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When learning disconnected distributions, Generative adversarial networks (GANs) are known to face model misspecification. Indeed, a continuous mapping from a unimodal latent distribution to a disconnected one is impossible, so GANs necessarily generate samples outside of the support of the target distribution. This raises a fundamental question: what is the latent space partition that minimizes the measure of these areas? Building on a recent result of geometric measure theory, we prove that an optimal GANs must structure its latent space as a 'simplicial cluster' - a Voronoi partition where cells are convex cones - when the dimension of the latent space is larger than the number of modes. In this configuration, each Voronoi cell maps to a distinct mode of the data. We derive both an upper and a lower bound on the optimal precision of GANs learning disconnected manifolds. Interestingly, these two bounds have the same order of decrease: $\sqrt{\log m}$, $m$ being the number of modes. Finally, we perform several experiments to exhibit the geometry of the latent space and experimentally show that GANs have a geometry with similar properties to the theoretical one.

As progress in AI continues to advance, it is crucial to know how advanced systems will make choices and in what ways they may fail. Machines can already outsmart humans in some domains, and understanding how to safely build ones which may have capabilities at or above the human level is of particular concern. One might suspect that artificially generally intelligent (AGI) and artificially superintelligent (ASI) systems should be modeled as as something which humans, by definition, can't reliably outsmart. As a challenge to this assumption, this paper presents the Achilles Heel hypothesis which states that even a potentially superintelligent system may nonetheless have stable decision-theoretic delusions which cause them to make obviously irrational decisions in adversarial settings. In a survey of relevant dilemmas and paradoxes from the decision theory literature, a number of these potential Achilles Heels are discussed in context of this hypothesis. Several novel contributions are made toward understanding the ways in which these weaknesses might be implanted into a system.

Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in high dimensions, such methods learn the mapping between functional state variables. While proposed methods have assumed noise only in the dependent variables, experimental and numerical data for operator learning typically exhibit noise in the independent variables as well, since both variables represent signals that are subject to measurement error. In regression on scalar data, failure to account for noisy independent variables can lead to biased parameter estimates. With noisy independent variables, linear models fitted via ordinary least squares (OLS) will show attenuation bias, wherein the slope will be underestimated. In this work, we derive an analogue of attenuation bias for linear operator regression with white noise in both the independent and dependent variables. In the nonlinear setting, we computationally demonstrate underprediction of the action of the Burgers operator in the presence of noise in the independent variable. We propose error-in-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems. Considering the Burgers operator in 1D and 2D, we demonstrate that EiV operator learning robustly recovers operators in high-noise regimes that defeat OLS operator learning. We also introduce an EiV model for time-evolving PDE discovery and show that OLS and EiV perform similarly in learning the Kuramoto-Sivashinsky evolution operator from corrupted data, suggesting that the effect of bias in OLS operator learning depends on the regularity of the target operator.

In a desired environmental protection system, groundwater may not be excluded. In addition to the problem of over-exploitation, in total disagreement with the concept of sustainable development, another not negligible issue concerns the groundwater contamination. Mainly, this aspect is due to intensive agricultural activities or industrialized areas. In literature, several papers have dealt with transport problem, especially for inverse problems in which the release history or the source location are identified. The innovative aim of the paper is to develop a data-driven model that is able to analyze multiple scenarios, even strongly non-linear, in order to solve forward and inverse transport problems, preserving the reliability of the results and reducing the uncertainty. Furthermore, this tool has the characteristic of providing extremely fast responses, essential to identify remediation strategies immediately. The advantages produced by the model were compared with literature studies. In this regard, a feedforward artificial neural network, which has been trained to handle different cases, represents the data-driven model. Firstly, to identify the concentration of the pollutant at specific observation points in the study area (forward problem); secondly, to deal with inverse problems identifying the release history at known source location; then, in case of one contaminant source, identifying the release history and, at the same time, the location of the source in a specific sub-domain of the investigated area. At last, the observation error is investigated and estimated. The results are satisfactorily achieved, highlighting the capability of the ANN to deal with multiple scenarios by approximating nonlinear functions without the physical point of view that describes the phenomenon, providing reliable results, with very low computational burden and uncertainty.

Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential recommendation. Recently, the generative models based on Variational Autoencoder (VAE) have shown the unique advantage in collaborative filtering. In particular, the sequential VAE model as a recurrent version of VAE can effectively capture temporal dependencies among items in user sequence and perform sequential recommendation. However, VAE-based models suffer from a common limitation that the representational ability of the obtained approximate posterior distribution is limited, resulting in lower quality of generated samples. This is especially true for generating sequences. To solve the above problem, in this work, we propose a novel method called Adversarial and Contrastive Variational Autoencoder (ACVAE) for sequential recommendation. Specifically, we first introduce the adversarial training for sequence generation under the Adversarial Variational Bayes (AVB) framework, which enables our model to generate high-quality latent variables. Then, we employ the contrastive loss. The latent variables will be able to learn more personalized and salient characteristics by minimizing the contrastive loss. Besides, when encoding the sequence, we apply a recurrent and convolutional structure to capture global and local relationships in the sequence. Finally, we conduct extensive experiments on four real-world datasets. The experimental results show that our proposed ACVAE model outperforms other state-of-the-art methods.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

Generative adversarial networks (GANs) have been extensively studied in the past few years. Arguably the revolutionary techniques are in the area of computer vision such as plausible image generation, image to image translation, facial attribute manipulation and similar domains. Despite the significant success achieved in computer vision field, applying GANs over real-world problems still have three main challenges: (1) High quality image generation; (2) Diverse image generation; and (3) Stable training. Considering numerous GAN-related research in the literature, we provide a study on the architecture-variants and loss-variants, which are proposed to handle these three challenges from two perspectives. We propose loss and architecture-variants for classifying most popular GANs, and discuss the potential improvements with focusing on these two aspects. While several reviews for GANs have been presented, there is no work focusing on the review of GAN-variants based on handling challenges mentioned above. In this paper, we review and critically discuss 7 architecture-variant GANs and 9 loss-variant GANs for remedying those three challenges. The objective of this review is to provide an insight on the footprint that current GANs research focuses on the performance improvement. Code related to GAN-variants studied in this work is summarized on //github.com/sheqi/GAN_Review.

We propose a new method for event extraction (EE) task based on an imitation learning framework, specifically, inverse reinforcement learning (IRL) via generative adversarial network (GAN). The GAN estimates proper rewards according to the difference between the actions committed by the expert (or ground truth) and the agent among complicated states in the environment. EE task benefits from these dynamic rewards because instances and labels yield to various extents of difficulty and the gains are expected to be diverse -- e.g., an ambiguous but correctly detected trigger or argument should receive high gains -- while the traditional RL models usually neglect such differences and pay equal attention on all instances. Moreover, our experiments also demonstrate that the proposed framework outperforms state-of-the-art methods, without explicit feature engineering.

We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.