Mathematics for Machine Learning | Companion webpage to the book “Mathematics for Machine Learning”. Copyright 2020 by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong. Published by Cambridge University Press. “I Mapped the Invisible”: American High School Student Groundbreaking AI Reveals 1.5 Million Space Objects Previously Hidden from Astronomers In a remarkable turn of events that challenges the way we think about space exploration, a high school student in California has made a discovery that could reshape our understanding of the cosmos. Matteo Paz, a teenager with a sharp aptitude for computer science, has developed an artificial intelligence model that uncovered 1.5 million space objects previously unknown to astronomers. The objects were hidden in plain sight within a vast dataset collected by NASA’s NEOWISE mission, a project designed to track near-Earth asteroids. The Genesis of an Unexpected Discovery Matteo Paz’s journey into deep space began during the summer of 2022 when he participated in Caltech’s Planet Finder Academy. The program, led by Professor Andrew Howard, aims to provide high school students with direct exposure to advanced astronomical research. Initially designed to observe and track asteroids near Earth, NEOWISE had spent more than a decade gathering infrared data that covered the entire sky.
Scientists just developed a new AI modeled on the human brain — it's outperforming LLMs like ChatGPT at reasoning tasks Scientists have developed a new type of artificial intelligence (AI) model that can reason differently from most large language models (LLMs) like ChatGPT, resulting in much better performance in key benchmarks. The new reasoning AI, called a hierarchical reasoning model (HRM), is inspired by the hierarchical and multi-timescale processing in the human brain — the way different brain regions integrate information over varying durations (from milliseconds to minutes). Scientists at Sapient, an AI company in Singapore, say this reasoning model can achieve better performance and can work more efficiently. The HRM model has 27 million parameters while using 1,000 training samples, the scientists said in a study uploaded June 26 to the preprint arXiv database (which has yet to be peer-reviewed). HRM scored 40.3% in ARC-AGI-1, compared with 34.5% for OpenAI's o3-mini-high, 21.2% for Anthropic's Claude 3.7 and 15.8% for Deepseek R1. Related: AI is entering an 'unprecedented regime.'
Deep learning, transformers and graph neural networks: a linear algebra perspective | Numerical Algorithms Graphs serve as powerful tools for representing relationships and interactions in various domains such as social networks (e.g. identify fake news, predict future friends, learn multi-faceted interactions among users) [50, 51], chemistry (generate new drugs and materials, predict chemical properties) [52, 53], recommender systems (e.g., leverage consumer-product choices) [54, 55], knowledge graphs (reasoning with entity relationships) [56, 57], natural language processing (e.g. large language models) [17], physics (e.g. learn from interactions of particles in systems, detect particles, accelerate physics research) [58, 59], neuroscience (e.g., learn functions of brain regions through connectivity, understand brain mechanisms and neuro-degenerative diseases) [60], transportation (e.g., learn traffic behavior across road networks, predict time estimates across multilayered networks) and more. 5.1 Graph neural networks (GNNs) 5.2 Graph convolutional networks (GCNs) 1. 1. Positional encoding
DeepMind AI One-Ups Mathematicians at a Calculation Crucial to Computing DeepMind has done it again. After solving a fundamental challenge in biology—predicting protein structure—and untangling the mathematics of knot theory, it’s taken aim at a fundamental computing process embedded inside thousands of everyday applications. From parsing images to modeling weather or even probing the inner workings of artificial neural networks, the AI could theoretically speed up calculations across a range of fields, increasing efficiency while cutting energy use and costs. But more impressive is how they did it. “Algorithms have been used throughout the world’s civilizations to perform fundamental operations for thousands of years,” wrote co-authors Drs. AlphaTensor blazes a trail to a new world where AI designs programs that outperform anything humans engineer, while simultaneously improving its own machine “brain.” Enter the Matrix Multiplication The problem AlphaTensor confronts is matrix multiplication. But what if there are even more efficient methods?
Visualizing Algorithms The power of the unaided mind is highly overrated… The real powers come from devising external aids that enhance cognitive abilities. —Donald Norman Algorithms are a fascinating use case for visualization. To visualize an algorithm, we don’t merely fit data to a chart; there is no primary dataset. But algorithms are also a reminder that visualization is more than a tool for finding patterns in data. #Sampling Before I can explain the first algorithm, I first need to explain the problem it addresses. Light — electromagnetic radiation — the light emanating from this screen, traveling through the air, focused by your lens and projected onto the retina — is a continuous signal. This reduction process is called sampling, and it is essential to vision. Sampling is made difficult by competing goals. Unfortunately, creating a Poisson-disc distribution is hard. You can see from these dots that best-candidate sampling produces a pleasing random distribution. Here’s how it works: Now here’s the code:
Deep Learning Is Going to Teach Us All the Lesson of Our Lives: Jobs Are for Machines — Basic income Deep Learning Is Going to Teach Us All the Lesson of Our Lives: Jobs Are for Machines (An alternate version of this article was originally published in the Boston Globe) On December 2nd, 1942, a team of scientists led by Enrico Fermi came back from lunch and watched as humanity created the first self-sustaining nuclear reaction inside a pile of bricks and wood underneath a football field at the University of Chicago. Known to history as Chicago Pile-1, it was celebrated in silence with a single bottle of Chianti, for those who were there understood exactly what it meant for humankind, without any need for words. Now, something new has occurred that, again, quietly changed the world forever. The language is a new class of machine learning known as deep learning, and the “whispered word” was a computer’s use of it to seemingly out of nowhere defeat three-time European Go champion Fan Hui, not once but five times in a row without defeat. What actually ended up happening when they faced off?
Researchers find that large language models struggle with math Join Transform 2021 this July 12-16. Register for the AI event of the year. Mathematics is the foundation of countless sciences, allowing us to model things like planetary orbits, atomic motion, signal frequencies, protein folding, and more. Moreover, it’s a valuable testbed for the ability to problem solve, because it requires problem solvers to analyze a challenge, pick out good methods, and chain them together to produce an answer. It’s revealing, then, that as sophisticated as machine learning models are today, even state-of-the-art models struggle to answer the bulk of math problems correctly. A new study published by researchers at the University of California, Berkeley finds that large language models including OpenAI’s GPT-3 can only complete 2.9% to 6.9% of problems from a dataset of over 12,500. Prior research has demonstrated the usefulness of AI that has a firm grasp of mathematical concepts. Image Credit: MATH VentureBeat