Improving the interactivity and interconnectivity between people is one of the highlights of the Metaverse. The Metaverse relies on a core approach, digital twinning, which is a means to replicate physical world objects, people, actions and scenes onto the virtual world. Being able to access scenes and information associated with the physical world, in the Metaverse in real-time and under mobility, is essential in developing a highly accessible, interactive and interconnective experience for all users. This development allows users from other locations to access high-quality real-world and up-to-date information about events happening in another location, and socialize with others hyper-interactively. Nevertheless, receiving continual, smooth updates generated by others from the Metaverse is a challenging task due to the large data size of the virtual world graphics and the need for low latency transmission. With the development of Mobile Augmented Reality (MAR), users can interact via the Metaverse in a highly interactive manner, even under mobility. Hence in our work, we considered an environment with users in moving Internet of Vehicles (IoV), downloading real-time virtual world updates from Metaverse Service Provider Cell Stations (MSPCSs) via wireless communications. We design an environment with multiple cell stations, where there will be a handover of users' virtual world graphic download tasks between cell stations. As transmission latency is the primary concern in receiving virtual world updates under mobility, our work aims to allocate system resources to minimize the total time taken for users in vehicles to download their virtual world scenes from the cell stations. We utilize deep reinforcement learning and evaluate the performance of the algorithms under different environmental configurations. Our work provides a use case of the Metaverse over AI-enabled 6G communications.
Evacuation planning is a crucial part of disaster management where the goal is to relocate people to safety and minimize casualties. Every evacuation plan has two essential components: routing and scheduling. However, joint optimization of these two components with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that combines heuristic search with mathematical optimization and can optimize a variety of objective functions. We use real-world road network and population data from Harris County in Houston, Texas, and apply MIP-LNS to find evacuation routes and schedule for the area. We show that, within a given time limit, our proposed method finds better solutions than existing methods in terms of average evacuation time, evacuation completion time and optimality guarantee of the solutions. We perform agent-based simulations of evacuation in our study area to demonstrate the efficacy and robustness of our solution. We show that our prescribed evacuation plan remains effective even if the evacuees deviate from the suggested schedule upto a certain extent. We also examine how evacuation plans are affected by road failures. Our results show that MIP-LNS can use information regarding estimated deadline of roads to come up with better evacuation plans in terms evacuating more people successfully and conveniently.
Supernova spectral time series can be used to reconstruct a spatially resolved explosion model known as supernova tomography. In addition to an observed spectral time series, a supernova tomography requires a radiative transfer model to perform the inverse problem with uncertainty quantification for a reconstruction. The smallest parametrizations of supernova tomography models are roughly a dozen parameters with a realistic one requiring more than 100. Realistic radiative transfer models require tens of CPU minutes for a single evaluation making the problem computationally intractable with traditional means requiring millions of MCMC samples for such a problem. A new method for accelerating simulations known as surrogate models or emulators using machine learning techniques offers a solution for such problems and a way to understand progenitors/explosions from spectral time series. There exist emulators for the TARDIS supernova radiative transfer code but they only perform well on simplistic low-dimensional models (roughly a dozen parameters) with a small number of applications for knowledge gain in the supernova field. In this work, we present a new emulator for the radiative transfer code TARDIS that not only outperforms existing emulators but also provides uncertainties in its prediction. It offers the foundation for a future active-learning-based machinery that will be able to emulate very high dimensional spaces of hundreds of parameters crucial for unraveling urgent questions in supernovae and related fields.
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's Entropy for any model under which the true normalized Entropy is neither zero nor one. We obtain the asymptotic distribution from the Central Limit Theorem (assuming large time series), the Multivariate Delta Method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's Entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's Entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.
Deep models are highly susceptible to adversarial attacks. Such attacks are carefully crafted imperceptible noises that can fool the network and can cause severe consequences when deployed. To encounter them, the model requires training data for adversarial training or explicit regularization-based techniques. However, privacy has become an important concern, restricting access to only trained models but not the training data (e.g. biometric data). Also, data curation is expensive and companies may have proprietary rights over it. To handle such situations, we propose a completely novel problem of 'test-time adversarial defense in absence of training data and even their statistics'. We solve it in two stages: a) detection and b) correction of adversarial samples. Our adversarial sample detection framework is initially trained on arbitrary data and is subsequently adapted to the unlabelled test data through unsupervised domain adaptation. We further correct the predictions on detected adversarial samples by transforming them in Fourier domain and obtaining their low frequency component at our proposed suitable radius for model prediction. We demonstrate the efficacy of our proposed technique via extensive experiments against several adversarial attacks and for different model architectures and datasets. For a non-robust Resnet-18 model pre-trained on CIFAR-10, our detection method correctly identifies 91.42% adversaries. Also, we significantly improve the adversarial accuracy from 0% to 37.37% with a minimal drop of 0.02% in clean accuracy on state-of-the-art 'Auto Attack' without having to retrain the model.
Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical utility of training such surrogates is contingent on their ability to model complex multi-scale spatio-temporal phenomena. Various neural network architectures have been proposed to target such phenomena, most notably Fourier Neural Operators (FNOs) which give a natural handle over local \& global spatial information via parameterization of different Fourier modes, and U-Nets which treat local and global information via downsampling and upsampling paths. However, generalizing across different equation parameters or different time-scales still remains a challenge. In this work, we make a comprehensive comparison between various FNO and U-Net like approaches on fluid mechanics problems in both vorticity-stream and velocity function form. For U-Nets, we transfer recent architectural improvements from computer vision, most notably from object segmentation and generative modeling. We further analyze the design considerations for using FNO layers to improve performance of U-Net architectures without major degradation of computational performance. Finally, we show promising results on generalization to different PDE parameters and time-scales with a single surrogate model.
In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs). We focus on a pair of benchmarks: discretized partial differential equations and harmonic oscillators, each of which has a tunable parameter that controls its complexity. Even by varying network architecture and applying a state-of-the-art training method that accounts for "difficult" training regions, we show that PINNs eventually fail to produce correct solutions to these benchmarks as their complexity -- the number of equations and the size of time domain -- increases. We identify several reasons why this may be the case, including insufficient network capacity, poor conditioning of the ODEs, and high local curvature, as measured by the Laplacian of the PINN loss.
The mean field variational inference (MFVI) formulation restricts the general Bayesian inference problem to the subspace of product measures. We present a framework to analyze MFVI algorithms, which is inspired by a similar development for general variational Bayesian formulations. Our approach enables the MFVI problem to be represented in three different manners: a gradient flow on Wasserstein space, a system of Fokker-Planck-like equations and a diffusion process. Rigorous guarantees are established to show that a time-discretized implementation of the coordinate ascent variational inference algorithm in the product Wasserstein space of measures yields a gradient flow in the limit. A similar result is obtained for their associated densities, with the limit being given by a quasi-linear partial differential equation. A popular class of practical algorithms falls in this framework, which provides tools to establish convergence. We hope this framework could be used to guarantee convergence of algorithms in a variety of approaches, old and new, to solve variational inference problems.
When applying differential privacy to sensitive data, a common way of getting improved performance is to use external information such as other sensitive data, public data, or human priors. We propose to use the algorithms with predictions framework -- previously applied largely to improve time complexity or competitive ratios -- as a powerful way of designing and analyzing privacy-preserving methods that can take advantage of such external information to improve utility. For four important tasks -- quantile release, its extension to multiple quantiles, covariance estimation, and data release -- we construct prediction-dependent differentially private methods whose utility scales with natural measures of prediction quality. The analyses enjoy several advantages, including minimal assumptions about the data, natural ways of adding robustness to noisy predictions, and novel "meta" algorithms that can learn predictions from other (potentially sensitive) data. Overall, our results demonstrate how to enable differentially private algorithms to make use of and learn noisy predictions, which holds great promise for improving utility while preserving privacy across a variety of tasks.
Hate speech is a global phenomenon, but most hate speech datasets so far focus on English-language content. This hinders the development of more effective hate speech detection models in hundreds of languages spoken by billions across the world. More data is needed, but annotating hateful content is expensive, time-consuming and potentially harmful to annotators. To mitigate these issues, we explore data-efficient strategies for expanding hate speech detection into under-resourced languages. In a series of experiments with mono- and multilingual models across five non-English languages, we find that 1) a small amount of target-language fine-tuning data is needed to achieve strong performance, 2) the benefits of using more such data decrease exponentially, and 3) initial fine-tuning on readily-available English data can partially substitute target-language data and improve model generalisability. Based on these findings, we formulate actionable recommendations for hate speech detection in low-resource language settings.