We revisit the sample and computational complexity of completing a rank-1 tensor in $\otimes_{i=1}^{N} \mathbb{R}^{d}$, given a uniformly sampled subset of its entries. We present a characterization of the problem (i.e. nonzero entries) which admits an algorithm amounting to Gauss-Jordan on a pair of random linear systems. For example, when $N = \Theta(1)$, we prove it uses no more than $m = O(d^2 \log d)$ samples and runs in $O(md^2)$ time. Moreover, we show any algorithm requires $\Omega(d\log d)$ samples. By contrast, existing upper bounds on the sample complexity are at least as large as $d^{1.5} \mu^{\Omega(1)} \log^{\Omega(1)} d$, where $\mu$ can be $\Theta(d)$ in the worst case. Prior work obtained these looser guarantees in higher rank versions of our problem, and tend to involve more complicated algorithms.

It has become a pronounced problem due to the increasing ubiquity of online platforms that provide a means to conduct it. A significant amount of this cyberbullying is conducted by and targets teenagers. It is difficult for teenage students to shut themselves off from the digital world in which the cyberbullying is taking place. Given how entrenched the use of digital apps is by today's youth, and the pronounced consequences of it - including victim self-harm, in some cases - cyberbullying is at least as much of a threat as physical bullying. Additionally, because of the obfuscation caused by the online environment, authorities (such as parents, teachers and law enforcement) may have difficulty determining what has occurred and who the actors participating are.

Scientific Machine Learning (ML) is gaining momentum as a cost-effective alternative to physics-based numerical solvers in many engineering applications. In fact, scientific ML is currently being used to build accurate and efficient surrogate models starting from high-fidelity numerical simulations, effectively encoding the parameterized temporal dynamics underlying Ordinary Differential Equations (ODEs), or even the spatio-temporal behavior underlying Partial Differential Equations (PDEs), in appropriately designed neural networks. We propose an extension of Latent Dynamics Networks (LDNets), namely Liquid Fourier LDNets (LFLDNets), to create parameterized space-time surrogate models for multiscale and multiphysics sets of highly nonlinear differential equations on complex geometries. LFLDNets employ a neurologically-inspired, sparse, liquid neural network for temporal dynamics, relaxing the requirement of a numerical solver for time advancement and leading to superior performance in terms of tunable parameters, accuracy, efficiency and learned trajectories with respect to neural ODEs based on feedforward fully-connected neural networks. Furthermore, in our implementation of LFLDNets, we use a Fourier embedding with a tunable kernel in the reconstruction network to learn high-frequency functions better and faster than using space coordinates directly as input. We challenge LFLDNets in the framework of computational cardiology and evaluate their capabilities on two 3-dimensional test cases arising from multiscale cardiac electrophysiology and cardiovascular hemodynamics. This paper illustrates the capability to run Artificial Intelligence-based numerical simulations on single or multiple GPUs in a matter of minutes and represents a significant step forward in the development of physics-informed digital twins.

Return-Conditioned Transformer Decision Models (RCTDM) have demonstrated the potential to enhance transformer performance in offline reinforcement learning by replacing rewards in the input sequence with returns-to-go. However, to achieve the goal of learning an optimal policy from offline datasets composed of limited suboptimal trajectories, RCTDM required alternative methods. One prominent approach, trajectory stitching, was designed to enable the network to combine multiple trajectories to find the optimal path. To implement this using only transformers without auxiliary networks, it was necessary to shorten the input sequence length to better capture the Markov property in reinforcement learnings. This, however, introduced a trade-off, as it reduced the accuracy of action inference. Our study introduces a model named Decision MetaMamba to resolve these challenges. DMM employs an input token mixer to extract patterns from short sequences and uses a State Space Model (SSM) to selectively combine information from relatively distant sequences. Inspired by Metaformer, this structure was developed by transforming Mamba's input layer into various multi-modal layers. Fortunately, with the advent of Mamba, implemented using parallel selective scanning, we achieved a high-performance sequence model capable of replacing transformers. Based on these innovations, DMM demonstrated excellent performance across various datasets in offline RL, confirming that models using SSM can improve performance by domain-specific alterations of the input layer. Additionally, it maintained its performance even in lightweight models with fewer parameters. These results suggest that decision models based on SSM can pave the way for improved outcomes in future developments.

Graph neural networks (GNNs) have recently been adapted to temporal settings, often employing temporal versions of the message-passing mechanism known from GNNs. We divide temporal message passing mechanisms from literature into two main types: global and local, and establish Weisfeiler-Leman characterisations for both. This allows us to formally analyse expressive power of temporal message-passing models. We show that global and local temporal message-passing mechanisms have incomparable expressive power when applied to arbitrary temporal graphs. However, the local mechanism is strictly more expressive than the global mechanism when applied to colour-persistent temporal graphs, whose node colours are initially the same in all time points. Our theoretical findings are supported by experimental evidence, underlining practical implications of our analysis.

What a large language model (LLM) would respond in ethically relevant context? In this paper, we curate a large benchmark CMoralEval for morality evaluation of Chinese LLMs. The data sources of CMoralEval are two-fold: 1) a Chinese TV program discussing Chinese moral norms with stories from the society and 2) a collection of Chinese moral anomies from various newspapers and academic papers on morality. With these sources, we aim to create a moral evaluation dataset characterized by diversity and authenticity. We develop a morality taxonomy and a set of fundamental moral principles that are not only rooted in traditional Chinese culture but also consistent with contemporary societal norms. To facilitate efficient construction and annotation of instances in CMoralEval, we establish a platform with AI-assisted instance generation to streamline the annotation process. These help us curate CMoralEval that encompasses both explicit moral scenarios (14,964 instances) and moral dilemma scenarios (15,424 instances), each with instances from different data sources. We conduct extensive experiments with CMoralEval to examine a variety of Chinese LLMs. Experiment results demonstrate that CMoralEval is a challenging benchmark for Chinese LLMs. The dataset is publicly available at \url{https://github.com/tjunlp-lab/CMoralEval}.

For many low-resource languages, the only available language models are large multilingual models trained on many languages simultaneously. However, using FLORES perplexity as a metric, we find that these models perform worse than bigrams for many languages (e.g. 24% of languages in XGLM 4.5B; 43% in BLOOM 7.1B). To facilitate research that focuses on low-resource languages, we pre-train and release Goldfish, a suite of monolingual autoregressive Transformer language models up to 125M parameters for 350 languages. The Goldfish reach lower FLORES perplexities than BLOOM, XGLM, and MaLA-500 on 98 of 204 FLORES languages, despite each Goldfish model being over 10x smaller. However, the Goldfish significantly underperform larger multilingual models on reasoning benchmarks, suggesting that for low-resource languages, multilinguality primarily improves general reasoning abilities rather than basic text generation. We release models trained on 5MB (350 languages), 10MB (288 languages), 100MB (166 languages), and 1GB (83 languages) of text data where available. The Goldfish models are available as baselines, fine-tuning sources, or augmentations to existing models in low-resource NLP research, and they are further useful for crosslinguistic studies requiring maximally comparable models across languages.

Event Cameras, also known as Neuromorphic sensors, capture changes in local light intensity at the pixel level, producing asynchronously generated data termed ``events''. This distinct data format mitigates common issues observed in conventional cameras, like under-sampling when capturing fast-moving objects, thereby preserving critical information that might otherwise be lost. However, leveraging this data often necessitates the development of specialized, handcrafted event representations that can integrate seamlessly with conventional Convolutional Neural Networks (CNNs), considering the unique attributes of event data. In this study, We evaluate event-based Face and Eye tracking. The core objective of our study is to showcase the viability of integrating conventional algorithms with event-based data, transformed into a frame format while preserving the unique benefits of event cameras. To validate our approach, we constructed a frame-based event dataset by simulating events between RGB frames derived from the publicly accessible Helen Dataset. We assess its utility for face and eye detection tasks through the application of GR-YOLO -- a pioneering technique derived from YOLOv3. This evaluation includes a comparative analysis with results derived from training the dataset with YOLOv8. Subsequently, the trained models were tested on real event streams from various iterations of Prophesee's event cameras and further evaluated on the Faces in Event Stream (FES) benchmark dataset. The models trained on our dataset shows a good prediction performance across all the datasets obtained for validation with the best results of a mean Average precision score of 0.91. Additionally, The models trained demonstrated robust performance on real event camera data under varying light conditions.

Peer analysis is a critical component of investment management, often relying on expert-provided categorization systems. These systems' consistency is questioned when they do not align with cohorts from unsupervised clustering algorithms optimized for various metrics. We investigate whether unsupervised clustering can reproduce ground truth classes in a labeled dataset, showing that success depends on feature selection and the chosen distance metric. Using toy datasets and fund categorization as real-world examples we demonstrate that accurately reproducing ground truth classes is challenging. We also highlight the limitations of standard clustering evaluation metrics in identifying the optimal number of clusters relative to the ground truth classes. We then show that if appropriate features are available in the dataset, and a proper distance metric is known (e.g., using a supervised Random Forest-based distance metric learning method), then an unsupervised clustering can indeed reproduce the ground truth classes as distinct clusters.

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this research data FAIR, two previously distinct ontologies were merged and extended, becoming a living knowledge graph. The link between the two ontologies is established by introducing computational tasks, as they occur in modeling, corresponding to algorithmic tasks. Moreover, controlled vocabularies are incorporated and a new class, distinguishing base quantities from specific use case quantities, was introduced. Also, both models and algorithms can now be enriched with metadata. Subject-specific metadata is particularly relevant here, such as the symmetry of a matrix or the linearity of a mathematical model. This is the only way to express specific workflows with concrete models and algorithms, as the feasible solution algorithm can only be determined if the mathematical properties of a model are known. We demonstrate this using two examples from different application areas of applied mathematics. In addition, we have already integrated over 250 research assets from applied mathematics into our knowledge graph.