A fundamental property of deep learning normalization techniques, such as batch normalization, is making the pre-normalization parameters scale invariant. The intrinsic domain of such parameters is the unit sphere, and therefore their gradient optimization dynamics can be represented via spherical optimization with varying effective learning rate (ELR), which was studied previously. However, the varying ELR may obscure certain characteristics of the intrinsic loss landscape structure. In this work, we investigate the properties of training scale-invariant neural networks directly on the sphere using a fixed ELR. We discover three regimes of such training depending on the ELR value: convergence, chaotic equilibrium, and divergence. We study these regimes in detail both on a theoretical examination of a toy example and on a thorough empirical analysis of real scale-invariant deep learning models. Each regime has unique features and reflects specific properties of the intrinsic loss landscape, some of which have strong parallels with previous research on both regular and scale-invariant neural networks training. Finally, we demonstrate how the discovered regimes are reflected in conventional training of normalized networks and how they can be leveraged to achieve better optima.

A generic D-dimensional Gaussian can be conditioned or projected onto the D-1 unit sphere, thereby leading to the well-known Fisher-Bingham (FB) or Angular Gaussian (AG) distribution families, respectively. These are some of the most fundamental distributions on the sphere, yet cannot straightforwardly be written as a normalizing flow except in two special cases: the von-Mises Fisher in D=3 and the central angular Gaussian in any D. In this paper, we describe how to generalize these special cases to a family of normalizing flows that behave similarly to the full FB or AG family in any D. We call them "zoom-linear-project" (ZLP)-Fisher flows. Unlike a normal Fisher-Bingham distribution, their composition allows to gradually add complexity as needed. Furthermore, they can naturally handle conditional density estimation with target distributions that vary by orders of magnitude in scale - a setting that is important in astronomical applications but that existing flows often struggle with. A particularly useful member of the new family is the Kent analogue that can cheaply upgrade any flow in this situation to yield better performance.

Fox News correspondent William La Jeunesse joins'Fox News Sunday' to discuss the evolution of AI and the push lawmakers are making to regulate it. The use of artifical intelligence to reimagine the classic film "The Wizard of Oz" will likely see mixed reactions from fans, experts told Fox News Digital. While "film purists" may resist the idea of using generative AI to give classic films an entire makeover, the technology could "breathe new life" into hit movies -- including "The Wizard of Oz." Warner Bros. Discovery, Google Cloud and Magnopus have set out to do just that by creating an immersive experience for fans of the 1939 classic. The new "Wizard of Oz" experience is set to premiere at the Las Vegas Sphere on Aug. 28. "The fan reaction will likely split into two distinct camps," Michael Walker, CEO of AI-First at Trilogy, told Fox News Digital.

Google has used AI to revamp one of the most beloved films of all time for a 360-degree Sin City screen with the highest resolution in the world. The rerolled version of The Wizard of Oz will debut this August at The Sphere, the Las Vegas entertainment venue with a famously globular LED screen. Whether a technical marvel, dystopian nightmare fuel or some combination, the project will surely continue The Sphere's penchant for extravagant spectacles that persuade tourists to plunk down hundreds of dollars to sit for a few hours in one of its 17,600 seats. Sphere Entertainment, the company behind the venue, worked on the project with Google, Magnopus and Warner Bros. Discovery, which owns The Wizard of Oz rights. Google describes it as an "epic undertaking of creativity and technology," humbly likening it to the cinematic boundaries broken by the acclaimed Technicolor original.

Large language models (LLMs) have significantly improved their reasoning capabilities; however, they still struggle with complex multi-step mathematical problem-solving due to error propagation, lack of self-correction, and limited adaptability to diverse reasoning styles. Existing methods rely on static fine-tuning or prompt engineering, which fail to generalize across problem complexities, while the scarcity of high-quality preference data further hinders reliable reasoning. We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs) by iteratively generating, correcting, and diversifying reasoning chains. SPHERE operates in three stages: (i) Self-Generation, where the model autonomously constructs problem-solving steps; (ii) Self-Correction, enabling it to identify and rectify errors; and (iii) Diversity Induction, improving robustness through multiple valid reasoning trajectories. This self-evolution mechanism strengthens mathematical reasoning and enhances model reliability. Evaluations on MATH 500, GSM8K, AIME, AMC, and Olympiad show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks. Our findings demonstrate that self-evolving models can close the reasoning gap between SLMs and state-of-the-art LLMs, making mathematical AI more reliable, scalable, and efficient.

Meta has open-sourced a machine-learning resource that could one day supplant Wikipedia as the world's biggest publicly available knowledge-verification database. Dubbed Sphere, it can be used to perform knowledge-intensive natural language processing, or KI-NLP, we're told. In practical terms, that means it can be used to answer complicated questions using natural language, and find sources for claims. A given example of its use is asking Sphere, "Who is Joëlle Sambi Nzeba?" Wikipedia doesn't have an entry for her, but Sphere said she was "born in Belgium and grew up partly in Kinshasa (Congo). She currently lives in Brussels. She is a writer and slammer, alongside her activism in a feminist movement," and links to a website where it got that information about her work.

Insta360, best known for its action and 360 degree cameras, has just launched an interesting drone camera. The Insta360 Sphere attaches around the body of DJI's Mavic Air 2 or Air 2S drones, letting you film 5.7K 360 footage or create regular 2D videos with the option of reframing them later in post. Better still, Insta360's tech ensures that the drone is "invisible" in shots. Since 360 cameras film in all directions, half the video can be obstructed by the drone itself. However, Insta360 mounted cameras on either side of the drone to ensure it doesn't appear in the footage.

Robot bees are no replacement for our vital pollinators here on Earth. Up on the International Space Station, however, robots bearing the bee name could help spacefaring humans save precious time. On Friday, NASA astronaut Anne McClain took one of the trio of Astrobees out for a spin. Bumble and its companion Honey both arrived on the ISS a month ago, and are currently going through a series of checks. Bumble passed the first hurdle when McClain manually flew it around the Japanese Experiment Module.

Quantum computing and machine learning are two of the most exciting technologies that can transform businesses. We can only imagine how powerful it can be if we can combine the power of both of these technologies. When we can integrate quantum algorithms in programs based on machine learning, that is called quantum machine learning. This fascinating area has been a major area of tech firms, and they have brought out tools and platforms to deploy such algorithms effectively. Some of these include TensorFlow Quantum from Google, Quantum Machine Learning (QML) library from Microsoft, QC Ware Forge built on Amazon Braket, etc. Students skilled in working with quantum machine learning algorithms can be in great demand due to the opportunities the field holds.

Artificial intelligence (AI) systems, such as machine learning algorithms, have allowed scientists, marketers and governments to shed light on correlations that remained invisible until now. Beforehand, the dots that we had to connect in order to imagine a new knowledge were either too numerous, too sparse or not even detected. Sometimes, the information was not stored in the same data lake or format and was not able to communicate. But in creating new bridges with AI, many problems appeared such as bias reproduction, unfair inferences or mass surveillance. Our aim is to show that, on one hand, the AI's deep ethical problem lays essentially in these new connections made possible by systems interoperability. In connecting the spheres of our life, these systems undermine the notion of justice particular to each of them, because the new interactions create dominances of social goods from a sphere to another. These systems make therefore spheres permeable to one another and, in doing so, they open to progress as well as to tyranny. On another hand, however, we would like to emphasize that the act to connect what used to seem a priori disjoint is a necessary move of knowledge and scientific progress. This article was presented during The Society for Philosophy and Technology Conference (June 28-30, 2021).