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Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning

arXiv:2603.08651v2 Announce Type: replace Abstract: We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite, flexible family of Mirror Descent (MD) optimization algorithms. Our approach exploits the rich structure of group entropies, which are generalized entropic functionals governed by group composition laws, encompassing and significantly extending all trace-form...

arXiv CS 9d ago

A Utah high school removed the mirrors from all its bathrooms. Has it made a difference?

A Utah high school removed the mirrors from all its bathrooms. Has it made a difference? One student called the decision to remove the mirrors ‘horrendous’ - Bookmark - CommentsGo to comments A high school near Salt Lake City, Utah is one of the latest to remove the mirrors from its restrooms in an effort to cut down on students showing up late to class.

The Independent World 3h ago

A Unified Variational Design of Predictive Mirror Descent in Convex Games under Stochastic Feedback

Announce Type: cross Abstract: Mirror descent provides a geometric framework for learning in games, but its last-iterate behavior can fail in weakly stable regimes, where the dynamics may exhibit rotational or recurrent transients. Predictive mirror methods mitigate this issue by modifying the feedback entering the mirror update, yet standard predictive variants are typically introduced algorithmically and analyzed one at a time. This letter gives a variational route to predictive feedback...

arXiv CS 8d ago

Carol Vorderman on why Mirror's Pride of Britain is needed 'more than ever'

Carol Vorderman on why Mirror's Pride of Britain is needed 'more than ever' The 2026 Pride of Britain Award nominations are now open, with long-time host Carol Vorderman urging Mirror readers to consider voting for the remarkable everyday heroes in their lives TV legend Carol Vorderman says anyone looking for hope in these dark times will be blown away by “the goodness of people” at the Daily Mirror Pride of Britain Awards. Carol, 65, has been presenting the celebration of the most amazing...

Daily Mirror 4d ago

Iconic 1914 Daily Mirror front page found inside the Royal Box at Epsom as King and Queen head to Derby

Iconic 1914 Daily Mirror front page found inside the Royal Box at Epsom as King and Queen head to Derby EXCLUSIVE: An iconic Daily Mirror front page from 1914 is framed inside the Royal Box at Epsom as King Charles and Queen Camilla head to Derby When the King and Queen walk in to the Royal Box at the Derby - one of the first things they will see is this incredible page one of the Daily Mirror. It’s so special that racecourse bosses have chosen to put it in pride of place on the wall. The...

Daily Mirror 6d ago

Roman telescope's massive infrared mirror is ready to fly

Roman telescope's massive infrared mirror is ready to fly Sadie Harley Scientific Editor Andrew Zinin Lead Editor NASA has completed its final inspection of the primary mirror on the Roman Space Telescope, which measures 2.4 meters (7.9 feet) in diameter and contains a layer of silver hundreds of times thinner than a human hair, at 400 nanometers. The primary mirror will help accomplish Roman's mission objectives using near-infrared light, including studying dark matter and dark energy,...

Phys.org 8d ago

Octopuses use mirrors to find food they cannot see

Octopuses use mirrors to find food they cannot see Octopuses just joined an exclusive intelligence club by learning to use mirrors to find hidden food. - Date: - June 5, 2026 - Source: - Dartmouth College - Summary: - Octopuses may be even smarter than we thought.

Science Daily 5d ago

Octopuses learn mirror-guided navigation to locate prey

Octopuses learn mirror-guided navigation to locate prey Lisa Lock Scientific Editor Robert Egan Associate Editor Octopuses are remarkably intelligent creatures, as was demonstrated by Inky the Octopus's famous escape from the National Aquarium of New Zealand through a drainpipe back to sea in 2016. A new Dartmouth study shows octopuses can use mirrors to find food out of sight, demonstrating spatial cognitive abilities. The results are published in Current Biology.

Phys.org 7d ago

England fan who planned to sell home to fund US World Cup trip gets Hilton offer thanks to the Mirror

England fan who planned to sell home to fund US World Cup trip gets Hilton offer thanks to the Mirror EXCLUSIVE: 'World Cup Guy' Andy Milne received an offer he couldn't refuse: hotel accommodation before and after England's games during the tournament. England's No. 1 fan was inundated with offers of help from the US after the Mirror revealed his plan to sell his home to fund his World Cup trip. But Andy Milne, 63, then received an offer he couldn't refuse: hotel accommodation before and...

Daily Mirror 3d ago

Whatever the mirror test tells us, beluga whales pass it

In hours of underwater video footage from a New York aquarium, a beluga whale named Natasha stretches her neck, pirouettes, nods, and shakes her head in front of a two-way mirror. Her daughter Maris does much the same. According to a new study published in PLOS One, both animals show the behavioral hallmarks of mirror self-recognition—a cognitive ability long considered a marker of self-awareness, and one that had never before been documented in beluga whales.

Ars Technica Science 17d ago