They are used to test the proposed enhancement approach iGA T. In general, ADP employs an ensemble by averaging, i.e., (C 1) ( C 1) Adversarial examples are generated to compute the losses by using the PGD attack. Our main theorem builds on a supporting Lemma 2.1. We start from the cross-entropy loss curvature measured by Eq. The above new expression of T (x) helps bound the difference between h(x) and h(x). Note that these three cases are mutually exclusive.

Guided by this theory, we propose an effective approach to improve ensemble adversarial defense, named interactive global adversarial training (iGA T).

Along with the dataset, two tasks are proposed to evaluate machines'

By now Bayesian methods are routinely used in practice for solving inverse problems.

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren't the most advanced in the mathematical canon, the success of AI models in tackling them shows that their mathematical performance has passed a significant threshold, say researchers, and could fundamentally change the way we do mathematics. The questions being solved by AI originate from Hungarian mathematician Paul Erdős, who was famous for his ability to pose useful but difficult questions during a career that spanned over six decades. "The questions tended to be very simple, but very hard," says Thomas Bloom at the University of Manchester, UK. By his death in 1996, there were more than 1000 of these unsolved Erdős problems, spanning a wide range of mathematical disciplines, from combinatorics (the study of combinations) to number theory.

The era of hype first, think later. Demis Hassabis, CEO of Google DeepMind, summed it up in three words: "This is embarrassing." Hassabis was replying on X to an overexcited post by Sébastien Bubeck, a research scientist at the rival firm OpenAI, announcing that two mathematicians had used OpenAI's latest large language model, GPT-5, to find solutions to 10 unsolved problems in mathematics. "Science acceleration via AI has officially begun," Bubeck crowed. Put your math hats on for a minute, and let's take a look at what this beef from mid-October was about. Bubeck was excited that GPT-5 seemed to have somehow solved a number of puzzles known as Erdős problems.

New Scientist changed the UK's freedom of information laws in 2025 By requesting copies of the then-UK technology secretary's ChatGPT logs, New Scientist set a precedent for how freedom of information laws apply to chatbot interactions, helping to hold governments to account Our successful request for Peter Kyle's ChatGPT logs stunned observers When I fired off an email at the start of 2025, I hadn't intended to set a legal precedent for how the UK government handles its interactions with AI chatbots, but that is exactly what happened. It all began in January when I read an interview with the then-UK tech secretary Peter Kyle in . Trying to suggest he used first-hand the technology his department was set up to regulate, Kyle said that he would often have conversations with ChatGPT. AI may blunt our thinking skills - here's what you can do about it That got me wondering: could I obtain his chat history? Freedom of information (FOI) laws are often deployed to obtain emails and other documents produced by public bodies, but past precedent has suggested that some private data - such as search queries - aren't eligible for release in this way. I was interested to see which way the chatbot conversations would be categorised.

This proposed tutorial focuses on Healthcare Domain Applications of NLP, what we have achieved around HealthcareNLP, and the challenges that lie ahead for the future. Existing reviews in this domain either overlook some important tasks, such as synthetic data generation for addressing privacy concerns, or explainable clinical NLP for improved integration and implementation, or fail to mention important methodologies, including retrieval augmented generation and the neural symbolic integration of LLMs and KGs. In light of this, the goal of this tutorial is to provide an introductory overview of the most important sub-areas of a patient- and resource-oriented HealthcareNLP, with three layers of hierarchy: data/resource layer: annotation guidelines, ethical approvals, governance, synthetic data; NLP-Eval layer: NLP tasks such as NER, RE, sentiment analysis, and linking/coding with categorised methods, leading to explainable HealthAI; patients layer: Patient Public Involvement and Engagement (PPIE), health literacy, translation, simplification, and summarisation (also NLP tasks), and shared decision-making support. A hands-on session will be included in the tutorial for the audience to use HealthcareNLP applications. The target audience includes NLP practitioners in the healthcare application domain, NLP researchers who are interested in domain applications, healthcare researchers, and students from NLP fields. The type of tutorial is "Introductory to CL/NLP topics (HealthcareNLP)" and the audience does not need prior knowledge to attend this. Tutorial materials: https://github.com/4dpicture/HealthNLP