Lifeboat Foundation

Artificial neural networks (ANNs) show a remarkable pattern when trained on natural data irrespective of exact initialization, dataset, or training objective; models trained on the same data domain converge to similar learned patterns. For example, for different image models, the initial layer weights tend to converge to Gabor filters and color-contrast detectors. Many such features suggest global representation that goes beyond biological and artificial systems, and these features are observed in the visual cortex. These findings are practical and well-established in the field of machines that can interpret literature but lack theoretical explanations.

Localized versions of canonical 2D Fourier basis functions are the most observed universal features in image models, e.g. Gabor filters or wavelets. When vision models are trained on tasks like efficient coding, classification, temporal coherence, and next-step prediction goals, these Fourier features pop up in the model’s initial layers. Apart from this, Non-localized Fourier features have been observed in networks trained to solve tasks where cyclic wraparound is allowed, for example, modular arithmetic, more general group compositions, or invariance to the group of cyclic translations.

Researchers from KTH, Redwood Center for Theoretical Neuroscience, and UC Santa Barbara introduced a mathematical explanation for the rise of Fourier features in learning systems like neural networks. This rise is due to the downstream invariance of the learner that becomes insensitive to certain transformations, e.g., planar translation or rotation. The team has derived theoretical guarantees regarding Fourier features in invariant learners that can be used in different machine-learning models. This derivation is based on the concept that invariance is a fundamental bias that can be injected implicitly and sometimes explicitly into learning systems due to the symmetries in natural data.

Cheap data and the absence of coincidences make maths an ideal testing ground for AI-assisted discovery — but only humans will be able to tell good conjectures from bad ones.

Did you hear the news? OpenAI’s newest model can reason across audio, vision, and text in real time.

How does GPT-4o do with math tutoring? 🤔

Sal and his son test it out on a Khan Academy math problem.

Continue reading “AI-powered tutor Khanmigo by Khan Academy: Your 24/7 homework helper” »

This is “OpenAI GPT-4o math with Sal and Imran Khan from Khan Academy” by OpenAI on Vimeo, the home for high quality videos and the people who love them.

In a recent study merging the fields of quantum physics and computer science, Dr. Jun-Jie Zhang and Prof. Deyu Meng have explored the vulnerabilities of neural networks through the lens of the uncertainty principle in physics. Their work, published in the National Science Review, draws a parallel between the susceptibility of neural networks to targeted attacks and the limitations imposed by the uncertainty principle—a well-established theory in quantum physics that highlights the challenges of measuring certain pairs of properties simultaneously.

The researchers’ quantum-inspired analysis of neural network vulnerabilities suggests that adversarial attacks leverage the trade-off between the precision of input features and their computed gradients. “When considering the architecture of deep neural networks, which involve a loss function for learning, we can always define a conjugate variable for the inputs by determining the gradient of the loss function with respect to those inputs,” stated in the paper by Dr. Jun-Jie Zhang, whose expertise lies in mathematical physics.

This research is hopeful to prompt a reevaluation of the assumed robustness of neural networks and encourage a deeper comprehension of their limitations. By subjecting a neural network model to adversarial attacks, Dr. Zhang and Prof. Meng observed a compromise between the model’s accuracy and its resilience.

Here is an interview concerning the current AI and generative AI waves, and their relation to neuroscience. We propose solutions based on new technology from neuroAI – which includes humans ability for reasoning, thought, logic, mathematics, proof etc. – and are therefore poorly modeled by data analysis on its own. Some of our work – also with scholars – has been published, while more is to come in a spin-off setting.

Irina Conboy, Michael Conboy and Josh Mitteldorf discuss one of the central questions in aging research: is aging an active process of the body or is aging a passive process of damage accumulation? See the whole debate on our YouTube Channel: @HealesMovies Josh Mitteldorf, PhD, runs the blog “Aging Matters” (https://joshmitteldorf.scienceblog.com/) and is a consultant in mathematical modeling and creative data analysis. His research areas include evolutionary ecology, biology of aging, and the epidemiology of COVID-19. On the field of aging research, he has published two books,” Cracking The Aging Code”, co-written with Dorion Sagan (https://www.amazon.com/Cracking-Aging-Code-Science-Growing/d…atfound-20 and “Aging is a Group-Selected Adaptation” (https://drive.google.com/file/d/1bs0faQEV3T9cu-Eq079-e5bIGgMwNH08/view). Heales website (Healthy Life Extension Society): https://heales.org/ Subscribe to our newsletter: https://heales.org/newsletter/ Contact e-mail: [email protected] #science #aging #rejuvenation #biology #health #longevity #antiaging #debate #stemcells #programmedaging #entropy #cancer #conboy #conboys #mitteldorf Music: Closer To Your Dream by Keys of Moon | https://soundcloud.com/keysofmoon (CC BY 4.0)

Ever wonder what happens when you fall into a black hole? Now, thanks to a new, immersive visualization produced on a NASA supercomputer, viewers can plunge into the event horizon, a black hole’s point of no return.

In this visualization of a flight toward a supermassive black hole, labels highlight many of the fascinating features produced by the effects of general relativity along the way. Produced on a NASA supercomputer, the simulation tracks a camera as it approaches, briefly orbits, and then crosses the event horizon — the point of no return — of a monster black hole much like the one at the center of our galaxy. (Video: NASA’s Goddard Space Flight Center/J. Schnittman and B. Powell)

“People often ask about this, and simulating these difficult-to-imagine processes helps me connect the mathematics of relativity to actual consequences in the real universe,” said Jeremy Schnittman, an astrophysicist at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, who created the visualizations. “So I simulated two different scenarios, one where a camera — a stand-in for a daring astronaut — just misses the event horizon and slingshots back out, and one where it crosses the boundary, sealing its fate.”

Often perceived as abstract and challenging, physics covers fundamental aspects of the universe, from the tiny world of quantum mechanics to the vast cosmos of general relativity. However, it often comes with intricate mathematical formulations that intimidate many learners. Visual Intuitive Physics is an emerging field that seeks to transform this complexity into accessible visual experiences, making physics more tangible and relatable. By employing visual aids and intuitive methodologies, this approach enhances the understanding of physical principles for students, researchers, and enthusiasts.

Understanding complex physics concepts often requires intuitive visualization that transcends verbal and mathematical explanations. Visualization in physics involves using graphs, diagrams, simulations, and other visual tools to provide a tangible understanding of abstract concepts. For instance, Marr and Bruce emphasized that visual tools significantly enhance conceptual understanding in students by providing concrete ways to comprehend physical laws.

Visualization helps bridge the gap between theoretical concepts and practical understanding. Per Kozma and Russell, visualization is pivotal in building cognitive structures that make understanding and remembering scientific principles easier. This is particularly significant for concepts that lack direct physical analogs, such as quantum mechanics and relativity.