This paper investigates the Age of Incorrect Information (AoII) in a communication system whose channel suffers a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through the communication channel. The threshold policy, under which the transmitter initiates transmission only when the AoII exceeds the threshold, governs the transmitter's decision. In this paper, we analyze and calculate the performance of the threshold policy in terms of the achieved AoII. Using the Markov chain to characterize the system evolution, the expected AoII can be obtained precisely by solving a system of linear equations whose size is finite and depends on the threshold. We also give closed-form expressions of the expected AoII under two particular thresholds. Finally, calculation results show that there are better strategies than the transmitter constantly transmitting new updates.
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Deep generative models (DGMs) have the potential to revolutionize diagnostic imaging. Generative adversarial networks (GANs) are one kind of DGM which are widely employed. The overarching problem with deploying GANs, and other DGMs, in any application that requires domain expertise in order to actually use the generated images is that there generally is not adequate or automatic means of assessing the domain-relevant quality of generated images. In this work, we demonstrate several objective tests of images output by two popular GAN architectures. We designed several stochastic context models (SCMs) of distinct image features that can be recovered after generation by a trained GAN. Several of these features are high-order, algorithmic pixel-arrangement rules which are not readily expressed in covariance matrices. We designed and validated statistical classifiers to detect specific effects of the known arrangement rules. We then tested the rates at which two different GANs correctly reproduced the feature context under a variety of training scenarios, and degrees of feature-class similarity. We found that ensembles of generated images can appear largely accurate visually, and show high accuracy in ensemble measures, while not exhibiting the known spatial arrangements. Furthermore, GANs trained on a spectrum of distinct spatial orders did not respect the given prevalence of those orders in the training data. The main conclusion is that SCMs can be engineered to quantify numerous errors, per image, that may not be captured in ensemble statistics but plausibly can affect subsequent use of the GAN-generated images.
In this work, we study the problem of real-time tracking and reconstruction of an information source with the purpose of actuation. A device monitors an $N$-state Markov process and transmits status updates to a receiver over a wireless erasure channel. We consider a set of joint sampling and transmission policies, including a semantics-aware one, and we study their performance with respect to relevant metrics. Specifically, we investigate the real-time reconstruction error and its variance, the consecutive error, the cost of memory error, and the cost of actuation error. Furthermore, we propose a randomized stationary sampling and transmission policy and derive closed-form expressions for all aforementioned metrics. We then formulate an optimization problem for minimizing the real-time reconstruction error subject to a sampling cost constraint. Our results show that in the scenario of constrained sampling generation, the optimal randomized stationary policy outperforms all other sampling policies when the source is rapidly evolving. Otherwise, the semantics-aware policy performs the best.
The Age of Incorrect Information (AoII) is a recently proposed metric for real-time remote monitoring systems. In particular, AoII measures the time the information at the monitor is incorrect, weighted by the magnitude of this incorrectness, thereby combining the notions of freshness and distortion. This paper addresses the definition of an AoII-optimal transmission policy in a discrete-time communication scheme with a resource constraint and a hybrid automatic repeat request (HARQ) protocol. Considering an $N$-ary symmetric Markov source, the problem is formulated as an infinite-horizon average-cost constrained Markov decision process (CMDP). The source model is characterized by the cardinality of the state space and the probability of staying at the same state. Interestingly, it is proved that under some conditions, the optimal transmission policy is to never transmit. This reveals that there exists a region of the source dynamics where communication is inadequate in reducing the AoII. Elsewhere, there exists an optimal transmission policy, which is a randomized mixture of two discrete threshold-based policies that randomize at one state. The optimal threshold and the randomization component are derived analytically. Numerical results illustrate the impact of source dynamics, channel conditions, and the resource constraint on the average AoII.
As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While many of these approaches rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and a latent state, making it considerably more challenging to design controllers with performance guarantees. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.
Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB have been reported each year in China. Analyzing the case data from 2004-2018, we find significant differences in TB incidence by age group. Therefore, the effect of age heterogeneous structure on TB transmission needs further study. We develop a model of TB to explore the role of age heterogeneity as a factor in TB transmission. The model is fitted numerically using the nonlinear least squares method to obtain the key parameters in the model, and the basic reproduction number Rv 0.8017 is calculated and the sensitivity anal-ysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of tuberculosis. Furthermore the feasibility of achieving the goals of the WHO End TB Strategy in China is assessed, and we obtain that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by year 2049. However, in theoretical it is feasible to reach the WHO strategic goal of ending tuberculosis by 2035 if the group contact rate in the elderly population can be reduced though it is difficulty to reduce the contact rate.
The information bottleneck (IB) method offers an attractive framework for understanding representation learning, however its applications are often limited by its computational intractability. Analytical characterization of the IB method is not only of practical interest, but it can also lead to new insights into learning phenomena. Here we consider a generalized IB problem, in which the mutual information in the original IB method is replaced by correlation measures based on Renyi and Jeffreys divergences. We derive an exact analytical IB solution for the case of Gaussian correlated variables. Our analysis reveals a series of structural transitions, similar to those previously observed in the original IB case. We find further that although solving the original, Renyi and Jeffreys IB problems yields different representations in general, the structural transitions occur at the same critical tradeoff parameters, and the Renyi and Jeffreys IB solutions perform well under the original IB objective. Our results suggest that formulating the IB method with alternative correlation measures could offer a strategy for obtaining an approximate solution to the original IB problem.
Item response theory aims to estimate respondent's latent skills from their responses in tests composed of items with different levels of difficulty. Several models of item response theory have been proposed for different types of tasks, such as binary or probabilistic responses, response time, multiple responses, among others. In this paper, we propose a new version of $\beta^3$-IRT, called $\beta^{4}$-IRT, which uses the gradient descent method to estimate the model parameters. In $\beta^3$-IRT, abilities and difficulties are bounded, thus we employ link functions in order to turn $\beta^{4}$-IRT into an unconstrained gradient descent process. The original $\beta^3$-IRT had a symmetry problem, meaning that, if an item was initialised with a discrimination value with the wrong sign, e.g. negative when the actual discrimination should be positive, the fitting process could be unable to recover the correct discrimination and difficulty values for the item. In order to tackle this limitation, we modelled the discrimination parameter as the product of two new parameters, one corresponding to the sign and the second associated to the magnitude. We also proposed sensible priors for all parameters. We performed experiments to compare $\beta^{4}$-IRT and $\beta^3$-IRT regarding parameter recovery and our new version outperformed the original $\beta^3$-IRT. Finally, we made $\beta^{4}$-IRT publicly available as a Python package, along with the implementation of $\beta^3$-IRT used in our experiments.
Deep neural networks are proven to be vulnerable to backdoor attacks. Detecting the trigger samples during the inference stage, i.e., the test-time trigger sample detection, can prevent the backdoor from being triggered. However, existing detection methods often require the defenders to have high accessibility to victim models, extra clean data, or knowledge about the appearance of backdoor triggers, limiting their practicality. In this paper, we propose the test-time corruption robustness consistency evaluation (TeCo), a novel test-time trigger sample detection method that only needs the hard-label outputs of the victim models without any extra information. Our journey begins with the intriguing observation that the backdoor-infected models have similar performance across different image corruptions for the clean images, but perform discrepantly for the trigger samples. Based on this phenomenon, we design TeCo to evaluate test-time robustness consistency by calculating the deviation of severity that leads to predictions' transition across different corruptions. Extensive experiments demonstrate that compared with state-of-the-art defenses, which even require either certain information about the trigger types or accessibility of clean data, TeCo outperforms them on different backdoor attacks, datasets, and model architectures, enjoying a higher AUROC by 10% and 5 times of stability.
AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
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