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Common smoothness indicators used in Weighted Essentially Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)] have quadratic cost with respect to the order. A set of novel smoothness indicators with linear cost of computation with respect to the order is presented. These smoothness indicators can be used in the context of schemes of the type introduced by Yamaleev and Carpenter [Yamaleev, N.K., Carpenter, M.H.: A systematic methodology to for constructing high-order energy stable WENO schemes. J. Comput. Phys. \textbf{228}(11), 4248-4272 (2009)]. The accuracy properties of the resulting non-linear weights are the same as those arising from using the traditional Jiang-Shu smoothness indicators in Yamaleev-Carpenter-type reconstructions. The increase of the efficiency and ease of implementation are shown.

It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.

Large Language Models (LLMs) and, more specifically, the Generative Pre-Trained Transformers (GPT) can help stakeholders in climate action explore digital knowledge bases and extract and utilize climate action knowledge in a sustainable manner. However, LLMs are "probabilistic models of knowledge bases" that excel at generating convincing texts but cannot be entirely relied upon due to the probabilistic nature of the information produced. This brief report illustrates the problem space with examples of LLM responses to some of the questions of relevance to climate action.

Gene set analysis, a popular approach for analysing high-throughput gene expression data, aims to identify sets of genes that show enriched expression patterns between two conditions. In addition to the multitude of methods available for this task, users are typically left with many options when creating the required input and specifying the internal parameters of the chosen method. This flexibility can lead to uncertainty about the 'right' choice, further reinforced by a lack of evidence-based guidance. Especially when their statistical experience is scarce, this uncertainty might entice users to produce preferable results using a 'trial-and-error' approach. While it may seem unproblematic at first glance, this practice can be viewed as a form of 'cherry-picking' and cause an optimistic bias, rendering the results non-replicable on independent data. After this problem has attracted a lot of attention in the context of classical hypothesis testing, we now aim to raise awareness of such over-optimism in the different and more complex context of gene set analyses. We mimic a hypothetical researcher who systematically selects the analysis variants yielding their preferred results, thereby considering three distinct goals they might pursue. Using a selection of popular gene set analysis methods, we tweak the results in this way for two frequently used benchmark gene expression data sets. Our study indicates that the potential for over-optimism is particularly high for a group of methods frequently used despite being commonly criticised. We conclude by providing practical recommendations to counter over-optimism in research findings in gene set analysis and beyond.

Network meta-analysis (NMA) is a useful tool to compare multiple interventions simultaneously in a single meta-analysis, it can be very helpful for medical decision making when the study aims to find the best therapy among several active candidates. However, the validity of its results is threatened by the publication bias issue. Existing methods to handle the publication bias issue in the standard pairwise meta-analysis are hard to extend to this area with the complicated data structure and the underlying assumptions for pooling the data. In this paper, we aimed to provide a flexible inverse probability weighting (IPW) framework along with several t-type selection functions to deal with the publication bias problem in the NMA context. To solve these proposed selection functions, we recommend making use of the additional information from the unpublished studies from multiple clinical trial registries. A comprehensive numerical study and a real example showed that our methodology can help obtain more accurate estimates and higher coverage probabilities, and improve other properties of an NMA (e.g., ranking the interventions).

Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern parallel computation. This paper constructs a novel many-short-chains Monte Carlo (MSC) estimator by averaging over multiple independent sums from Markov chains of a guaranteed short length. The computational advantage is the independent Markov chain simulations can be fast and may be run in parallel. The MSC estimator requires an importance sampling proposal and a drift condition on the Markov chain without requiring convergence analysis on the Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions. Empirical performance is illustrated on an autoregressive process and the P\'olya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease.

We revisit a self-supervised method that segments unlabelled speech into word-like segments. We start from the two-stage duration-penalised dynamic programming method that performs zero-resource segmentation without learning an explicit lexicon. In the first acoustic unit discovery stage, we replace contrastive predictive coding features with HuBERT. After word segmentation in the second stage, we get an acoustic word embedding for each segment by averaging HuBERT features. These embeddings are clustered using K-means to get a lexicon. The result is good full-coverage segmentation with a lexicon that achieves state-of-the-art performance on the ZeroSpeech benchmarks.

Data generation remains a bottleneck in training surrogate models to predict molecular properties. We demonstrate that multitask Gaussian process regression overcomes this limitation by leveraging both expensive and cheap data sources. In particular, we consider training sets constructed from coupled-cluster (CC) and density function theory (DFT) data. We report that multitask surrogates can predict at CC level accuracy with a reduction to data generation cost by over an order of magnitude. Of note, our approach allows the training set to include DFT data generated by a heterogeneous mix of exchange-correlation functionals without imposing any artificial hierarchy on functional accuracy. More generally, the multitask framework can accommodate a wider range of training set structures -- including full disparity between the different levels of fidelity -- than existing kernel approaches based on $\Delta$-learning, though we show that the accuracy of the two approaches can be similar. Consequently, multitask regression can be a tool for reducing data generation costs even further by opportunistically exploiting existing data sources.

Recent dramatic advances in artificial intelligence indicate that in the coming years, humanity may irreversibly cross a threshold by creating superhuman general-purpose AI: AI that is better than humans at cognitive tasks in general in the way that AI is currently unbeatable in certain domains. This would upend core aspects of human society, present many unprecedented risks, and is likely to be uncontrollable in several senses. We can choose to not do so, starting by instituting hard limits - placed at the national and international level, and verified by hardware security measures - on the computation that can be used to train and run neural networks. With these limits in place, AI research and industry can focus on making both narrow and general-purpose AI that humans can understand and control, and from which we can reap enormous benefit.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.