens like a sluice in a dam, letting current through.

But it鈥檚 finicky. This complementary metal-oxide semiconductor (CMOS) technology only works well when it has a reliable 5-volt power supply. Start to lower that and the channel becomes unstable 鈥� sometimes switching, sometimes not.

In 2003, Palem, then at the Georgia Institute of Technology in Atlanta, saw trouble coming. It was clear that the ability of the electronics industry to continue doubling the number of transistors on a chip every 18 to 24 months 鈥� a miniaturisation trend known as Moore鈥檚 law 鈥� was coming to an end. Miniaturisation was introducing errors at the chip level. This was largely due to overheating and interference, or crosstalk, between the densely packed transistors. 鈥淚t was quite likely ultra-small devices would become quite unstable,鈥� says Palem. Power was now the critical issue. What if you could harness instabilities in some way that would also save energy?

Palem鈥檚 answer was to design a probabilistic version of CMOS technology that was deliberately unstable. His team built digital circuits in which the most significant bits 鈥� those representing values that need to be accurate 鈥� get a regular 5-volt supply, but the least significant bits get 1 volt. 鈥淭he significant bits are running at a proper, well-behaved voltage, but the least significant get really slack,鈥� says Palem. As many as half the bits representing a number can be hobbled like this.

This means that Palem鈥檚 version of an adder, a common logic circuit that simply adds two numbers, doesn鈥檛 work with the usual precision (see 鈥�Missing bits鈥�). 鈥淲hen it adds two numbers, it gives an answer that is reasonably good but not exact,鈥� he says. 鈥淏ut it is much cheaper in terms of energy use.鈥�

Spread that over billions of transistors and you have a significant power saving. The trick is to choose applications for which the least significant bits don鈥檛 matter too much: for example, using a large range of numbers to represent the colour of a pixel. In one experiment, Palem and his colleagues built a digital video decoder that interpreted the least significant bits in an imprecise way when converting pixel data into screen colours. They found that human viewers perceived very little loss in image quality. 鈥淭he human eye averages a lot of things out,鈥� says Palem. 鈥淭hink about how we see illusions. The brain does a lot of work to compensate.鈥�

Encouraged by that success, the Rice University researchers have moved on to another application involving the senses: hearing aids. Their initial tests show that inexact digital processing in a hearing aid can halve power consumption while reducing intelligibility by only 5 per cent. The results suggest that we could use such techniques to slash the power used by smartphones and personal computers, given that these are basically audiovisual devices.

Tim Palmer, a climate physicist at the University of Oxford, sees even greater potential. He thinks that computers based on Palem鈥檚 ideas could be the answer to what is presently an intractable problem: how to improve the accuracy of climate predictions for the next century without waiting years for a new generation of supercomputers.

鈥淭he crucial question about climate change centres on the role of clouds,鈥� says Palmer, in terms of whether they amplify or dampen the effects of global warming. 鈥淵ou can鈥檛 really answer that question with any great confidence unless you can simulate cloud systems directly.鈥� And right now, it鈥檚 not clear how to do that.

鈥淒oing 20 calculations inexactly may be more useful than 10 done exactly鈥�

Today鈥檚 supercomputers don鈥檛 have the brawn to do it, and their successors, expected in the next decade or so, will just be too energy-hungry. 鈥淏ased on current estimates, the amount of power needed for such a machine is going to be around 100 megawatts,鈥� says Palmer, five to 10 times what today鈥檚 top supercomputers use. Assuming they don鈥檛 just melt, running them could prove prohibitively costly.

Supercomputers burn so much power because they are generally optimised for computing with 64-bit-long numbers. In principle, this gives greater accuracy. But climate models involve millions of variables, simulating complex interacting factors such as winds, convection, temperatures, air pressures, ocean temperatures and salinity. The result, says Palmer, is that they have too much power-draining data to crunch. What鈥檚 needed, he says, is for different variables to be represented in data strings of varying length, depending on their importance to the model.

Chipmakers are starting to accommodate such needs. Nvidia has launched a graphics processor unit, the TX1, that is capable of 鈥渕ixed-precision鈥� processing, allowing software to switch between 16 and 32-bit operation as it runs. But Palmer wants to see Palem鈥檚 inexact chips adopted too. 鈥淚f we can reduce the number of bits that you need to do calculations, that would have an enormous impact on energy consumption,鈥� he says. Palmer and his colleagues are talking to supercomputer makers like IBM and Cray about developing a new breed of energy-efficient hybrid machines that allow varying levels of accuracy, and that may even adopt Palem鈥檚 strategy. And Palem鈥檚 team is working on mixed-precision computing with the US government鈥檚 Argonne National Laboratory in Illinois and the European Centre for Medium-Range Weather Forecasts in Reading, UK.

The pay-offs could be huge. Today鈥檚 climate models tackle Earth鈥檚 atmosphere by breaking it into regions roughly 100 kilometres square and a kilometre high. Palmer thinks inexact computing would get this down to cubes a kilometre across 鈥� detailed enough to model individual clouds.

鈥淒oing 20 calculations inexactly could be much more useful than 10 done exactly,鈥� says Palmer. This is because at 100-kilometre scales, the simulation is a crude reflection of reality. The computations may be accurate, but the model is not. Cutting precision to get a finer-grained model would actually give you greater accuracy overall. 鈥淚t is more valuable to have an inexact answer to an exact equation than an exact answer to an inexact equation,鈥� he says. 鈥淲ith the exact equation, I鈥檓 really describing the physics of clouds.鈥�

Degrees of accuracy

You can鈥檛 just give up on accuracy across the board, of course. 鈥淭here is no doubt that if you represent all of the variables in the climate model with just 16 bits rather than 64 bits it would be a disaster: it would fail very quickly,鈥� says Palmer. The challenge is choosing which parts can be treated more crudely than others.

Researchers are attacking the problem from several different angles. Mostly, it comes down to devising ways to specify thresholds of accuracy in code so that programmers can say when and where errors are acceptable. The software then computes inexactly only in parts that have been designated safe.

Approximation is not the answer for everyone, however. Rashid Mansoor is a London-based computer scientist and entrepreneur who invented Adbrain, an algorithm that tracks millions of web users as they move between devices. He is now looking at ways to speed up computing done in the cloud. But Mansoor sees inexactness as a last resort. 鈥淲e don鈥檛 yield approximate results for the sake of speeding up computation,鈥� he says. 鈥淲e鈥檇 consider it to be cheating.鈥�

Even so, Stan Posey, who heads Nvidia鈥檚 high-performance computing team in Santa Clara, California, sees a host of applications for which inexact computing will make a big difference, including accident investigations. After the Columbia space-shuttle disaster of 2003, caused by a chunk of insulating foam breaking off and making a hole in a wing, Posey and his colleagues spent countless hours simulating scenarios that could have led to this happening. He thinks inexact computing would now allow a number of simulations an order of magnitude higher within the same time frame. Scenarios that are worth looking into more closely can then be pursued with higher accuracy.

Some think inexact simulations could ultimately help us understand the brain. Supercomputers like IBM鈥檚 Blue Gene are being used to model neurological functions in the Human Brain Project, for example. But there is a huge discrepancy in power consumption between the brain and a supercomputer, says Palmer (see 鈥淧ower hungry鈥�). 鈥淎 supercomputer needs megawatts of power, yet a human brain runs on the power of a light bulb.鈥� What could account for this?

Palmer and colleagues at the University of Sussex in Brighton, UK, are exploring whether random electrical fluctuations might provide probabilistic signals in the brain. His theory is that this is what lets it do so much with so little power. Indeed, the brain could be the perfect example of inexact computing, shaped by pressure to keep energy consumption down.

What鈥檚 clear is that to make computers better, we need to make them worse. Palmer is convinced that partly abandoning Turing鈥檚 concept of how a computer should work is the way forward if we are to discover the true risks we face from global warming. 鈥淚t could be the difference between climate change being a relatively manageable problem and one that will be an existential problem for humanity.鈥�

And if approximate computing seems a shaky foundation on which to build the future of computing, it鈥檚 worth remembering that computers are always dealing with the abstract. 鈥淎ll computing is approximation,鈥� says Posey. Some are just more approximate than others.

This article appeared in print under the headline 鈥淟et鈥檚 cut them some slack鈥�