Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative latent variable tensor model that incorporates both high rank and low rank models, including but not limited to, simple hypergraphon models, single index models, low-rank CP models, and low-rank Tucker models. Comprehensive results are developed on both the statistical and computational limits for the signal tensor estimation. We find that high-dimensional latent variable tensors are of log-rank; the fact explains the pervasiveness of low-rank tensors in applications. Furthermore, we propose a polynomial-time spectral algorithm that achieves the computationally optimal rate. We show that the statistical-computational gap emerges only for latent variable tensors of order 3 or higher. Numerical experiments and two real data applications are presented to demonstrate the practical merits of our methods.

Named Entity Recognition (NER) plays a vital role in various Natural Language Processing tasks such as information retrieval, text classification, and question answering. However, NER can be challenging, especially in low-resource languages with limited annotated datasets and tools. This paper adds to the effort of addressing these challenges by introducing MphayaNER, the first Tshivenda NER corpus in the news domain. We establish NER baselines by \textit{fine-tuning} state-of-the-art models on MphayaNER. The study also explores zero-shot transfer between Tshivenda and other related Bantu languages, with chiShona and Kiswahili showing the best results. Augmenting MphayaNER with chiShona data was also found to improve model performance significantly. Both MphayaNER and the baseline models are made publicly available.

Tesla assures its millions of electric car owners that their privacy "is and will always be enormously important to us". The cameras it builds into vehicles to assist driving, it notes on its website, are "designed from the ground up to protect your privacy". But between 2019 and 2022, groups of Tesla employees privately shared via an internal messaging system sometimes highly invasive videos and images recorded by customers' car cameras, according to interviews by Reuters with nine former employees. Some of the recordings caught Tesla customers in embarrassing situations. One ex-employee described a video of a man approaching a vehicle completely naked.

Starting from 2021, more demanding $\text{NO}_\text{x}$ emission restrictions were introduced for ships operating in the North and Baltic Sea waters. Since all methods currently used for ship compliance monitoring are financially and time demanding, it is important to prioritize the inspection of ships that have high chances of being non-compliant. The current state-of-the-art approach for a large-scale ship $\text{NO}_\text{2}$ estimation is a supervised machine learning-based segmentation of ship plumes on TROPOMI/S5P images. However, challenging data annotation and insufficiently complex ship emission proxy used for the validation limit the applicability of the model for ship compliance monitoring. In this study, we present a method for the automated selection of potentially non-compliant ships using a combination of machine learning models on TROPOMI satellite data. It is based on a proposed regression model predicting the amount of $\text{NO}_\text{2}$ that is expected to be produced by a ship with certain properties operating in the given atmospheric conditions. The model does not require manual labeling and is validated with TROPOMI data directly. The differences between the predicted and actual amount of produced $\text{NO}_\text{2}$ are integrated over observations of the ship in time and are used as a measure of the inspection worthiness of a ship. To assure the robustness of the results, we compare the obtained results with the results of the previously developed segmentation-based method. Ships that are also highly deviating in accordance with the segmentation method require further attention. If no other explanations can be found by checking the TROPOMI data, the respective ships are advised to be the candidates for inspection.

In this work we derive the performance achievable by a network of distributed agents that solve, adaptively and in the presence of communication constraints, a regression problem. Agents employ the recently proposed ACTC (adapt-compress-then-combine) diffusion strategy, where the signals exchanged locally by neighboring agents are encoded with randomized differential compression operators. We provide a detailed characterization of the mean-square estimation error, which is shown to comprise a term related to the error that agents would achieve without communication constraints, plus a term arising from compression. The analysis reveals quantitative relationships between the compression loss and fundamental attributes of the distributed regression problem, in particular, the stochastic approximation error caused by the gradient noise and the network topology (through the Perron eigenvector). We show that knowledge of such relationships is critical to allocate optimally the communication resources across the agents, taking into account their individual attributes, such as the quality of their data or their degree of centrality in the network topology. We devise an optimized allocation strategy where the parameters necessary for the optimization can be learned online by the agents. Illustrative examples show that a significant performance improvement, as compared to a blind (i.e., uniform) resource allocation, can be achieved by optimizing the allocation by means of the provided mean-square-error formulas.

Previous work has established that RNNs with an unbounded activation function have the capacity to count exactly. However, it has also been shown that RNNs are challenging to train effectively and generally do not learn exact counting behaviour. In this paper, we focus on this problem by studying the simplest possible RNN, a linear single-cell network. We conduct a theoretical analysis of linear RNNs and identify conditions for the models to exhibit exact counting behaviour. We provide a formal proof that these conditions are necessary and sufficient. We also conduct an empirical analysis using tasks involving a Dyck-1-like Balanced Bracket language under two different settings. We observe that linear RNNs generally do not meet the necessary and sufficient conditions for counting behaviour when trained with the standard approach. We investigate how varying the length of training sequences and utilising different target classes impacts model behaviour during training and the ability of linear RNN models to effectively approximate the indicator conditions.

Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral analysis of weight matrices in deep neural networks, offer valuable clues to address this issue. A key finding indicates that the generalization performance of a neural network is associated with the degree of heavy tails in the spectrum of its weight matrices. To capitalize on this discovery, we introduce a novel regularization technique, termed Heavy-Tailed Regularization, which explicitly promotes a more heavy-tailed spectrum in the weight matrix through regularization. Firstly, we employ the Weighted Alpha and Stable Rank as penalty terms, both of which are differentiable, enabling the direct calculation of their gradients. To circumvent over-regularization, we introduce two variations of the penalty function. Then, adopting a Bayesian statistics perspective and leveraging knowledge from random matrices, we develop two novel heavy-tailed regularization methods, utilizing Power-law distribution and Fréchet distribution as priors for the global spectrum and maximum eigenvalues, respectively. We empirically show that heavytailed regularization outperforms conventional regularization techniques in terms of generalization performance.

There has been concern about ideological basis and possible discrimination in text generated by Large Language Models (LLMs). We test possible value biases in ChatGPT using a psychological value theory. We designed a simple experiment in which we used a number of different probes derived from the Schwartz basic value theory (items from the revised Portrait Value Questionnaire, the value type definitions, value names). We prompted ChatGPT via the OpenAI API repeatedly to generate text and then analyzed the generated corpus for value content with a theory-driven value dictionary using a bag of words approach. Overall, we found little evidence of explicit value bias. The results showed sufficient construct and discriminant validity for the generated text in line with the theoretical predictions of the psychological model, which suggests that the value content was carried through into the outputs with high fidelity. We saw some merging of socially oriented values, which may suggest that these values are less clearly differentiated at a linguistic level or alternatively, this mixing may reflect underlying universal human motivations. We outline some possible applications of our findings for both applications of ChatGPT for corporate usage and policy making as well as future research avenues. We also highlight possible implications of this relatively high-fidelity replication of motivational content using a linguistic model for the theorizing about human values.

The shipping industry is one of the strongest anthropogenic emitters of $\text{NO}_\text{x}$ -- substance harmful both to human health and the environment. The rapid growth of the industry causes societal pressure on controlling the emission levels produced by ships. All the methods currently used for ship emission monitoring are costly and require proximity to a ship, which makes global and continuous emission monitoring impossible. A promising approach is the application of remote sensing. Studies showed that some of the $\text{NO}_\text{2}$ plumes from individual ships can visually be distinguished using the TROPOspheric Monitoring Instrument on board the Copernicus Sentinel 5 Precursor (TROPOMI/S5P). To deploy a remote sensing-based global emission monitoring system, an automated procedure for the estimation of $\text{NO}_\text{2}$ emissions from individual ships is needed. The extremely low signal-to-noise ratio of the available data as well as the absence of ground truth makes the task very challenging. Here, we present a methodology for the automated segmentation of $\text{NO}_\text{2}$ plumes produced by seagoing ships using supervised machine learning on TROPOMI/S5P data. We show that the proposed approach leads to a more than a 20\% increase in the average precision score in comparison to the methods used in previous studies and results in a high correlation of 0.834 with the theoretically derived ship emission proxy. This work is a crucial step toward the development of an automated procedure for global ship emission monitoring using remote sensing data.

Quality-Diversity (QD) algorithms are designed to generate collections of high-performing solutions while maximizing their diversity in a given descriptor space. However, in the presence of unpredictable noise, the fitness and descriptor of the same solution can differ significantly from one evaluation to another, leading to uncertainty in the estimation of such values. Given the elitist nature of QD algorithms, they commonly end up with many degenerate solutions in such noisy settings. In this work, we introduce Archive Reproducibility Improvement Algorithm (ARIA); a plug-and-play approach that improves the reproducibility of the solutions present in an archive. We propose it as a separate optimization module, relying on natural evolution strategies, that can be executed on top of any QD algorithm. Our module mutates solutions to (1) optimize their probability of belonging to their niche, and (2) maximize their fitness. The performance of our method is evaluated on various tasks, including a classical optimization problem and two high-dimensional control tasks in simulated robotic environments. We show that our algorithm enhances the quality and descriptor space coverage of any given archive by at least 50%.