We provide the supplements of "Contextual Gaussian Process Bandits with Neural Networks" here. Specifically, we discuss alternative acquisition functions that can be incorporated with the neural network-accompanied Gaussian process (NN-AGP) model in Section 6. In Section 7, we discuss the bandit algorithm with NN-AGP, where the neural network approximation error is considered. In Section 8, we provide the detailed proof of theorems. We provide the experimental details and include additional numerical experiments in Section 9. Last we discuss the limitations of NN-AGP and propose the potential approaches to addressing the limitations for future work, including sparse NN-AGP for alleviating computational burdens and transfer learning with NN-AGP to address cold-start issue; see Section 10. In the main text, we employ the upper confidence bound function as the acquisition function in the contextual Bayesian optimization approach. Here, we provide two alternative choices: Thompson sampling (TS) and knowledge gradient (KG). We describe the two procedures of the contextual GP bandit problems with NN-AGP, where the acquisition function is replaced by TS or KG. It chooses the action that maximizes the expected reward with respect to a random belief that is drawn for a posterior distribution. Besides the multi-armed bandit problems, TS has also achieved both theoretical and practical success in BO and Gaussian process regression. For more detailed discussions on TS, we refer to [87, 88]. Specifically, we propose a neural network-accompanied Gaussian process Thompson sampling (NNAGP-TS) approach to address contextual GP bandits. The approach works as follows. In each iteration, NN-AGP-TS first fits an NN-AGP model with the historic data. Then, given the current contextual variable, a realization of the Gaussian process with respect to x X is sampled from the posterior distribution conditional on the historic data1.

Musk, who co-founded the company that created ChatGPT with Altman, wants more than $130 billion in damages in a lawsuit that could shakeup the artificial intelligence landscape. The BBC's Lily Jamali explains why the two tech giants are facing off in court. How much screen time is too much for under fives? Some major retailers and independent stores have introduced AI body scans, CCTV or facial recognition equipment to identify crimes like shoplifting. What does TikTok's deal mean for America's users?

Deep convolutional neural networks (CNNs) are often of sophisticated design with numerous learnable parameters for the accuracy reason. To alleviate the expensive costs of deploying them on mobile devices, recent works have made huge efforts for excavating redundancy in pre-defined architectures. Nevertheless, the redundancy on the input resolution of modern CNNs has not been fully investigated, i.e., the resolution of input image is fixed. In this paper, we observe that the smallest resolution for accurately predicting the given image is different using the same neural network. To this end, we propose a novel dynamic-resolution network (DRNet) in which the input resolution is determined dynamically based on each input sample. Wherein, a resolution predictor with negligible computational costs is explored and optimized jointly with the desired network.

Deep neural networks are known to be vulnerable to adversarial attacks (AA). For an image recognition task, this means that a small perturbation of the original can result in the image being misclassified. Design of such attacks as well as methods of adversarial training against them are subject of intense research. We re-cast the problem using techniques of Wasserstein distributionally robust optimization (DRO) and obtain novel contributions leveraging recent insights from DRO sensitivity analysis. We consider a set of distributional threat models.

The Download: DeepSeek's latest AI breakthrough, and the race to build world models Plus: China has blocked Meta's $2 billion acquisition of AI startup Manus. On Friday, Chinese AI firm DeepSeek released a preview of V4, its long-awaited new flagship model. Notably, the model can process much longer prompts than its last generation, thanks to a new design that handles large amounts of text more efficiently. While the model remains open source, its performance matches leading closed-source rivals from Anthropic, OpenAI, and Google. Here are three ways V4 could shake up AI . AI systems have already gained impressive mastery over the digital world, but the physical world remains humanity's domain.

A recent attack on Sam Altman's home and OpenAI offices has put corporate security under renewed scrutiny. Records reveal how much some tech firms spend to arm up. Elon Musk called violent crime in San Francisco " horrific " and moved the offices of his social media business X outside the city in 2024 because of safety and business considerations. Other local tech companies have attempted to address their security concerns by partnering directly with cops. Airbnb and Salesforce are among businesses that for years have contracted San Francisco police to protect their offices on a regular basis, according to public records obtained by WIRED.