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The generative autoencoders, such as the variational autoencoders or the adversarial autoencoders, have achieved great success in lots of real-world applications, including image generation, and signal communication. However, little concern has been devoted to their robustness during practical deployment. Due to the probabilistic latent structure, variational autoencoders (VAEs) may confront problems such as a mismatch between the posterior distribution of the latent and real data manifold, or discontinuity in the posterior distribution of the latent. This leaves a back door for malicious attackers to collapse VAEs from the latent space, especially in scenarios where the encoder and decoder are used separately, such as communication and compressed sensing. In this work, we provide the first study on the adversarial robustness of generative autoencoders in the latent space. Specifically, we empirically demonstrate the latent vulnerability of popular generative autoencoders through attacks in the latent space. We also evaluate the difference between variational autoencoders and their deterministic variants and observe that the latter performs better in latent robustness. Meanwhile, we identify a potential trade-off between the adversarial robustness and the degree of the disentanglement of the latent codes. Additionally, we also verify the feasibility of improvement for the latent robustness of VAEs through adversarial training. In summary, we suggest concerning the adversarial latent robustness of the generative autoencoders, analyze several robustness-relative issues, and give some insights into a series of key challenges.

Synthetic time series are often used in practical applications to augment the historical time series dataset for better performance of machine learning algorithms, amplify the occurrence of rare events, and also create counterfactual scenarios described by the time series. Distributional-similarity (which we refer to as realism) as well as the satisfaction of certain numerical constraints are common requirements in counterfactual time series scenario generation requests. For instance, the US Federal Reserve publishes synthetic market stress scenarios given by the constrained time series for financial institutions to assess their performance in hypothetical recessions. Existing approaches for generating constrained time series usually penalize training loss to enforce constraints, and reject non-conforming samples. However, these approaches would require re-training if we change constraints, and rejection sampling can be computationally expensive, or impractical for complex constraints. In this paper, we propose a novel set of methods to tackle the constrained time series generation problem and provide efficient sampling while ensuring the realism of generated time series. In particular, we frame the problem using a constrained optimization framework and then we propose a set of generative methods including ``GuidedDiffTime'', a guided diffusion model to generate realistic time series. Empirically, we evaluate our work on several datasets for financial and energy data, where incorporating constraints is critical. We show that our approaches outperform existing work both qualitatively and quantitatively. Most importantly, we show that our ``GuidedDiffTime'' model is the only solution where re-training is not necessary for new constraints, resulting in a significant carbon footprint reduction.

The advent of the Metaverse concept has further expedited the evolution of haptic, tactile internet, and multimedia applications with their VR/AR/XR services, and therefore, fully-immersive sensing is most likely to define the next generation of wireless networks as a key to realize the speculative vision of the Metaverse. In this magazine, we articulate different types of media that we envision will be communicated between the cyber and physical twins in the Metaverse. In particular, we explore the advantages grasped by exploiting each kind, and we point out critical challenges pertinent to 3D data processing, coding, transporting, and rendering. We further shed light on the role of future wireless networks in delivering the anticipated quality of immersion through the reliable streaming of multimedia signals between the digital twin and its physical counterpart. Specifically, we explore emergent communication paradigms, including semantic, holographic, and goal-oriented communication, which we expect to realize energy and spectrally efficient Metaverse while ensuring ultra-low latency.

Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in geostatistical models as some covariance parameters are poorly identified, the problem is severe enough that the differentiability parameter of the Matern correlation function is typically treated as fixed. The problem is compounded with anisotropic spatial models as there are two additional parameters to consider. In this paper, we make the following contributions: 1, A methodology is created for profile likelihoods for Gaussian spatial models with Mat\'ern family of correlation functions, including anisotropic models. This methodology adopts a novel reparametrization for generation of representative points, and uses GPUs for parallel profile likelihoods computation in software implementation. 2, We show the profile likelihood of the Mat\'ern shape parameter is often quite flat but still identifiable, it can usually rule out very small values. 3, Simulation studies and applications on real data examples show that profile-based confidence intervals of covariance parameters and regression parameters have superior coverage to the traditional standard Wald type confidence intervals.

While evolutionary computation is well suited for automatic discovery in engineering, it can also be used to gain insight into how humans and organizations could perform more effectively. Using a real-world problem of innovation search in organizations as the motivating example, this article first formalizes human creative problem solving as competitive multi-agent search (CMAS). CMAS is different from existing single-agent and team search problems in that the agents interact through knowledge of other agents' searches and through the dynamic changes in the search landscape that result from these searches. The main hypothesis is that evolutionary computation can be used to discover effective strategies for CMAS; this hypothesis is verified in a series of experiments on the NK model, i.e.\ partially correlated and tunably rugged fitness landscapes. Different specialized strategies are evolved for each different competitive environment, and also general strategies that perform well across environments. These strategies are more effective and more complex than hand-designed strategies and a strategy based on traditional tree search. Using a novel spherical visualization of such landscapes, insight is gained about how successful strategies work, e.g.\ by tracking positive changes in the landscape. The article thus provides a possible framework for studying various human creative activities as competitive multi-agent search in the future.

The solution set of a system of polynomial equations typically contains ill-behaved, singular points. Resolution is a fundamental process in geometry in which we replace singular points with smooth points, while keeping the rest of the solution set unchanged. Resolutions are not unique: the usual way to describe them involves repeatedly performing a fundamental operation known as "blowing-up", and the complexity of the resolution highly depends on certain choices. The process can be translated into various versions of a 2-player game, the so-called Hironaka game, and a winning strategy for the first player provides a solution to the resolution problem. In this paper we introduce a new approach to the Hironaka game that uses reinforcement learning agents to find optimal resolutions of singularities. In certain domains, the trained model outperforms state-of-the-art selection heuristics in total number of polynomial additions performed, which provides a proof-of-concept that recent developments in machine learning have the potential to improve performance of algorithms in symbolic computation.

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by formulating the problem of finding a reproducing kernel Hilbert space (RKHS) to approximate a PDE solution. The approximated solution lies in the span of base functions generated by evaluating derivatives of different orders of kernels at sample points. However, the RKHS specified by GPs can result in an expensive computational burden due to the cubic computation order of the matrix inverse. Therefore, we conjecture that a solution exists on a ``condensed" subspace that can achieve similar approximation performance, and we propose a SGP-based method to reformulate the optimization problem in the ``condensed" subspace. This significantly reduces the computation burden while retaining desirable accuracy. The paper rigorously formulates this problem and provides error analysis and numerical experiments to demonstrate the effectiveness of this method. The numerical experiments show that the SGP method uses fewer than half the uniform samples as inducing points and achieves comparable accuracy to the GP method using the same number of uniform samples, resulting in a significant reduction in computational cost. Our contributions include formulating the nonlinear PDE problem as an optimization problem on a ``condensed" subspace of RKHS using SGP, as well as providing an existence proof and rigorous error analysis. Furthermore, our method can be viewed as an extension of the GP method to account for general positive semi-definite kernels.

We propose to enhance the training of physics-informed neural networks (PINNs). To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear preconditioners are constructed by utilizing the Schwarz domain-decomposition framework, where the parameters of the network are decomposed in a layer-wise manner. Through a series of numerical experiments, we demonstrate that both, additive and multiplicative preconditioners significantly improve the convergence of the standard L-BFGS optimizer, while providing more accurate solutions of the underlying partial differential equations. Moreover, the additive preconditioner is inherently parallel, thus giving rise to a novel approach to model parallelism.

Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.