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An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than the one proposed by Kutschan (2019). Such an approximate projection enables, e.g., to compute gradient-related directions in the tangent cone, as required by algorithms aiming at minimizing a continuously differentiable function on the variety, a problem appearing notably in tensor completion. A numerical experiment is presented which indicates that, in practice, the angle condition satisfied by the proposed approximate projection is better than both the one satisfied by the approximate projection introduced by Kutschan and the proven theoretical bound.

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The accurate calculation and uncertainty quantification of the characteristics of spent nuclear fuel (SNF) play a crucial role in ensuring the safety, efficiency, and sustainability of nuclear energy production, waste management, and nuclear safeguards. State of the art physics-based models, while reliable, are computationally intensive and time-consuming. This paper presents a surrogate modeling approach using neural networks (NN) to predict a number of SNF characteristics with reduced computational costs compared to physics-based models. An NN is trained using data generated from CASMO5 lattice calculations. The trained NN accurately predicts decay heat and nuclide concentrations of SNF, as a function of key input parameters, such as enrichment, burnup, cooling time between cycles, mean boron concentration and fuel temperature. The model is validated against physics-based decay heat simulations and measurements of different uranium oxide fuel assemblies from two different pressurized water reactors. In addition, the NN is used to perform sensitivity analysis and uncertainty quantification. The results are in very good alignment to CASMO5, while the computational costs (taking into account the costs of generating training samples) are reduced by a factor of 10 or more. Our findings demonstrate the feasibility of using NNs as surrogate models for fast characterization of SNF, providing a promising avenue for improving computational efficiency in assessing nuclear fuel behavior and associated risks.

Many players in the automotive field support scenario-based assessment of automated vehicles (AVs), where individual traffic situations can be tested and, thus, facilitate concluding on the performance of AVs in different situations. Since a large number of different scenarios can occur in real-world traffic, the question is how to find a finite set of relevant scenarios. Scenarios extracted from large real-world datasets represent real-world traffic since real driving data is used. Extracting scenarios, however, is challenging because (1) the scenarios to be tested should assess the AVs behave safely, which conflicts with the fact that the majority of the data contains scenarios that are not interesting from a safety perspective, and (2) extensive data processing is required, which hinders the utilization of large real-world datasets. In this work, we propose an approach for extracting scenarios from real-world driving data. The first step is data preprocessing to tackle the errors and noise in real-world data by reconstructing the data. The second step performs data tagging to label actors' activities, their interactions with each other and the environment. Finally, the scenarios are extracted by searching for combinations of tags. The proposed approach is evaluated using data simulated with CARLA and applied to a part of a large real-world driving dataset, i.e., the Waymo Open Motion Dataset (WOMD). The code and scenarios extracted from WOMD are open to the research community to facilitate the assessment of the automated driving functions in different scenarios.

Teaching motor skills such as playing music, handwriting, and driving, can greatly benefit from recently developed technologies such as wearable gloves for haptic feedback or robotic sensorimotor exoskeletons for the mediation of effective human-human and robot-human physical interactions. At the heart of such teacher-learner interactions still stands the critical role of the ongoing feedback a teacher can get about the student's engagement state during the learning and practice sessions. Particularly for motor learning, such feedback is an essential functionality in a system that is developed to guide a teacher on how to control the intensity of the physical interaction, and to best adapt it to the gradually evolving performance of the learner. In this paper, our focus is on the development of a near real-time machine-learning model that can acquire its input from a set of readily available, noninvasive, privacy-preserving, body-worn sensors, for the benefit of tracking the engagement of the learner in the motor task. We used the specific case of violin playing as a target domain in which data were empirically acquired, the latent construct of engagement in motor learning was carefully developed for data labeling, and a machine-learning model was rigorously trained and validated.

Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading fairness in favor of automation. To advance automation in the design and fair grading of (functional programming) e-exams, we introduce the following: A novel algorithm to check Proof Puzzles based on finding correct sequences of proof lines that improves fairness compared to an existing, edit distance based algorithm; an open-source static analysis tool to check source code for task relevant features by traversing the abstract syntax tree; a higher-level language and open-source tool to specify regular expressions that makes creating complex regular expressions less error-prone. Our findings are embedded in a complete experience report on transforming a paper exam to an e-exam. We evaluated the resulting e-exam by analyzing the degree of automation in the grading process, asking students for their opinion, and critically reviewing our own experiences. Almost all tasks can be graded automatically at least in part (correct solutions can almost always be detected as such), the students agree that an e-exam is a fitting examination format for the course but are split on how well they can express their thoughts compared to a paper exam, and examiners enjoy a more time-efficient grading process while the point distribution in the exam results was almost exactly the same compared to a paper exam.

Randomized Controlled Trials (RCTs) often adjust for baseline covariates in order to increase power. This technical note provides a short derivation of a simple rule of thumb for approximating the ratio of the power of an adjusted analysis to that of an unadjusted analysis. Specifically, if the unadjusted analysis is powered to approximately 80\%, then the ratio of the power of the adjusted analysis to the power of the unadjusted analysis is approximately $1 + \frac{1}{2} R^2$, where $R$ is the correlation between the baseline covariate and the outcome.

Effective multi-robot teams require the ability to move to goals in complex environments in order to address real-world applications such as search and rescue. Multi-robot teams should be able to operate in a completely decentralized manner, with individual robot team members being capable of acting without explicit communication between neighbors. In this paper, we propose a novel game theoretic model that enables decentralized and communication-free navigation to a goal position. Robots each play their own distributed game by estimating the behavior of their local teammates in order to identify behaviors that move them in the direction of the goal, while also avoiding obstacles and maintaining team cohesion without collisions. We prove theoretically that generated actions approach a Nash equilibrium, which also corresponds to an optimal strategy identified for each robot. We show through extensive simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, and is able to avoid obstacles and collisions, maintain connectivity, and respond robustly to sensor noise.

The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

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