Abstract: Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the methodological implications of such differences remain largely unknown. This work aims to specifically address these questions. In particular, we clarify the subtle difference between PCA and singular value decomposition (SVD) for multiway data, and show that multiway principal components (PCs) can be estimated reliably in absence of the eigengaps required by the usual PCA, and in general much more efficiently than the usual PCs. Furthermore, the sample multiway PCs are asymptotically independent and hence allow for separate and more accurate inferences about the population PCs.

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBench, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBench comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBench allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

We consider the problem of correct motion planning for T-intersection merge-ins of arbitrary geometry and vehicle density. A merge-in support system has to estimate the chances that a gap between two consecutive vehicles can be taken successfully. In contrast to previous models based on heuristic gap size rules, we present an approach which optimizes the integral risk of the situation using parametrized velocity ramps. It accounts for the risks from curves and all involved vehicles (front and rear on all paths) with a so-called survival analysis. For comparison, we also introduce a specially designed extension of the Intelligent Driver Model (IDM) for entering intersections. We show in a quantitative statistical evaluation that the survival method provides advantages in terms of lower absolute risk (i.e., no crash happens) and better risk-utility tradeoff (i.e., making better use of appearing gaps). Furthermore, our approach generalizes to more complex situations with additional risk sources.

This work addresses the task of risk evaluation in traffic scenarios with limited observability due to restricted sensorial coverage. Here, we concentrate on intersection scenarios that are difficult to access visually. To identify the area of sight, we employ ray casting on a local dynamic map providing geometrical information and road infrastructure. Based on the area with reduced visibility, we first model scene entities that pose a potential risk without being visually perceivable yet. Then, we predict a worst-case trajectory in the survival analysis for collision risk estimation. Resulting risk indicators are utilized to evaluate the driver's current behavior, to warn the driver in critical situations, to give suggestions on how to act safely or to plan safe trajectories. We validate our approach by applying the resulting intersection warning system on real world scenarios. The proposed system's behavior reveals to mimic the general behavior of a correctly acting human driver.

State-sponsored trolls are the main actors of influence campaigns on social media and automatic troll detection is important to combat misinformation at scale. Existing troll detection models are developed based on training data for known campaigns (e.g.\ the influence campaign by Russia's Internet Research Agency on the 2016 US Election), and they fall short when dealing with {\em novel} campaigns with new targets. We propose MetaTroll, a text-based troll detection model based on the meta-learning framework that enables high portability and parameter-efficient adaptation to new campaigns using only a handful of labelled samples for few-shot transfer. We introduce \textit{campaign-specific} transformer adapters to MetaTroll to ``memorise'' campaign-specific knowledge so as to tackle catastrophic forgetting, where a model ``forgets'' how to detect trolls from older campaigns due to continual adaptation. Our experiments demonstrate that MetaTroll substantially outperforms baselines and state-of-the-art few-shot text classification models. Lastly, we explore simple approaches to extend MetaTroll to multilingual and multimodal detection. Source code for MetaTroll is available at: https://github.com/ltian678/metatroll-code.git.

We provide a unified framework, applicable to a general family of convex losses and across binary and multiclass settings in the overparameterized regime, to approximately characterize the implicit bias of gradient descent in closed form. Specifically, we show that the implicit bias is approximated (but not exactly equal to) the minimum-norm interpolation in high dimensions, which arises from training on the squared loss. In contrast to prior work which was tailored to exponentially-tailed losses and used the intermediate support-vector-machine formulation, our framework directly builds on the primal-dual analysis of Ji and Telgarsky (2021), allowing us to provide new approximate equivalences for general convex losses through a novel sensitivity analysis. Our framework also recovers existing exact equivalence results for exponentially-tailed losses across binary and multiclass settings. Finally, we provide evidence for the tightness of our techniques, which we use to demonstrate the effect of certain loss functions designed for out-of-distribution problems on the closed-form solution.

As we all know, multi-view data is more expressive than single-view data and multi-label annotation enjoys richer supervision information than single-label, which makes multi-view multi-label learning widely applicable for various pattern recognition tasks. In this complex representation learning problem, three main challenges can be characterized as follows: i) How to learn consistent representations of samples across all views? ii) How to exploit and utilize category correlations of multi-label to guide inference? iii) How to avoid the negative impact resulting from the incompleteness of views or labels? To cope with these problems, we propose a general multi-view multi-label learning framework named label-guided masked view- and category-aware transformers in this paper. First, we design two transformer-style based modules for cross-view features aggregation and multi-label classification, respectively. The former aggregates information from different views in the process of extracting view-specific features, and the latter learns subcategory embedding to improve classification performance. Second, considering the imbalance of expressive power among views, an adaptively weighted view fusion module is proposed to obtain view-consistent embedding features. Third, we impose a label manifold constraint in sample-level representation learning to maximize the utilization of supervised information. Last but not least, all the modules are designed under the premise of incomplete views and labels, which makes our method adaptable to arbitrary multi-view and multi-label data. Extensive experiments on five datasets confirm that our method has clear advantages over other state-of-the-art methods.

Humans possess the extraordinary capability of learning a new concept even after minimal observation. To a greater extent, a child can distinguish a dog from a cat through a single picture [1]. This critical characteristic of human intelligence lies in the humans' ability to leverage obtained knowledge of prior experiences to unforeseen circumstances with small observation. Unlike the human learning paradigm, traditional machine learning (ML) and deep learning (DL) models train a specific task from scratch through: (a) the training phase in which a model is initiated randomly and then updated, and (b) the test phase in which the model evaluates. While ML and DL have obtained remarkable success in a wide range of applications, they are notorious for requiring a huge number of samples to generalize. In many real-world problems, collecting more data is costly, time-consuming, and even might not feasible due to physical system constraints [2]. Moreover, most ML and DL models presume that training and testing datasets have the same distribution [3]. Thus, their performance suffers under data distribution shifts [4].

Deep neural networks (DNNs) often perform poorly in the presence of domain shift and category shift. How to upcycle DNNs and adapt them to the target task remains an important open problem. Unsupervised Domain Adaptation (UDA), especially recently proposed Source-free Domain Adaptation (SFDA), has become a promising technology to address this issue. Nevertheless, existing SFDA methods require that the source domain and target domain share the same label space, consequently being only applicable to the vanilla closed-set setting. In this paper, we take one step further and explore the Source-free Universal Domain Adaptation (SF-UniDA). The goal is to identify "known" data samples under both domain and category shift, and reject those "unknown" data samples (not present in source classes), with only the knowledge from standard pre-trained source model. To this end, we introduce an innovative global and local clustering learning technique (GLC). Specifically, we design a novel, adaptive one-vs-all global clustering algorithm to achieve the distinction across different target classes and introduce a local k-NN clustering strategy to alleviate negative transfer. We examine the superiority of our GLC on multiple benchmarks with different category shift scenarios, including partial-set, open-set, and open-partial-set DA. Remarkably, in the most challenging open-partial-set DA scenario, GLC outperforms UMAD by 14.8\% on the VisDA benchmark. The code is available at https://github.com/ispc-lab/GLC.

Inspired by the success of Self-supervised learning (SSL) in learning visual representations from unlabeled data, a few recent works have studied SSL in the context of continual learning (CL), where multiple tasks are learned sequentially, giving rise to a new paradigm, namely self-supervised continual learning (SSCL). It has been shown that the SSCL outperforms supervised continual learning (SCL) as the learned representations are more informative and robust to catastrophic forgetting. However, if not designed intelligently, the training complexity of SSCL may be prohibitively high due to the inherent training cost of SSL. In this work, by investigating the task correlations in SSCL setup first, we discover an interesting phenomenon that, with the SSL-learned background model, the intermediate features are highly correlated between tasks. Based on this new finding, we propose a new SSCL method with layer-wise freezing which progressively freezes partial layers with the highest correlation ratios for each task to improve training computation efficiency and memory efficiency. Extensive experiments across multiple datasets are performed, where our proposed method shows superior performance against the SoTA SSCL methods under various SSL frameworks. For example, compared to LUMP, our method achieves 12\%/14\%/12\% GPU training time reduction, 23\%/26\%/24\% memory reduction, 35\%/34\%/33\% backward FLOPs reduction, and 1.31\%/1.98\%/1.21\% forgetting reduction without accuracy degradation on three datasets, respectively.