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Category: mathematics – Page 2

Reservoir computing (RC) is a powerful machine learning module designed to handle tasks involving time-based or sequential data, such as tracking patterns over time or analyzing sequences. It is widely used in areas such as finance, robotics, speech recognition, weather forecasting, natural language processing, and predicting complex nonlinear dynamical systems. What sets RC apart is its efficiency―it delivers powerful results with much lower training costs compared to other methods.

RC uses a fixed, randomly connected network layer, known as the reservoir, to turn input data into a more complex representation. A readout layer then analyzes this representation to find patterns and connections in the data. Unlike traditional neural networks, which require extensive training across multiple network layers, RC only trains the readout layer, typically through a simple linear regression process. This drastically reduces the amount of computation needed, making RC fast and computationally efficient.

Inspired by how the brain works, RC uses a fixed network structure but learns the outputs in an adaptable way. It is especially good at predicting and can even be used on physical devices (called physical RC) for energy-efficient, high-performance computing. Nevertheless, can it be optimized further?

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Artificial intelligence (AI) once seemed like a fantastical construct of science fiction, enabling characters to deploy spacecraft to neighboring galaxies with a casual command. Humanoid AIs even served as companions to otherwise lonely characters. Now, in the very real 21st century, AI is becoming part of everyday life, with tools like chatbots available and useful for everyday tasks like answering questions, improving writing, and solving mathematical equations.

AI does, however, have the potential to revolutionize —in ways that can feel like but are within reach.

At the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory, scientists are already using AI to automate experiments and discover new materials. They’re even designing an AI scientific companion that communicates in ordinary language and helps conduct experiments. Kevin Yager, the Electronic Nanomaterials Group leader at the Center for Functional Nanomaterials (CFN), has articulated an overarching vision for the role of AI in scientific research.

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Quantum computers may soon dramatically enhance our ability to solve problems modeled by nonreversible Markov chains, according to a study published on the pre-print server arXiv.

The researchers from Qubit Pharmaceuticals and Sorbonne University, demonstrated that quantum algorithms could achieve exponential speedups in sampling from such chains, with the potential to surpass the capabilities of classical methods. These advances — if fully realized — have a range of implications for fields like drug discovery, machine learning and financial modeling.

Markov chains are mathematical frameworks used to model systems that transition between various states, such as stock prices or molecules in motion. Each transition is governed by a set of probabilities, which defines how likely the system is to move from one state to another. Reversible Markov chains — where the probability of moving from, let’s call them, state A to state B equals the probability of moving from B to A — have traditionally been the focus of computational techniques. However, many real-world systems are nonreversible, meaning their transitions are biased in one direction, as seen in certain biological and chemical processes.

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Western researchers have developed a novel technique using math to understand exactly how neural networks make decisions—a widely recognized but poorly understood process in the field of machine learning.

Many of today’s technologies, from digital assistants like Siri and ChatGPT to and self-driving cars, are powered by machine learning. However, the —computer models inspired by the —behind these machine learning systems have been difficult to understand, sometimes earning them the nickname “” among researchers.

“We create neural networks that can perform , while also allowing us to solve the equations that govern the networks’ activity,” said Lyle Muller, mathematics professor and director of Western’s Fields Lab for Network Science, part of the newly created Fields-Western Collaboration Centre. “This mathematical solution lets us ‘open the black box’ to understand precisely how the network does what it does.”

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00:00 — Self-Improving Models.
00:23 — AllStar Math Overview.
01:34 — Monte-Carlo Tree.
02:59 — Framework Steps Explained.
04:46 — Iterative Model Training.
06:11 — Surpassing GPT-4
07:18 — Small Models Dominate.
08:01 — Training Feedback Loop.
10:09 — Math Benchmark Results.
13:19 — Emergent Capabilities Found.
16:09 — Recursive AI Concerns.
20:04 — Towards Superintelligence.
23:34 — Math as Foundation.
27:08 — Superintelligence Predictions.

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Links From Todays Video:
https://arxiv.org/pdf/2501.

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The amorphous state of matter is the most abundant form of visible matter in the universe, and includes all structurally disordered systems, such as biological cells or essential materials like glass and polymers.

An is a solid whose molecules and atoms form disordered structures, meaning that they do not occupy regular, well-defined positions in space.

This is the opposite of what happens in crystals, whose ordered structure facilitates their , as well as the identification of those “defects,” which practically control the physical properties of crystals, such as their plastic yielding and melting, or the way an electric current propagates through them.

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In the early 20th century, the mathematician Godel showed that any mathematical system is incomplete, using a version of the self-referential paradox: ‘this sentence is not true’. Here, neuroscientist and philosopher, Erik Hoel, argues this incompleteness extends to the scientific project as a whole; in part due to science’s reliance on mathematics. More radically, Hoel argues, this incompleteness of science may account for why we can’t find scientific evidence for consciousness anywhere in the world.

Let’s say you lived in a universe where you really were some sort of incarnated soul in a corporeal body. Or some sort of agent from a vaster reality embedded in a simulation (depending on definitions, the two scenarios might not be that different). What would the science in such a dualistic universe look like?

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Exploring the most important questions we face as we age.

Dr. Debra Whitman, Ph.D. is Executive Vice President and Chief Public Policy Officer, at AARP (https://www.aarp.org/) where she leads policy development, analysis and research, as well as global thought leadership supporting and advancing the interests of individuals age 50-plus and their families. She oversees AARP’s Public Policy Institute, AARP Research, Office of Policy Development and Integration, Thought Leadership, and AARP International.

Dr. Whitman is an authority on aging issues with extensive experience in national policy making, domestic and international research, and the political process. An economist, she is a strategic thinker whose career has been dedicated to solving problems affecting economic and health security, and other issues related to population aging.

Continue reading “Dr. Debra Whitman, Ph.D. — Chief Public Policy Officer, AARP — Author, The Second Fifty” | >