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Category: mathematics – Page 12

Neural networks are at the core of artificial intelligence (AI), fueling a variety of applications from spotting objects in photos to translating languages. In this article, we’ll dive into what neural networks are, how they work, and why they’re a big deal in our technology-driven world today.

Index · 1: Understanding the Basics ∘ 1.1: What are Neural Networks? ∘ 1.2: Types of Neural Networks

· 2: The Architecture of Neural Networks ∘ 2.1: The Structure of a Neuron ∘ 2.2: Layers ∘ 2.3: The Role of Layers in Learning.

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Data is the new oil, as they say, and perhaps that makes Harvard University the new Exxon. The school announced Thursday the launch of a dataset containing nearly one million public domain books that can be used for training AI models. Under the newly formed Institutional Data Initiative, the project has received funding from both Microsoft and OpenAI, and contains books scanned by Google Books that are old enough that their copyright protection has expired.

Wired in a piece on the new project says the dataset includes a wide variety of books with “classics from Shakespeare, Charles Dickens, and Dante included alongside obscure Czech math textbooks and Welsh pocket dictionaries.” As a general rule, copyright protections last for the lifetime of the author plus an additional 70 years.

Foundational language models, like ChatGPT, that behave like a verisimilitude of a real human require an immense amount of high-quality text for their training—generally the more information they ingest, the better the models perform at imitating humans and serving up knowledge. But that thirst for data has caused problems as the likes of OpenAI have hit walls on how much new information they can find—without stealing it, at least.

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📝 — Bertran, et al.

Full text is available 👇

Nonalcoholic fatty liver disease (NAFLD) is the most prevalent chronic hepatic disease; nevertheless, no definitive diagnostic method exists yet, apart from invasive liver biopsy, and nor is there a specific approved treatment. Runt-related transcription factor 1 (RUNX1) plays a major role in angiogenesis and inflammation; however, its link with NAFLD is unclear as controversial results have been reported. Thus, the objective of this work was to determine the proteins involved in the molecular mechanisms between RUNX1 and NAFLD, by means of systems biology. First, a mathematical model that simulates NAFLD pathophysiology was generated by analyzing Anaxomics databases and reviewing available scientific literature.

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Will AI ever surpass human intelligence, discover new laws of physics, and solve the greatest mysteries of our universe?

This week on Into the Impossible, I explore the potential and dangers of artificial intelligence with none other than Max Tegmark!

Max Tegmark is a renowned physicist and machine learning expert who dedicated his career to uncovering the mathematical fabric of reality, proposing that our universe itself might be a vast mathematical structure and that we could be living in a multiverse of endless possibilities. His work goes beyond physics to tackle the transformative power and ethical challenges of artificial intelligence, an area where he believes humanity must tread carefully.

Continue reading “Max Tegmark: Will AI Surpass Human Intelligence?” | >

A new hypothesis suggests that the very fabric of space-time may act as a dynamic reservoir for quantum information, which, if it holds, would address the long-standing Black Hole Information Paradox and potentially reshape our understanding of quantum gravity, according to a research team including scientists from pioneering quantum computing firm, Terra Quantum and Leiden University.

Published in Entropy, the Quantum Memory Matrix (QMM) hypothesis offers a mathematical framework to reconcile quantum mechanics and general relativity while preserving the fundamental principle of information conservation.

The study proposes that space-time, quantized at the Planck scale — a realm where the physics of quantum mechanics and general relativity converge — stores information from quantum interactions in “quantum imprints.” These imprints encode details of quantum states and their evolution, potentially enabling information retrieval during black hole evaporation through mechanisms like Hawking radiation. This directly addresses the Black Hole Information Paradox, which highlights the conflict between quantum mechanics — suggesting information cannot be destroyed — and classical black hole descriptions, where information appears to vanish once the black hole evaporates.

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A mathematician at Yonsei University, in Korea, claims to have solved the moving sofa problem. Jineon Baek has posted a 100+-page proof of the problem on the arXiv preprint server.

Most people who have moved their place of residence have encountered the moving sofa problem—it comes up when attempting to carry a couch around a corner. What is the largest couch that can be carried around a given corner without getting stuck? This problem was posited mathematically by Leo Moser back in 1966, and until now, has remained unsolved.

Moser’s initial thoughts centered on the possibility of developing a proof showing how mathematics could be used to solve any such problem using a given shape of a plane as it was moved around a right-angled corner of an empty space (such as a hallway) that was one unit in width.

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Cellular death is a fundamental concept in biological sciences. Despite its importance, its definition varies depending on the context in which it occurs and lacks a general mathematical definition.

Researchers from the University of Tokyo propose a new mathematical definition of death based on whether a potentially dead cell can return to a predefined “representative state of living,” which are the states of being that we can confidently call “alive.” The researchers’ work could be useful for biological researchers and future medical research.

While it’s not something we like to think about, death comes for us all eventually, whether you’re an animal, a plant, or even a cell. And even though we can all differentiate between what is alive and dead, it might be surprising to know that death at a cellular level lacks a widely recognized mathematical definition.

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Originally published on Towards AI.

AI hallucinations are a strange and sometimes worrying phenomenon. They happen when an AI, like ChatGPT, generates responses that sound real but are actually wrong or misleading. This issue is especially common in large language models (LLMs), the neural networks that drive these AI tools. They produce sentences that flow well and seem human, but without truly “understanding” the information they’re presenting. So, sometimes, they drift into fiction. For people or companies who rely on AI for correct information, these hallucinations can be a big problem — they break trust and sometimes lead to serious mistakes.

So, why do these models, which seem so advanced, get things so wrong? The reason isn’t only about bad data or training limitations; it goes deeper, into the way these systems are built. AI models operate on probabilities, not concrete understanding, so they occasionally guess — and guess wrong. Interestingly, there’s a historical parallel that helps explain this limitation. Back in 1931, a mathematician named Kurt Gödel made a groundbreaking discovery. He showed that every consistent mathematical system has boundaries — some truths can’t be proven within that system. His findings revealed that even the most rigorous systems have limits, things they just can’t handle.

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The search for quantum gravity has gone on for 100 years, but it is not the only unification challenge in physics. Many of us believe that one day there will be a unification theory—a theory that will reconcile many divergent physical theories.

Our new article published in Physica Scripta brings new hope that such a theory exists. It demonstrates that the use of a certain mathematical object called Alena Tensor reconciles various physical theories, including , electrodynamics, and continuum mechanics. Will this finally allow scientists to unify descriptions used in physics?

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