Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural framework for capturing hierarchical relationships between datapoints and allowing for finer separability between their embeddings. However, current hyperbolic learning approaches are still prone to overfitting, computationally expensive, and prone to instability, especially when attempting to learn the manifold curvature to adapt to tasks and different datasets. To address these issues, our paper presents a derivation for Riemannian AdamW that helps increase hyperbolic generalization ability. For improved stability, we introduce a novel fine-tunable hyperbolic scaling approach to constrain hyperbolic embeddings and reduce approximation errors. Using this along with our curvature-aware learning schema for Riemannian Optimizers enables the combination of curvature and non-trivialized hyperbolic parameter learning. Our approach demonstrates consistent performance improvements across Computer Vision, EEG classification, and hierarchical metric learning tasks while greatly reducing runtime.

Polynomial Neural Networks (PNNs) possess a rich algebraic and geometric structure. However, their identifiability--a key property for ensuring interpretability-- remains poorly understood. In this work, we present a comprehensive analysis of the identifiability of deep PNNs, including architectures with and without bias terms. Our results reveal an intricate interplay between activation degrees and layer widths in achieving identifiability. As special cases, we show that architectures with non-increasing layer widths are generically identifiable under mild conditions, while encoder-decoder networks are identifiable when the decoder widths do not grow too rapidly compared to the activation degrees. Our proofs are constructive and center on a connection between deep PNNs and low-rank tensor decompositions, and Kruskal-type uniqueness theorems. We also settle an open conjecture on the dimension of PNN's neurovarieties, and provide new bounds on the activation degrees required for it to reach the expected dimension.

'Ringleader' of alleged UFC drone attack to kill Trump is unmasked as illegal migrant who was granted DACA stay under Obama Watch horrifying drone video that follows woman's plunge to death after bungee team threw her from bridge without rope Horrific new videos blow Texas woman's mystery death wide open: Her agonizing'final gasp'... unthinkably vile corpse claims... and sick past of man who saw her last Taylor Swift's bottomless thirst for attention, her greed and sheer tackiness are now truly unbearable... this latest stunt has shown her true colors: MAUREEN CALLAHAN Spy world panic as Tulsi Gabbard prepares to unleash bombshell file dumps on secret CIA'mind control' project and Dr. Fauci Beloved mattress company backed by Travis Kelce files for bankruptcy... but makes key promise to customers Olivia Wilde, 42, complains about being on Maxim's Hot 100 List calling it the'most f***** up thing in the world' All my friends are suddenly getting divorced. Mid-life wives share taboo sex confessions about why they really leave... including common position that made one hate her husband: JANA HOCKING Kanye West's wife Bianca Censori raises eyebrows in plunging white lace lingerie as she photographs a nude model at Art Basel in Switzerland Knicks set to come face to face with Trump after president was'thunderously booed' at NBA Finals game Sensational REAL reason Jelly Roll is divorcing Bunnie XO: Insiders reveal'preacher's wife' bombshell that's the talk of Nashville... truth about legendary rocker cuckolding rumor... and G-string mishap Has Taylor Swift already revealed her wedding dress designer? Teen tourist thrown to death by Central Park horse was trying to save mom who flew out of carriage during family's first visit to Big Apple Father keeps his cool as shouting man calls cops on him for taking his two young daughters into women's restroom Trump privately frets Bibi Netanyahu's zeal to'bomb everyone' could turn him into another disgraced president'Moscow will burn', Zelensky vows as Russia's capital is blanketed in toxic smoke following huge Ukraine drone attack He drove a Rolls-Royce and lived the American dream. But behind the Gucci was the ATF's most unlikely secret weapon. What do aliens EAT? Scientist reveals the foods extraterrestrials would go for on Earth - and why E.T.'s favourite Reese's Pieces are off the cards In the 1982 blockbuster, E.T. the Extra-Terrestrial, E.T. is lured out of hiding using a trail of Reese's Pieces.

We study the fundamental problem of estimating an unknown discrete distribution p over d symbols, given n i.i.d.

A Border Force officer and his handler who worked for Chinese intelligence in the UK have been jailed. Chi Leung Peter Wai, 40, was sentenced to 10 years and Chung Biu Bill Yuen, 65, given an eight year term after being found guilty of assisting a foreign intelligence service, an offence under the National Security Act. Wai used his position as a Border Force officer to access to the Home Office computer system to track Hong Kong dissidents in the UK, was also convicted of misconduct in public office. The judge Mrs Justice Cheema-Grubb told the men that their actions threaten the sovereignty of the state during sentencing remarks at the Old Bailey on Thursday. The dual Chinese-British nationals were found guilty after a trial last month.

Repeated multi-unit auctions, where a seller allocates multiple identical items over many rounds, are common mechanisms in electricity markets and treasury auctions. We compare the two predominant formats: uniform-price and discriminatory auctions, focusing on the perspective of a single bidder learning to bid against stochastic adversaries. We characterize the learning difficulty in each format, showing that the regret scales similarly for both auction formats under both fullinformation and bandit feedback, as Θ( T)and Θ(T2/3), respectively. However, analysis beyond worst-case regret reveals structural differences: uniform-price auctions may admit faster learning rates, with regret scaling as Θ( T)in settings where discriminatory auctions remain at Θ(T2/3). Finally, we provide a specific analysis for auctions in which the other participants are symmetric and have unitdemand, and show that in these instances, a similar regret rate separation appears.

AI makes Pompeii victim's final moments look shockingly real The archaeologists behind the video believe the man covered his head with a bowl to protect himself from volcanic debris. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. This victim of the 79 CE eruption of Mount Vesuvius was discovered in the Pompeii archaeological area near Naples in southern Italy. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

Current transformer-based imitation learning approaches introduce discrete action representations and train an autoregressive transformer decoder on the resulting latent code. However, the initial quantization breaks the continuous structure of the action space thereby limiting the capabilities of the generative model. We propose a quantization-free method instead that leverages Generative InfiniteVocabulary Transformers (GIVT) as a direct, continuous policy parametrization for autoregressive transformers.

We study the regret in stochastic Multi-Armed Bandits (MAB) with multiple agents that communicate over an arbitrary connected communication graph. We analyzed a variant of Cooperative Successive Elimination algorithm, Coop-SE, and show an individual regret bound of O(R/m+A2 +A logT) and a nearly matching lower bound. Here Ais the number of actions, T the time horizon, mthe number of agents, and R= P i>0 log(T)/ i is the optimal single agent regret, where i is the sub-optimality gap of action i. Our work is the first to show an individual regret bound in cooperative stochastic MAB that is independent of the graph's diameter. When considering communication networks there are additional considerations beyond regret, such as message size and number of communication rounds. First, we show that our regret bound holds even if we restrict the messages to be of logarithmic size. Second, for logarithmic number of communication rounds, we obtain a regret bound of O(R/m+AlogT).

Accurate polyp sizing during endoscopy is crucial for cancer risk assessment but is hindered by subjective methods and inadequate datasets lacking integrated 2D appearance, 3D structure, and real-world size information. We introduce PolypSense3D, the first multi-source benchmark dataset specifically targeting depth-aware polyp size measurement. It uniquely integrates over 43,000 frames from virtual simulations, physical phantoms, and clinical sequences, providing synchronized RGB, dense/sparse depth, segmentation masks, camera parameters, and millimeter-scale size labels derived via a novel forceps-assisted in-vivo annotation technique. To establish its value, we benchmark state-of-the-art segmentation and depth estimation models. Results quantify significant domain gaps between simulated/phantom and clinical data and reveal substantial error propagation from perception stages to final size estimation, with the best fully automated pipelines achieving an average Mean Absolute Error (MAE) of 0.95 mm on the clinical data subset. Publicly released under CCBY-SA 4.0 with code and evaluation protocols, PolypSense3D offers a standardized platform to accelerate research in robust, clinically relevant quantitative endoscopic vision.