Mathpresso, the creator of QANDA — Asia’s most extensive AI-driven learning platform — has announced that their large language model called MathGPT has achieved a new world record in math, beating OpenAI and Microsoft models.
MathGPT reportedly is now ranked no. 1 in benchmarks that evaluate mathematical ability such as ‘MATH’ (12,500 difficult math problems) and ‘GSM8K’ (8,500 elementary school math problems), beating Microsoft’s ‘ToRA 13B’, the model that held the previous record.
In the MATH benchmark, MathGPT surpassed the performance of OpenAI’s GPT-4.
Scientists have grown a tiny brain-like organoid out of human stem cells, hooked it up to a computer, and demonstrated its potential as a kind of organic machine learning chip, showing it can quickly pick up speech recognition and math predictions.
Clusters of brain cells grown in the lab have shown potential as a new type of hybrid bio-computer.
A #mathematics “A Bernoulli trial is a #random experiment with exactly two possible outcomes “success” and “failure” in which #probability of success is the same every time the experiment is conducted.”
In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, “success” and “failure”, in which the probability of success is the same every time the experiment is conducted.[1] It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).[2]
The mathematical formalisation of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.
Since a Bernoulli trial has only two possible outcomes, it can be framed as some “yes or no” question. For example:
One of the greatest challenges of modern physics is to find a coherent method for describing phenomena, on the cosmic and microscale. For over a hundred years, to describe reality on a cosmic scale we have been using general relativity theory, which has successfully undergone repeated attempts at falsification.
Albert Einstein curved space-time to describe gravity, and despite still-open questions about dark matter or dark energy, it seems, today, to be the best method of analyzing the past and future of the universe.
To describe phenomena on the scale of atoms, we use the second great theory: quantum mechanics, which differs from general relativity in basically everything. It uses flat space-time and a completely different mathematical apparatus, and most importantly, perceives reality radically differently.
Scientists have fused brain-like tissue with electronics to make an ‘organoid neural network’ that can recognise voices and solve a complex mathematical problem. Their invention extends neuromorphic computing – the practice of modelling computers after the human brain – to a new level by directly including brain tissue in a computer.
The system was developed by a team of researchers from Indiana University, Bloomington; the University of Cincinnati and Cincinnati Children’s Hospital Medical Centre, Cincinnati; and the University of Florida, Gainesville. Their findings were published on December 11.
Researchers taking part in the Human Brain Project have identified a mathematical rule that governs the distribution of neurons in our brains.
The rule predicts how neurons are distributed in different parts of the brain, and could help scientists create precise models to understand how the brain works and develop new treatments for neurological diseases.
In the wonderful world of statistics, if you consider any continuous random variable, the logarithm of that variable will often follow what’s known as a lognormal distribution. Defined by the mean and standard deviation, it can be visualized as a bell-shaped curve, only with the curve being wider than what you’d find in a normal distribution.
ChatGPT may do an impressive job at correctly answering complex questions, but a new study suggests it may be absurdly easy to convince the AI chatbot that it’s in the wrong.
A team at Ohio State University challenged large language models (LLMs) like ChatGPT to a variety of debate-like conversations in which a user pushed back when the chatbot presented a correct answer.
Through experimenting with a broad range of reasoning puzzles, including math, common sense, and logic, the study found that when presented with a challenge, the model was often unable to defend its correct beliefs and instead blindly believed invalid arguments made by the user.
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The full, weird story of the quantum world is much too large for a single article, but the period from 1905, when Einstein first published his solution to the photoelectric puzzle, to the 1960’s, when a complete, well-tested, rigorous, and insanely complicated quantum theory of the subatomic world finally emerged, is quite the story.
This quantum theory would come to provide, in its own way, its own complete and total revision of our understanding of light. In the quantum picture of the subatomic world, what we call the electromagnetic force is really the product of countless microscopic interactions, the work of indivisible photons, who interact in mysterious ways. As in, literally mysterious. The quantum framework provides no picture as to how subatomic interactions actually proceed. Rather, it merely gives us a mathematical toolset for calculating predictions. And so while we can only answer the question of how photons actually work with a beleaguered shrug, we are at least equipped with some predictive power, which helps assuage the pain of quantum incomprehensibility.
Doing the business of physics – that is, using mathematical models to make predictions to validate against experiment – is rather hard in quantum mechanics. And that’s because of the simple fact that quantum rules are not normal rules, and that in the subatomic realm all bets are off.
