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Despite their superior performance, deep learning models often lack interpretability. In this paper, we explore the modeling of insightful relations between words, in order to understand and enhance predictions. To this effect, we propose the Self-Attention Network (SANet), a flexible and interpretable architecture for text classification. Experiments indicate that gains obtained by self-attention is task-dependent. For instance, experiments on sentiment analysis tasks showed an improvement of around 2% when using selfattention compared to a baseline without attention, while topic classification showed no gain. Interpretability brought forward by our architecture highlighted the importance of neighboring word interactions to extract sentiment.

We use machine learning to generate metamodels for sawing simulation. Simulation is widely used in the wood industry for decision making. These simulators are particular since their response for a given input is a structured object, i.e., a basket of lumbers. We demonstrate how we use simple machine learning algorithms (e.g., a tree) to obtain a good approximation of the simulator's response. The generated metamodels are guaranteed to output physically realistic baskets (i.e., there exists at least one log that can produce the basket). We also propose to use kernel ridge regression. While having the power to exploit the structure of a basket, it can predict previously unseen baskets. We finally evaluate the impact of possibly predicting unrealistic baskets using ridge regression jointly with a nearest neighbor approach in the output space. All metamodels are evaluated using standard machine learning metrics and novel metrics especially designed for the problem.

The well-separated pair decomposition (WSPD) of the complete Euclidean graph defined on points in Although competitive local-routing strategies exist for various spanners such as Yao-graphs, Θ-graphs, and variants of Delaunay graphs, few local-routing strategies are known for any WSPD-spanner. Our main contribution is a local-routing algorithm with a near-optimal competitive routing ratio of 1 + O(1/s) on a WSPD-spanner.Specifically, using Callahan and Kosaraju's fair split-tree, we show how to build a WSPD-spanner with spanning ratio 1 + 4/s + 4/(s − 2) which is a slight improvement over 1 + 8/(s − 4). We then present a 2-local and a 1-local routing algorithm on this spanner with competitive routing ratios of 1 + 6/(s − 2) + 4/s and 1 + 8/(s − 2) + 4/s + 8/s 2 , respectively. Moreover, we prove that there exists a point set for which our WSPD-spanner has a spanning ratio of at least 1 + 8/s, thereby proving the near-optimality of its spanning ratio and the near-optimality of the routing ratio of both our routing algorithms.ii

We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of 10 −5 . In contrast to the classical potential, the quantum potential has a triple-well if the classical wells are deep enough. Its minima are located at the position of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instatons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semi-classical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such case is illustrated by an example.

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U (1 ) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.

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