Noah Stein’s first love has always been mathematics. From his grade school days in Connecticut to his time at Cornell University, where he got a bachelor’s degree in Electrical and Computer Engineering in 2005, he knew that he liked studying math, but he was also interested in computers.
“[Math] got kind of boring in high school, I think because it wasn’t challenging….But halfway through [my time at Cornell], I discovered real math, pure math,” he says. All of his passion for the subject returned, and that is what led him to LIDS. He chose to apply only to applied math departments for graduate school, and he came to LIDS because of the unique blend of engineering and pure math that it offers, along with its excellent opportunities for funding.
Once at LIDS, Noah settled in, researching the “very theoretical side” of game theory with faculty such as Asu Ozdaglar and Pablo Parrilo, who was new to LIDS at the time. “Game theory is supposed to be the study of strategic interactions between self-interested agents, so there are plenty of times you could try to apply that in real life. But I was interested in the very math-y end of it, like, what would it mean to behave optimally in a particular situation? Can you compute what that optimal behavior would be, or write a program to compute it?” Noah went from taking a few game theory classes as an undergraduate to immersing himself in game theory, in problems with “an algebraic structure,” with both Asu and Pablo as his advisors. He found the environment at LIDS to be exciting and stimulating, saying, “It was a great place to learn from other students,” whether by attending the many talks LIDS hosts or by having discussions of students’ work and research outside of class. He even found time to become a “chocolate snob” through MIT’s Laboratory for Chocolate Science. Through Pablo’s contacts, he landed first an internship and then, after receiving his Ph.D. in Electrical Engineering and Computer Science from MIT in 2011, a fulltime job at Lyric Labs. “My approach during school had been that I should take as many math classes as I could because it would be much easier to learn applied stuff on the job than it would be to take applied classes at school and learn theory stuff on the job….They hired me for what they knew of my problem-solving skills,” he says. “It’s helpful to have the more abstract theoretical mindset in how you frame the problems, and reframe the problems.”
Lyric Labs began as the startup Lyric Semiconductor. It was founded by MIT grads and specialized in probabilistic processing. After being acquired by tech giant Analog Devices, Inc. (ADI) in 2011, Lyric continued on as a research group within the company. This research group is now expanding and its new name will be analog garage. As Noah explains, it has a new purpose. “They’ve expanded their research lab to include a lot of other things besides algorithms, and they have a new name for that umbrella. It’s a hybrid between research lab and internal startup incubator. They’re trying to take ideas that maybe don’t have a good place to fit within the company and fund them, give them room to grow.”
Right now, Noah works on what’s popularly known as the cocktail party problem: audio source separation. “You have some sort of noisy soundscape, where there are one or more sources of sound of interest, usually a voice, and potentially a lot of background noises that could be whatever. Your goal is to pick out some particular source of interest. It’s an extremely broad problem that people have worked on for a long time, and you have to narrow it down somewhat to be able to tackle it. We’re trying to improve the performance of speech recognition software where there’s a lot of background noise, meaning how many of the words it gets correct.” Approaches to this problem involve multiple microphones. Classical methods usually require the microphones to be at least five to ten centimeters apart in order to pick up differences in sound (if they are too close together, the mixtures of sounds you record in each mic are nearly identical and almost impossible to distinguish). As Noah explains it, “Depending on the wavelength of the sound and other details, if you add together the two signals, there’s some cancellation and the signal is attenuated.” However, Noah and his colleagues at Lyric have developed a new algorithm that allows the microphones to be placed much closer together. Using tiny mics called MEMS (microelectrical-mechanical systems; there are three in an iPhone, to give you an idea of size), he and his colleagues have been able to place their mics as close together as a single millimeter apart from center to center and still be able to successfully separate the recorded sounds.
The ultimate goal of all of this research and work is to get voice recognition on a device such as a phone or a car’s command system to work successfully more frequently. “We want to cross that usability threshold in noisier environments,” Noah says, such as a car on the highway with sounds from the road and the air conditioner and even other passengers interfering. Lyric Lab’s goal has always been to clean up the signal (they do not make speech recognition software themselves). Their initial project was to improve speech intelligibility in hearing aids, but they had to set that aside after realizing that there isn’t currently enough space within the devices physically to make significant improvements in how they work. “Hearing aids are an extremely resource-constrained environment already,” Noah says. The difficulties are not just due to the constrained environment though. “It’s not at all obvious even what function you would want to optimize if you had some sort of magic routine that could do it, because capturing this, [that is] how good does this audio signal sound in terms of it sounding like clean, undistorted speech, that’s an extremely subjective thing, and coming up with a really rough surrogate for how to measure that is really hard.” There are times when a human can distinguish between audio files but a metric can’t, and others when the opposite is true. As Noah points out, much of optimization theory “goes out the window when you can’t formulate your problem in a way that captures the stuff that you really care about.”
To relax away from work, Noah moves from hobby to hobby, with current interests including yoga and European-style board and card games. He also enjoys travel, saying, “I will travel to tropical locations and read math books there.” That joke has a kernel of truth, however. For a man who loves theory, a return to pure math is enjoyable and a complement to the more applied work he does each day. The ability to move back and forth between the theoretical and the applied aspects of math, to see the multiple approaches to a problem, is crucial to Noah’s work, and one of the most important things he learned at LIDS.