Lifeboat Foundation

AlphaTensor opens the door to a world where AI designs programs that outperform anything humans engineer—including AI itself.

It was a big year. Researchers found a way to idealize deep neural networks using kernel machines—an important step toward opening these black boxes. There were major developments toward an answer about the nature of infinity. And a mathematician finally managed to model quantum gravity. Read the articles in full at Quanta Magazine: https://www.quantamagazine.org/the-year-in-math-and-computer-science-20211223/

Quanta Magazine is an editorially independent publication supported by the Simons Foundation.

In this episode we explore a User Interface Theory of reality. Since the invention of the computer virtual reality theories have been gaining in popularity, often to explain some difficulties around the hard problem of consciousness (See Episode #1 with Sue Blackmore to get a full analysis of the problem of how subjective experiences might emerge out of our brain neurology); but also to explain other non-local anomalies coming out of physics and psychology, like ‘quantum entanglement’ or ‘out of body experiences’. Do check the devoted episodes #4 and #28 respectively on those two phenomena for a full breakdown.
As you will hear today the vast majority of cognitive scientists believe consciousness is an emergent phenomena from matter, and that virtual reality theories are science fiction or ‘Woowoo’ and new age. One of this podcasts jobs is to look at some of these Woowoo claims and separate the wheat from the chaff, so the open minded among us can find the threshold beyond which evidence based thinking, no matter how contrary to the consensus can be considered and separated from wishful thinking.
So you can imagine my joy when a hugely respected cognitive scientist and User Interface theorist, who can cut through the polemic and orthodoxy with calm, respectful, evidence based argumentation, agreed to come on the show, the one and only Donald D Hoffman.

Hoffman is a full professor of cognitive science at the University of California, Irvine, where he studies consciousness, visual perception and evolutionary psychology using mathematical models and psychophysical experiments. His research subjects include facial attractiveness, the recognition of shape, the perception of motion and colour, the evolution of perception, and the mind-body problem. So he is perfectly placed to comment on how we interpret reality.

Continue reading “#29 Don Hoffman PHD — USER INTERFACE THEORY EXPLAINED” »

Improving the efficiency of algorithms for fundamental computations is a crucial task nowadays as it influences the overall pace of a large number of computations that might have a significant impact. One such simple task is matrix multiplication, which can be found in systems like neural networks and scientific computing routines. Machine learning has the potential to go beyond human intuition and beat the most exemplary human-designed algorithms currently available. However, due to the vast number of possible algorithms, this process of automated algorithm discovery is complicated. DeepMind recently made a breakthrough discovery by developing AplhaTensor, the first-ever artificial intelligence (AI) system for developing new, effective, and indubitably correct algorithms for essential operations like matrix multiplication. Their approach answers a mathematical puzzle that has been open for over 50 years: how to multiply two matrices as quickly as possible.

AlphaZero, an agent that showed superhuman performance in board games like chess, go, and shogi, is the foundation upon which AlphaTensor is built. The system expands on AlphaZero’s progression from playing traditional games to solving complex mathematical problems for the first time. The team believes this study represents an important milestone in DeepMind’s objective to improve science and use AI to solve the most fundamental problems. The research has also been published in the established Nature journal.

Matrix multiplication has numerous real-world applications despite being one of the most simple algorithms taught to students in high school. This method is utilized for many things, including processing images on smartphones, identifying verbal commands, creating graphics for video games, and much more. Developing computing hardware that multiplies matrices effectively consumes many resources; therefore, even small gains in matrix multiplication efficiency can have a significant impact. The study investigates how the automatic development of new matrix multiplication algorithms could be advanced by using contemporary AI approaches. In order to find algorithms that are more effective than the state-of-the-art for many matrix sizes, AlphaTensor further leans on human intuition. Its AI-designed algorithms outperform those created by humans, which represents a significant advancement in algorithmic discovery.

Non-scientific versions of the answer have invoked many gods and have been the basis of all religions and most philosophy since the beginning of recorded time.

Now a team of mathematicians from Canada and Egypt have used cutting edge scientific theory and a mind-boggling set of equations to work out what preceded the universe in which we live.

In (very) simple terms they applied the theories of the very small – the world of quantum mechanics – to the whole universe – explained by general theory of relativity, and discovered the universe basically goes though four different phases.

A physicist from the University of Campinas in Brazil isn’t a big fan of the idea that time started with a so-called Big Bang. So Instead, Juliano César Silva Neves imagines a collapse followed by a sudden expansion, one that could even still carry the scars of a previous timeline.

Updated version of the previous article.

The idea itself isn’t new, but Neves has used a fifty-year-old mathematical trick describing black holes to show how our Universe needn’t have had such a compact start to existence. At first glance, our Universe doesn’t seem to have a lot in common with black holes. One is expanding space full of clumpy bits; the other is mass pulling at space so hard that even light has no hope of escape. But at the heart of both lies a concept known as a singularity – a volume of energy so infinitely dense, we can’t even begin to explain what’s going on inside it.

Algorithms have helped mathematicians perform fundamental operations for thousands of years. The ancient Egyptians created an algorithm to multiply two numbers without requiring a multiplication table, and Greek mathematician Euclid described an algorithm to compute the greatest common divisor, which is still in use today.

During the Islamic Golden Age, Persian mathematician Muhammad ibn Musa al-Khwarizmi designed new algorithms to solve linear and quadratic equations. In fact, al-Khwarizmi’s name, translated into Latin as Algoritmi, led to the term algorithm. But, despite the familiarity with algorithms today – used throughout society from classroom algebra to cutting edge scientific research – the process of discovering new algorithms is incredibly difficult, and an example of the amazing reasoning abilities of the human mind.

In our paper, published today in Nature, we introduce AlphaTensor, the first artificial intelligence (AI) system for discovering novel, efficient, and provably correct algorithms for fundamental tasks such as matrix multiplication. This sheds light on a 50-year-old open question in mathematics about finding the fastest way to multiply two matrices.

The rise of quantum computing and its implications for current encryption standards are well known. But why exactly should quantum computers be especially adept at breaking encryption? The answer is a nifty bit of mathematical juggling called Shor’s algorithm. The question that still leaves is: What is it that this algorithm does that causes quantum computers to be so much better at cracking encryption? In this video, YouTuber minutephysics explains it in his traditional whiteboard cartoon style.

“Quantum computation has the potential to make it super, super easy to access encrypted data — like having a lightsaber you can use to cut through any lock or barrier, no matter how strong,” minutephysics says. “Shor’s algorithm is that lightsaber.”

Continue reading “How Quantum Physics Leads to Decrypting Common Algorithms” »

Some mathematicians have sought a logical proof for the existence of God. Here’s what they discovered.