Archive for the ‘mathematics’ category: Page 3

Sep 12, 2020

OpenAI ‘GPT-f’ Delivers SOTA Performance in Automated Mathematical Theorem Proving

Posted by in categories: mathematics, robotics/AI

San Francisco-based AI research laboratory OpenAI has added another member to its popular GPT (Generative Pre-trained Transformer) family. In a new paper, OpenAI researchers introduce GPT-f, an automated prover and proof assistant for the Metamath formalization language.

While artificial neural networks have made considerable advances in computer vision, natural language processing, robotics and so on, OpenAI believes they also have potential in the relatively underexplored area of reasoning tasks. The new research explores this potential by applying a transformer language model to automated theorem proving.

Automated theorem proving tends to require general and flexible reasoning to efficiently check the correctness of proofs. This makes it an appealing domain for checking the reasoning capabilities of language models and for the study of reasoning in general. The ability to verify proofs also helps researchers as it enables the automatic generation of new problems that can be used as training data.

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Sep 11, 2020

The Mathematics Behind Deep Learning

Posted by in categories: mathematics, robotics/AI

Deep neural networks (DNNs) are essentially formed by having multiple connected perceptrons, where a perceptron is a single neuron. Think of an artificial neural network (ANN) as a system which contains a set of inputs that are fed along weighted paths. These inputs are then processed, and an output is…

Sep 10, 2020

2021 Breakthrough Prize Winners Announced: Researcher Who Developed Protein Design Technology Awarded $3 Million

Posted by in categories: biotech/medical, mathematics

Baker won one of the six $3 million Breakthrough Prizes this year, which were awarded to eight different scientists in Mathematics, Fundamental Physics and Life Sciences.

David Baker, whose protein design technology is being used to develop therapies for Covid-19 and cancer, received one of several awards to scientists from the Breakthrough Prize Foundation that add up to a combined total of $21.75 million.

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Sep 10, 2020

Joscha Bach — GPT-3: Is AI Deepfaking Understanding?

Posted by in categories: existential risks, information science, mathematics, media & arts, particle physics, quantum physics, robotics/AI, singularity

On GPT-3, achieving AGI, machine understanding and lots more… Will GPT-3 or an equivalent be used to deepfake human understanding?

Joscha Bach on GPT-3, achieving AGI, machine understanding and lots more
02:40 What’s missing in AI atm? Unified coherent model of reality
04:14 AI systems like GPT-3 behave as if they understand — what’s missing?
08:35 Symbol grounding — does GPT-3 have it?
09:35 GPT-3 for music generation, GPT-3 for image generation, GPT-3 for video generation
11:13 GPT-3 temperature parameter. Strange output?
13:09 GPT-3 a powerful tool for idea generation
14:05 GPT-3 as a tool for writing code. Will GPT-3 spawn a singularity?
16:32 Increasing GPT-3 input context may have a high impact
16:59 Identifying grammatical structure & language
19:46 What is the GPT-3 transformer network doing?
21:26 GPT-3 uses brute force, not zero-shot learning, humans do ZSL
22:15 Extending the GPT-3 token context space. Current Context = Working Memory. Humans with smaller current contexts integrate concepts over long time-spans
24:07 GPT-3 can’t write a good novel
25:09 GPT-3 needs to become sensitive to multi-modal sense data — video, audio, text etc
26:00 GPT-3 a universal chat-bot — conversations with God & Johann Wolfgang von Goethe
30:14 What does understanding mean? Does it have gradients (i.e. from primitive to high level)?
32:19 (correlation vs causation) What is causation? Does GPT-3 understand causation? Does GPT-3 do causation?
38:06 Deep-faking understanding
40:06 The metaphor of the Golem applied to civ
42:33 GPT-3 fine with a person in the loop. Big danger in a system which fakes understanding. Deep-faking intelligible explanations.
44:32 GPT-3 babbling at the level of non-experts
45:14 Our civilization lacks sentience — it can’t plan ahead
46:20 Would GTP-3 (a hopfield network) improve dramatically if it could consume 1 to 5 trillion parameters?
47:24 GPT3: scaling up a simple idea. Clever hacks to formulate the inputs
47:41 Google GShard with 600 billion input parameters — Amazon may be doing something similar — future experiments
49:12 Ideal grounding in machines
51:13 We live inside a story we generate about the world — no reason why GPT-3 can’t be extended to do this
52:56 Tracking the real world
54:51 MicroPsi
57:25 What is computationalism? What is it’s relationship to mathematics?
59:30 Stateless systems vs step by step Computation — Godel, Turing, the halting problem & the notion of truth
1:00:30 Truth independent from the process used to determine truth. Constraining truth that which can be computed on finite state machines
1:03:54 Infinities can’t describe a consistent reality without contradictions
1:06:04 Stevan Harnad’s understanding of computation
1:08:32 Causation / answering ‘why’ questions
1:11:12 Causation through brute forcing correlation
1:13:22 Deep learning vs shallow learning
1:14:56 Brute forcing current deep learning algorithms on a Matrioshka brain — would it wake up?
1:15:38 What is sentience? Could a plant be sentient? Are eco-systems sentient?
1:19:56 Software/OS as spirit — spiritualism vs superstition. Empirically informed spiritualism
1:23:53 Can we build AI that shares our purposes?
1:26:31 Is the cell the ultimate computronium? The purpose of control is to harness complexity
1:31:29 Intelligent design
1:33:09 Category learning & categorical perception: Models — parameters constrain each other
1:35:06 Surprise minimization & hidden states; abstraction & continuous features — predicting dynamics of parts that can be both controlled & not controlled, by changing the parts that can be controlled. Categories are a way of talking about hidden states.
1:37:29 ‘Category’ is a useful concept — gradients are often hard to compute — so compressing away gradients to focus on signals (categories) when needed
1:38:19 Scientific / decision tree thinking vs grounded common sense reasoning
1:40:00 Wisdom/common sense vs understanding. Common sense, tribal biases & group insanity. Self preservation, dunbar numbers
1:44:10 Is g factor & understanding two sides of the same coin? What is intelligence?
1:47:07 General intelligence as the result of control problems so general they require agents to become sentient
1:47:47 Solving the Turing test: asking the AI to explain intelligence. If response is an intelligible & testable implementation plan then it passes?
1:49:18 The term ‘general intelligence’ inherits it’s essence from behavioral psychology; a behaviorist black box approach to measuring capability
1:52:15 How we perceive color — natural synesthesia & induced synesthesia
1:56:37 The g factor vs understanding
1:59:24 Understanding as a mechanism to achieve goals
2:01:42 The end of science?
2:03:54 Exciting currently untestable theories/ideas (that may be testable by science once we develop the precise enough instruments). Can fundamental physics be solved by computational physics?
2:07:14 Quantum computing. Deeper substrates of the universe that runs more efficiently than the particle level of the universe?
2:10:05 The Fermi paradox
2:12:19 Existence, death and identity construction.

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Sep 10, 2020

UK mathematician wins richest prize in academia

Posted by in categories: innovation, mathematics

Martin Hairer takes $3m Breakthrough prize for work a colleague said must have been done by aliens.

Sep 10, 2020

Quantum Simulations of Curved Space

Posted by in categories: computing, cosmology, mathematics, particle physics, quantum physics

A heptagonal-lattice superconducting circuit, and the mathematics that describe it, provide tools for studying quantum mechanics in curved space.

According to John Wheeler’s summary of general relativity, “space-time tells matter how to move; matter tells space-time how to curve.” How this relationship plays out at the quantum scale is not known, because extending quantum experiments to curved space poses a challenge. In 2019, Alicia Kollár and colleagues at Princeton University met that challenge with a photonic circuit that represents the negatively curved space of an expanding universe [1]. Now, Igor Boettcher and colleagues at the University of Maryland, College Park, describe those experiments with a new theoretical framework [2]. Together, the studies offer a toolkit for studying quantum mechanics in curved space that could help answer fundamental questions about cosmology.

In a universe that expands at an accelerating rate, space curves away from itself at every point, producing a saddle-like, hyperbolic geometry. To project hyperbolic space onto a plane, Kollár’s team etched a centimeter-sized chip with superconducting resonators arranged in a lattice of heptagonal tiles. By decreasing the tile size toward the edge of the chip, the researchers reproduced a perplexing property of hyperbolic space: most of its points exist on its boundary. As a result, photons moving through the circuit behave like particles moving in negatively curved space.

Sep 9, 2020

Math Riddle From Decades Ago Finally Solved After Being Lost And Found

Posted by in categories: computing, information science, mathematics

A pair of Danish computer scientists have solved a longstanding mathematics puzzle that lay dormant for decades, after researchers failed to make substantial progress on it since the 1990s.

The abstract problem in question is part of what’s called graph theory, and specifically concerns the challenge of finding an algorithm to resolve the planarity of a dynamic graph. That might sound a bit daunting, so if your graph theory is a little rusty, there’s a much more fun and accessible way of thinking about the same inherent ideas.

Going as far back as 1913 – although the mathematical concepts can probably be traced back much further – a puzzle called the three utilities problem was published.

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Sep 9, 2020

Unity in Knowledge: From Ethics and Islam to Exponential Technology and Robotics

Posted by in categories: bioengineering, ethics, mathematics, physics, robotics/AI, transhumanism

Discussing STEM, the future, and transhumanism with an islamic scholar / scientist.

Ira Pastor, ideaXme life sciences ambassador interviews Imam Sheikh Dr. Usama Hasan, PhD, MSc, MA, Fellow of the Royal Astronomical Society and Research Consultant at the Tony Blair Institute For Global Change.

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Sep 4, 2020

Vision-free MIT Cheetah

Posted by in categories: bioengineering, mathematics, physics, robotics/AI

MIT’s Cheetah 3 robot can now leap and gallop across rough terrain, climb a staircase littered with debris, and quickly recover its balance when suddenly yanked or shoved, all while essentially blind.

Watch more videos from MIT:

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Sep 3, 2020

Teaching evolutionary theory to artificial intelligence reveals cancer’s life history

Posted by in categories: biotech/medical, genetics, information science, mathematics, robotics/AI

Scientists have developed the most accurate computing method to date to reconstruct the patchwork of genetic faults within tumors and their history during disease development, in new research funded by Cancer Research UK and published in Nature Genetics.

Their powerful approach combines with the mathematical models of Charles Darwin’s theory of evolution to analyze genetic data more accurately than ever before, paving the way for a fundamental shift in how ’s genetic diversity is used to deliver tailored treatments to patients.

Applying these to DNA data taken from patient samples revealed that tumors had a simpler genetic structure than previously thought. The algorithms showed that tumors had fewer distinct subpopulations of cells, called “subclones,” than previously suggested. The scientists, based at The Institute of Cancer Research, London, and Queen Mary University of London, could also tell how old each subclone was and how fast it was growing.

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