We consider the optimization of cost functionals on manifolds and derive a variational approach to accelerated methods on manifolds. We demonstrate the methodology on the infinite-dimensional manifold of diffeomorphisms, motivated by registration problems in computer vision. We build on the variational approach to accelerated optimization by Wibisono, Wilson and Jordan, which applies in finite dimensions, and generalize that approach to infinite dimensional manifolds. We derive the continuum evolution equations, which are partial differential equations (PDE), and relate them to simple mechanical principles. Our approach can also be viewed as a generalization of the $L^2$ optimal mass transport problem. Our approach evolves an infinite number of particles endowed with mass, represented as a mass density.

Regression with group-sparsity penalty plays a central role in high-dimensional prediction problems. Most of existing methods require the group structure to be known a priori. In practice, this may be a too strong assumption, potentially hampering the effectiveness of the regularization method. To circumvent this issue, we present a method to estimate the group structure by means of a continuous bilevel optimization problem where the data is split into training and validation sets. Our approach relies on an approximation scheme where the lower level problem is replaced by a smooth dual forward-backward algorithm with Bregman distances. We provide guarantees regarding the convergence of the approximate procedure to the exact problem and demonstrate the well behaviour of the proposed method on synthetic experiments. Finally, a preliminary application to genes expression data is tackled with the purpose of unveiling functional groups.

Multilingual topic models can reveal patterns in cross-lingual document collections. However, existing models lack speed and interactivity, which prevents adoption in everyday corpora exploration or quick moving situations (e.g., natural disasters, political instability). First, we propose a multilingual anchoring algorithm that builds an anchor-based topic model for documents in different languages. Then, we incorporate interactivity to develop MTAnchor (Multilingual Topic Anchors), a system that allows users to refine the topic model. We test our algorithms on labeled English, Chinese, and Sinhalese documents. Within minutes, our methods can produce interpretable topics that are useful for specific classification tasks.

In this paper, we study the problems of principle Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing Markov chains and two-Time-Scale Stochastic Approximation, showing that it achieves the optimal rate of convergence. In the process, we develop tools for understanding stochastic processes with Markovian noise which might be of independent interest.

A technical challenge of deep learning is recognizing target classes without seen data. Zero-shot learning leverages semantic representations such as attributes or class prototypes to bridge source and target classes. Existing standard zero-shot learning methods may be prone to overfitting the seen data of source classes as they are blind to the semantic representations of target classes. In this paper, we study generalized zero-shot learning that assumes accessible to target classes for unseen data during training, and prediction on unseen data is made by searching on both source and target classes. We propose a novel Deep Calibration Network (DCN) approach towards this generalized zero-shot learning paradigm, which enables simultaneous calibration of deep networks on the confidence of source classes and uncertainty of target classes. Our approach maps visual features of images and semantic representations of class prototypes to a common embedding space such that the compatibility of seen data to both source and target classes are maximized. We show superior accuracy of our approach over the state of the art on benchmark datasets for generalized zero-shot learning, including AwA, CUB, SUN, and aPY.

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Trump announces White House Chief of Staff Susie Wiles diagnosed with'early stage' breast cancer Trump's billionaire adviser publicly rebukes Iran war as JD Vance camp erupts over Israel nuke threat Kristi Noem referred for criminal investigation after'lying under oath' about $220M vanity scheme You don't have to fly to Turkey or Thailand... and can do it on your lunch break! Diet that cures pain and inflammation, devised by experts: Constant sickness and aching joints are the first signs of problems that left unchecked can turn deadly. Timothee Chalamet and Kylie Jenner's strained Oscars chat decoded by lip-reader as he gets snubbed and mocked The snubbed A-lister, drunken pics and C-List stars who plagued the most'exclusive' party: All the Oscars gossip Hollywood didn't want you to see at very messy afterparty Proof Leonardo DiCaprio sent a CLONE to the Oscars... alarming truth about Teyana Taylor's blow up... and a very dirty Barbra Streisand rumor: KENNEDY's most brutal review yet NYC's smiling socialist mayor is VERY different behind the scenes, as progressives who crossed him allege tyrannical and ruthless behavior Awful Timothee Chalamet's ego is bigger than Kylie's inflated butt... but it's so clear what's really going on here. Trump stunned by lurid rumor about Iran's new'gay' ayatollah Chilling new details of dismembered Emily Pike's final hours after she was snatched in Arizona desert and man detectives now believe murdered her'It's like he was possessed': Terrifying moment Alexander brother turned into a'monster' and raped me... and the four chilling words he said after horror attack - alleged victim claims After Oscars 2026, the whispered fear among Hollywood doctors is now massive... this is so much bigger than Ozempic. A-list stars ditch formal Oscars red carpet dresses for sexy party looks - with Jeff Goldblum's wife Emilie Livingston, Heidi Klum, Amelia Gray Hamlin and Kate Hudson turning up the heat at Vanity Fair bash Shock as man begs for death penalty for HIMSELF after pinning dead pastor's hands to wall and targeting other religious leaders How Oscars 2026 proved Hollywood has overdosed on Ozempic: Leading doctors name stars now at'extreme' risk... and reveal terrifying new side effects Billionaire Peter Thiel holds secret'Antichrist' meetings on the Vatican's doorstep READ MORE: Catholic priest warns'the stage is set' for the rise of the Antichrist US billionaire Peter Thiel is hosting a series of closed-door lectures in Rome on the doorstep of the Vatican, focused on the concept of the Antichrist.

Multiscale-structured miniaturized 3D force sensors CC BY 4.0 Robots are becoming increasingly capable in vision and movement, yet touch remains one of their major weaknesses. Now, researchers have developed a miniature tactile sensor that could give robots something much closer to a human sense of touch. The technology, developed by researchers at the University of Cambridge, is based on liquid metal composites and graphene - a two-dimensional form of carbon. The'skin' allows robots to detect not just how hard they are pressing on an object, but also the direction of applied forces, whether an object is slipping, and even how rough a surface is, at a scale small enough to rival the spatial resolution of human fingertips. Their results are reported in the journal .

Author Wynton Hall alleges Google Gemini flagged Republican senators' rhetoric as hate speech while identifying no Democratic violations, raising questions about AI bias.