Inspired by the results of a game-playing neural network, mathematicians have been making unexpected advances on an age-old math problem.
Continuous-time neural networks are one subset of machine learning systems capable of taking on representation learning for spatiotemporal decision-making tasks. Continuous differential equations are frequently used to depict these models (DEs). Numerical DE solvers, however, limit their expressive potential when used on computers. The scaling and understanding of many natural physical processes, like the dynamics of neural systems, have been severely hampered by this restriction.
Inspired by the brains of microscopic creatures, MIT researchers have developed “liquid” neural networks, a fluid, robust ML model that can learn and adapt to changing situations. These methods can be used in safety-critical tasks such as driving and flying.
However, as the number of neurons and synapses in the model grows, the underlying mathematics becomes more difficult to solve, and the processing cost of the model rises.
Gnawing on his left index finger with his chipped old British teeth, temporal veins bulging and brow pensively squinched beneath the day-before-yesterday’s hair, the mathematician John Horton Conway unapologetically whiles away his hours tinkering and thinkering — which is to say he’s ruminating, although he will insist he’s doing nothing, being lazy, playing games.
Based at Princeton University, though he found fame at Cambridge (as a student and professor from 1957 to 1987), Conway, 77, claims never to have worked a day in his life. Instead, he purports to have frittered away reams and reams of time playing. Yet he is Princeton’s John von Neumann Professor in Applied and Computational Mathematics (now emeritus). He’s a fellow of the Royal Society. And he is roundly praised as a genius. “The word ‘genius’ gets misused an awful lot,” said Persi Diaconis, a mathematician at Stanford University. “John Conway is a genius. And the thing about John is he’ll think about anything.… He has a real sense of whimsy. You can’t put him in a mathematical box.”
“It’s a novel contribution that uses different methods compared to what most people have been doing,” said Steffen Gielen, a cosmologist at the University of Sheffield in the United Kingdom.
The provocative conclusion rests on a mathematical trick involving switching to a clock that ticks with imaginary numbers. Using the imaginary clock, as Hawking did in the ’70s, Turok and Boyle could calculate a quantity, known as entropy, that appears to correspond to our universe. But the imaginary time trick is a roundabout way of calculating entropy, and without a more rigorous method, the meaning of the quantity remains hotly debated. While physicists puzzle over the correct interpretation of the entropy calculation, many view it as a new guidepost on the road to the fundamental, quantum nature of space and time.
This could help achieve even world peace ✌️ called equilibrium theory by John Nash.
Game theory mathematics is used to predict outcomes in conflict situations. Now it is being adapted through big data to resolve highly contentious issues between people and the environment.
Game theory is a mathematical concept that aims to predict outcomes and solutions to an issue in which parties with conflicting, overlapping or mixed interests interact.
Continue reading “Using game theory mathematics to resolve human conflicts” »
Its why we should reverse engineer lab rat brains, crow brains, pigs, and chimps, ending on fully reverse engineering the human brain. even if its a hassle. i still think could all be done by end of 2025.
Last year, MIT researchers announced that they had built “liquid” neural networks, inspired by the brains of small species: a class of flexible, robust machine learning models that learn on the job and can adapt to changing conditions, for real-world safety-critical tasks, like driving and flying. The flexibility of these “liquid” neural nets meant boosting the bloodline to our connected world, yielding better decision-making for many tasks involving time-series data, such as brain and heart monitoring, weather forecasting, and stock pricing.
But these models become computationally expensive as their number of neurons and synapses increase and require clunky computer programs to solve their underlying, complicated math. And all of this math, similar to many physical phenomena, becomes harder to solve with size, meaning computing lots of small steps to arrive at a solution.
Continue reading “Solving brain dynamics gives rise to flexible machine-learning models” »
Circa 2020 face_with_colon_three
For the Sustaining Peace Project, astrophysicist Larry Liebovitch created a mathematical model to calculate whether a society is moving toward or away from peace.
“Neutron stars apparently behave a bit like chocolate pralines”.
Neutron stars were first discovered more than 60 years ago, but very little is known about the interior of neutron stars, the incredibly compact cores of dead stars.
According to their findings, a press statement reveals, they bear a surprising resemblance to chocolate pralines.
Continue reading “Mathematical models shed new light on the interior of neutron stars” »
Are we soon going to be traveling enormous distances via wormholes?
A team of scientists from the University of Sofia in Bulgaria believes they have discovered a new method for detecting wormholes — though they still only exist in theory.
Wormholes are theorized shortcuts through space and time. Sci-fi depictions traditionally show a spacecraft traveling through a wormhole, or creating one, to traverse immense distances to far-off regions of the universe in a short amount of time.
Continue reading “Sci-fi or reality? Scientists may know how to pinpoint wormholes in space” »
Last year, MIT developed an AI/ML algorithm capable of learning and adapting to new information while on the job, not just during its initial training phase. These “liquid” neural networks (in the Bruce Lee sense) literally play 4D chess — their models requiring time-series data to operate — which makes them ideal for use in time-sensitive tasks like pacemaker monitoring, weather forecasting, investment forecasting, or autonomous vehicle navigation. But, the problem is that data throughput has become a bottleneck, and scaling these systems has become prohibitively expensive, computationally speaking.
On Tuesday, MIT researchers announced that they have devised a solution to that restriction, not by widening the data pipeline but by solving a differential equation that has stumped mathematicians since 1907. Specifically, the team solved, “the differential equation behind the interaction of two neurons through synapses… to unlock a new type of fast and efficient artificial intelligence algorithms.”
