Large language models still struggle with basic reasoning tasks. Two new papers that apply machine learning to math provide a blueprint for how that could change.
Say you have a cutting-edge gadget that can crack any safe in the world—but you haven’t got a clue how it works. What do you do? You could take a much older safe-cracking tool—a trusty crowbar, perhaps. You could use that lever to pry open your gadget, peek at its innards, and try to reverse-engineer it. As it happens, that’s what scientists have just done with mathematics.
Researchers have examined a deep neural network—one type of artificial intelligence, a type that’s notoriously enigmatic on the inside—with a well-worn type of mathematical analysis that physicists and engineers have used for decades. The researchers published their results in the journal PNAS Nexus on January 23. Their results hint their AI is doing many of the same calculations that humans have long done themselves.
The paper’s authors typically use deep neural networks to predict extreme weather events or for other climate applications. While better local forecasts can help people schedule their park dates, predicting the wind and the clouds can also help renewable energy operators plan what to put into the grid in the coming hours.
The “rank” of a graph is the number of loops it has; for each rank of graphs, there exists a moduli space. The size of this space grows quickly — if you fix the lengths of the graph’s edges, there are three graphs of rank 2, 15 of rank 3,111 of rank 4, and 2,314,204,852 of rank 10. On the moduli space, these lengths can vary, introducing even more complexity.
The shape of the moduli space for graphs of a given rank is determined by relationships between the graphs. As you walk around the space, nearby graphs should be similar, and should morph smoothly into one another. But these relationships are complicated, leaving the moduli space with mathematically unsettling features, such as regions where three walls of the moduli space pass through one another.
Mathematicians can study the structure of a space or shape using objects called cohomology classes, which can help reveal how a space is put together. For instance, consider one of mathematicians’ favorite shapes, the doughnut. On the doughnut, cohomology classes are simply loops.
It acted with rudimentary intelligence, learning, evolving and communicating with itself to grow more powerful.
A new model by a team of researchers led by Penn State and inspired by Crichton’s novel describes how biological or technical systems form complex structures equipped with signal-processing capabilities that allow the systems to respond to stimulus and perform functional tasks without external guidance.
“Basically, these little nanobots become self-organized and self-aware,” said Igor Aronson, Huck Chair Professor of Biomedical Engineering, Chemistry, and Mathematics at Penn State, explaining the plot of Crichton’s book. The novel inspired Aronson to study the emergence of collective motion among interacting, self-propelled agents. The research was recently published in Nature Communications.
Quantum computing has entered a bit of an awkward period. There have been clear demonstrations that we can successfully run quantum algorithms, but the qubit counts and error rates of existing hardware mean that we can’t solve any commercially useful problems at the moment. So, while many companies are interested in quantum computing and have developed software for existing hardware (and have paid for access to that hardware), the efforts have been focused on preparation. They want the expertise and capability needed to develop useful software once the computers are ready to run it.
For the moment, that leaves them waiting for hardware companies to produce sufficiently robust machines—machines that don’t currently have a clear delivery date. It could be years; it could be decades. Beyond learning how to develop quantum computing software, there’s nothing obvious to do with the hardware in the meantime.
But a company called QuEra may have found a way to do something that’s not as obvious. The technology it is developing could ultimately provide a route to quantum computing. But until then, it’s possible to solve a class of mathematical problems on the same hardware, and any improvements to that hardware will benefit both types of computation. And in a new paper, the company’s researchers have expanded the types of computations that can be run on their machine.
Antibiotic resistance is a global threat to public health and associated with the overuse of antibiotics. Although non-antibiotic drugs occupy 95% of the drug market, their impact on the emergence and spread of antibiotic resistance remains unclear. Here we demonstrate that antidepressants, one of the most frequently prescribed drugs, can induce antibiotic resistance and persistence. Such effects are associated with increased reactive oxygen species, enhanced stress signature responses, and stimulation of efflux pump expression. Mathematical modeling also supported a role for antidepressants in the occurrence of antibiotic-resistant mutants and persister cells. Considering the high consumption of antidepressants (16,850 kg annually in the United States alone), our findings highlight the need to re-evaluate the antibiotic-like side effects of antidepressants.
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Stephen Hawking was one of the greatest scientific and analytical minds of our time, says NASA’s Michelle Thaller. She posits that Hawking might be one of the parents of an entirely new school of physics because he was working on some incredible stuff—concerning quantum entaglement— right before he died. He was even humble enough to go back to his old work about black holes and rethink his hypotheses based on new information. Not many great minds would do that, she says, relaying just one of the reasons Stephen Hawking will be so deeply missed. You can follow Michelle Thaller on Twitter at @mlthaller.
A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its frequencies.
Packaging signals that represent sounds or images in terms of their frequencies allows us to analyze and adjust sound and image files, Richard Stern, professor of electrical and computer engineering at Carnegie Mellon University, tells Popular Mechanics. This mathematical operation also makes it possible for us to store data efficiently.
The invention of color TV is a great example of this, Stern explains. In the 1950s, television was just black and white. Engineers at RCA developed color television, and used Fourier transforms to simplify the data transmission so that the industry could introduce color without tripling the demands on the channels by adding data for red, green, and blue light. Viewers with black-and-white TVs could continue to see the same images as they saw before, while viewers with color TVs could now see the images in color.
Summary: Researchers explain how deep neural networks are able to learn complex physics.
Source: Rice University.
One of the oldest tools in computational physics — a 200-year-old mathematical technique known as Fourier analysis — can reveal crucial information about how a form of artificial intelligence called a deep neural network learns to perform tasks involving complex physics like climate and turbulence modeling, according to a new study.
