Neural networks have been extremely successful in modern machine learning, achieving the state-of-the-art inawiderangeofdomains, including image-recognition, speech-recognition, andgame-playing [ 14, 18, 23, 37]. Practitioners often train deep neural networks with hundreds of layers and millions of parameters and manage to find networks with good out-of-sample performance.However, this practical prowess isaccompanied by feeble theoreticalunderstanding.

Langevin dynamics (MFLD) (Mei et al., 2018; Hu et al., 2019) is particularly attractive due to the MFLD arises from a noisy gradient descent update on the parameters, where Gaussian noise is injected to the gradient to encourage "exploration". Furthermore, uniform-in-time estimates of the particle discretization error have also been established (Suzuki et al., The goal of this work is to address the following question.

Chinese robotics firm MirrorMe Technology unveiled Bolt, a 5-foot-7-inch humanoid robot that outran founder Wang Hongtao at 22 mph using advanced balance control.

PCWorld reports that Anthropic has significantly upgraded Claude's free tier with new Skills feature for automating recurring tasks and Connectors for integrating external services like Canva and Slack. Free users can now create and edit Word, Excel, PowerPoint, and PDF files directly within Claude, plus enjoy longer conversations and enhanced voice/image search capabilities. These improvements position Claude as a stronger competitor against ChatGPT, especially as OpenAI recently introduced ads to its platform. AI company Anthropic is now upgrading the free version of its Claude chatbot with several features that were previously exclusive to paying users, reports Engadget . Free users can now create and edit files like Word documents, Excel spreadsheets, PowerPoint presentations, and PDFs directly within Claude.

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Intheadversarialsetting,weintroduce the notion ofadversarial VC-dimensionwhich is the VC-dimension of the corrupted hypothesis class.

ALS stole this musician's voice. AI let him sing again. Patrick Darling used a music tool from ElevenLabs to perform a song with his former bandmates. There are tears in the audience as Patrick Darling's song begins to play. It's a heartfelt song written for his great-grandfather, whom he never got the chance to meet. But this performance is emotional for another reason: It's Darling's first time on stage with his bandmates since he lost the ability to sing two years ago.