While sorting is an important procedure in computer science, the argsort operator - which takes as input a vector and returns its sorting permutation - has a discrete image and thus zero gradients almost everywhere. This prohibits end-to-end, gradient-based learning of models that rely on the argsort operator. A natural way to overcome this problem is to replace the argsort operator with a continuous relaxation. Recent work has shown a number of ways to do this, but the relaxations proposed so far are computationally complex. In this work we propose a simple continuous relaxation for the argsort operator which has the following qualities: it can be implemented in three lines of code, achieves state-of-the-art performance, is easy to reason about mathematically - substantially simplifying proofs - and is faster than competing approaches. We open source the code to reproduce all of the experiments and results.

Manifold Learning occupies a vital role in the field of nonlinear dimensionality reduction and its ideas also serve for other relevant methods. Graph-based methods such as Graph Convolutional Networks (GCN) show ideas in common with manifold learning, although they belong to different fields. Inspired by GCN, we introduce neighbor propagation into LLE and propose Local Neighbor Propagation Embedding (LNPE). With linear computational complexity increase compared with LLE, LNPE enhances the local connections and interactions between neighborhoods by extending $1$-hop neighbors into $n$-hop neighbors. The experimental results show that LNPE could obtain more faithful and robust embeddings with better topological and geometrical properties.

When tasks change over time, meta-transfer learning seeks to improve the efficiency of learning a new task via both meta-learning and transfer-learning. While the standard attention has been effective in a variety of settings, we question its effectiveness in improving meta-transfer learning since the tasks being learned are dynamic and the amount of context can be substantially smaller. In this paper, using a recently proposed meta-transfer learning model, Sequential Neural Processes (SNP), we first empirically show that it suffers from a similar underfitting problem observed in the functions inferred by Neural Processes. However, we further demonstrate that unlike the meta-learning setting, the standard attention mechanisms are not effective in meta-transfer setting. To resolve, we propose a new attention mechanism, Recurrent Memory Reconstruction (RMR), and demonstrate that providing an imaginary context that is recurrently updated and reconstructed with interaction is crucial in achieving effective attention for meta-transfer learning. Furthermore, incorporating RMR into SNP, we propose Attentive Sequential Neural Processes-RMR (ASNP-RMR) and demonstrate in various tasks that ASNP-RMR significantly outperforms the baselines.

The Traveling Salesperson Problem (TSP) is a classical N P-hard optimization problem of utmost relevance, e.g., in transportation logistics, bioinformatics or circuit board fabrication. The goal is to route a salesperson through a set of cities such that each city is visited exactly once and the tour is of minimal length. In the past decades tremendous progress has been made in the development of high-performing heuristic TSP solvers. The local search-based Lin-Kernigham Heuristic (LKH) [14] and the genetic algorithm Edge-Assembly-Crossover (EAX) [35], along with their respective restart versions introduced in Kotthoff et al. [25], undeniably pose the state-of-the-art in inexact TSP solving. Automated Algorithm Selection (AS), originally proposed by Rice [39] back in 1976, is a powerful framework to predict the best-performing solver(s) from a portfolio of candidate solvers by means of machine learning. It has been successfully applied to a wide spectrum of challenging optimization problems in both the combinatorial [24, 29, 30, 40, 48] and continuous domain [21, 4] with partly astonishing performance gains - see the recent survey by Kerschke et al. [19] for a comprehensive overview. In particular, the TSP was subject to several successful ASstudies [25, 20, 33, 34, 37] which exploited the complementary performance profiles of simple heuristics on the one hand and the state-of-the-art solvers LKH and EAX on classical TSP benchmark sets on the other hand.

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering nonlinear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multi-fidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.

Machine learning models often pose a threat to the privacy of individuals whose data is part of the training set. Several recent attacks have been able to infer sensitive information from trained models, including model inversion or attribute inference attacks. These attacks are able to reveal the values of certain sensitive features of individuals who participated in training the model. It has also been shown that several factors can contribute to an increased risk of model inversion, including feature influence. We observe that not all features necessarily share the same level of privacy or sensitivity. In many cases, certain features used to train a model are considered especially sensitive and therefore propitious candidates for inversion. We present a solution for countering model inversion attacks in tree-based models, by reducing the influence of sensitive features in these models. This is an avenue that has not yet been thoroughly investigated, with only very nascent previous attempts at using this as a countermeasure against attribute inference. Our work shows that, in many cases, it is possible to train a model in different ways, resulting in different influence levels of the various features, without necessarily harming the model's accuracy. We are able to utilize this fact to train models in a manner that reduces the model's reliance on the most sensitive features, while increasing the importance of less sensitive features. Our evaluation confirms that training models in this manner reduces the risk of inference for those features, as demonstrated through several black-box and white-box attacks.

Regression via classification (RvC) is a common method used for regression problems in deep learning, where the target variable belongs to a set of continuous values. By discretizing the target into a set of non-overlapping classes, it has been shown that training a classifier can improve neural network accuracy compared to using a standard regression approach. However, it is not clear how the set of discrete classes should be chosen and how it affects the overall solution. In this work, we propose that using several discrete data representations simultaneously can improve neural network learning compared to a single representation. Our approach is end-to-end differentiable and can be added as a simple extension to conventional learning methods, such as deep neural networks. We test our method on three challenging tasks and show that our method reduces the prediction error compared to a baseline RvC approach while maintaining a similar model complexity.

Chain Event Graphs (CEGs) are a recent family of probabilistic graphical models - a generalisation of Bayesian Networks - providing an explicit representation of structural zeros and context-specific conditional independences within their graph topology. A CEG is constructed from an event tree through a sequence of transformations beginning with the colouring of the vertices of the event tree to identify one-step transition symmetries. This coloured event tree, also known as a staged tree, is the output of the learning algorithms used for this family. Surprisingly, no general algorithm has yet been devised that automatically transforms any staged tree into a CEG representation. In this paper we provide a simple iterative backward algorithm for this transformation. Additionally, we show that no information is lost from transforming a staged tree into a CEG. Finally, we demonstrate that with an optimal stopping time, our algorithm is more efficient than the generalisation of a special case presented in Silander and Leong (2013). We also provide Python code using this algorithm to obtain a CEG from any staged tree along with the functionality to add edges with sampling zeros.

These approaches, however, concept (for which there are many). Historically, most are based on general mixing patterns, which include community detection methods proposed have focused on assortativity only as a special case. In many ways this the detection of assortative communities, i.e. groups of is useful, and in fact arguably superior, since if assortativity nodes that tend to be more connected to themselves than happens to be the dominating pattern, then the to other nodes in the network. However, there are also general approach will capture it, otherwise it will reveal a community detection methods that are more general, and different structure. However, having only a more general attempt to cluster together nodes that have similar patterns method at our disposal also has its shortcomings. First, of connection, regardless if they are assortative or if it is true that assortativity is the main pattern for a not [3-5]. The widespread use of assortative community class of networks, then the more general representation detection methods has lead to the belief that the presence is needlessly wasteful for them, since it not only gives us of communities is a pervasive feature of many different more than we need, but in doing so it prevents us from kinds of real networks [6]. Although the concept of assortativity focusing on the more central features, at the cost of algorithmic is a central one in the study of social networks precision. Second, with a more general method (known as "homophily" in that context) [7], and is also an it can be difficult to quantify precisely how much has appealing construct in biology [8-10], it is to some extent been wasted in the representation, and what is indeed unclear if the perceived assortativity of many networks the simpler pattern hiding inside it.

The main success stories of deep learning, starting with ImageNet, depend on convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines. Is there something special about deep convolutional networks that other learning machines do not possess? Recent results in approximation theory have shown that there is an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure. These mathematical results, however, do not say which tasks are expected to have input-output functions with hierarchical locality. Among all the possible hierarchically local tasks in vision, text and speech we explore a few of them experimentally by studying how they are affected by disrupting locality in the input images. We also discuss a taxonomy of tasks ranging from local, to hierarchically local, to global and make predictions about the type of networks required to perform efficiently on these different types of tasks.