We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal experimental design problem, i.e., maximizing the expected information gain, is equivalent to minimizing the log-determinant of posterior covariance operator. We focus on finite-dimensional inverse problems. However, the presentation is kept generic to facilitate extensions to infinite-dimensional inverse problems.
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This article studies structure-preserving discretizations of Hilbert complexes with nonconforming spaces that rely on projections onto an underlying conforming subcomplex. This approach follows the conforming/nonconforming Galerkin (CONGA) method introduced in [doi.org/10.1090/mcom/3079, doi.org/10.5802/smai-jcm.20, doi.org/10.5802/smai-jcm.21] to derive efficient structure-preserving finite element schemes for the time-dependent Maxwell and Maxwell-Vlasov systems by relaxing the curl-conforming constraint in finite element exterior calculus (FEEC) spaces. Here, it is extended to the discretization of full Hilbert complexes with possibly nontrivial harmonic fields, and the properties of the CONGA Hodge Laplacian operator are investigated. By using block-diagonal mass matrices which may be locally inverted, this framework possesses a canonical sequence of dual commuting projection operators which are local, and it naturally yields local discrete coderivative operators, in contrast to conforming FEEC discretizations. The resulting CONGA Hodge Laplacian operator is also local, and its kernel consists of the same discrete harmonic fields as the underlying conforming operator, provided that a symmetric stabilization term is added to handle the space nonconformities. Under the assumption that the underlying conforming subcomplex admits a bounded cochain projection, and that the conforming projections are stable with moment-preserving properties, a priori convergence results are established for both the CONGA Hodge Laplace source and eigenvalue problems. Our theory is finally illustrated with a spectral element method, and numerical experiments are performed which corroborate our results. Applications to spline finite elements on multi-patch mapped domains are described in a related article [arXiv:2208.05238] for which the present work provides a theoretical background.
What are the root causes of hallucinations in large language models (LLMs)? We use Communication Complexity to prove that the Transformer layer is incapable of composing functions (e.g., identify a grandparent of a person in a genealogy) if the domains of the functions are large enough; we show through examples that this inability is already empirically present when the domains are quite small. We also point out that several mathematical tasks that are at the core of the so-called compositional tasks thought to be hard for LLMs are unlikely to be solvable by Transformers, for large enough instances and assuming that certain well accepted conjectures in the field of Computational Complexity are true.
The CTL learning problem consists in finding for a given sample of positive and negative Kripke structures a distinguishing CTL formula that is verified by the former but not by the latter. Further constraints may bound the size and shape of the desired formula or even ask for its minimality in terms of syntactic size. This synthesis problem is motivated by explanation generation for dissimilar models, e.g. comparing a faulty implementation with the original protocol. We devise a SAT-based encoding for a fixed size CTL formula, then provide an incremental approach that guarantees minimality. We further report on a prototype implementation whose contribution is twofold: first, it allows us to assess the efficiency of various output fragments and optimizations. Secondly, we can experimentally evaluate this tool by randomly mutating Kripke structures or syntactically introducing errors in higher-level models, then learning CTL distinguishing formulas.
The advancement of generative artificial intelligence (GAI) has driven revolutionary applications like ChatGPT. The widespread of these applications relies on the mixture of experts (MoE), which contains multiple experts and selectively engages them for each task to lower operation costs while maintaining performance. Despite MoE, GAI faces challenges in resource consumption when deployed on user devices. This paper proposes mobile edge networks supported MoE-based GAI. We first review the MoE from traditional AI and GAI perspectives, including structure, principles, and applications. We then propose a framework that transfers subtasks to devices in mobile edge networks, aiding GAI model operation on user devices. We discuss challenges in this process and introduce a deep reinforcement learning based algorithm to select edge devices for subtask execution. Experimental results will show that our framework not only facilitates GAI's deployment on resource-limited devices but also generates higher-quality content compared to methods without edge network support.
To understand why self-supervised learning (SSL) models have empirically achieved strong performances on several speech-processing downstream tasks, numerous studies have focused on analyzing the encoded information of the SSL layer representations in adult speech. Limited work has investigated how pre-training and fine-tuning affect SSL models encoding children's speech and vocalizations. In this study, we aim to bridge this gap by probing SSL models on two relevant downstream tasks: (1) phoneme recognition (PR) on the speech of adults, older children (8-10 years old), and younger children (1-4 years old), and (2) vocalization classification (VC) distinguishing cry, fuss, and babble for infants under 14 months old. For younger children's PR, the superiority of fine-tuned SSL models is largely due to their ability to learn features that represent older children's speech and then adapt those features to the speech of younger children. For infant VC, SSL models pre-trained on large-scale home recordings learn to leverage phonetic representations at middle layers, and thereby enhance the performance of this task.
We present a novel theoretical framework for understanding the expressive power of coupling-based normalizing flows such as RealNVP. Despite their prevalence in scientific applications, a comprehensive understanding of coupling flows remains elusive due to their restricted architectures. Existing theorems fall short as they require the use of arbitrarily ill-conditioned neural networks, limiting practical applicability. Additionally, we demonstrate that these constructions inherently lead to volume-preserving flows, a property which we show to be a fundamental constraint for expressivity. We propose a new distributional universality theorem for coupling-based normalizing flows, which overcomes several limitations of prior work. Our results support the general wisdom that the coupling architecture is expressive and provide a nuanced view for choosing the expressivity of coupling functions, bridging a gap between empirical results and theoretical understanding.
Anomaly detection requires detecting abnormal samples in large unlabeled datasets. While progress in deep learning and the advent of foundation models has produced powerful zero-shot anomaly detection methods, their deployment in practice is often hindered by the lack of labeled data -- without it, their detection performance cannot be evaluated reliably. In this work, we propose SWSA (Selection With Synthetic Anomalies): a general-purpose framework to select image-based anomaly detectors with a generated synthetic validation set. Our proposed anomaly generation method assumes access to only a small support set of normal images and requires no training or fine-tuning. Once generated, our synthetic validation set is used to create detection tasks that compose a validation framework for model selection. In an empirical study, we find that SWSA often selects models that match selections made with a ground-truth validation set, resulting in higher AUROCs than baseline methods. We also find that SWSA selects prompts for CLIP-based anomaly detection that outperform baseline prompt selection strategies on all datasets, including the challenging MVTec-AD and VisA datasets.
Conversational search has seen increased recent attention in both the IR and NLP communities. It seeks to clarify and solve users' search needs through multi-turn natural language interactions. However, most existing systems are trained and demonstrated with recorded or artificial conversation logs. Eventually, conversational search systems should be trained, evaluated, and deployed in an open-ended setting with unseen conversation trajectories. A key challenge is that training and evaluating such systems both require a human-in-the-loop, which is expensive and does not scale. One strategy is to simulate users, thereby reducing the scaling costs. However, current user simulators are either limited to only responding to yes-no questions from the conversational search system or unable to produce high-quality responses in general. In this paper, we show that existing user simulation systems could be significantly improved by a smaller finetuned natural language generation model. However, rather than merely reporting it as the new state-of-the-art, we consider it a strong baseline and present an in-depth investigation of simulating user response for conversational search. Our goal is to supplement existing work with an insightful hand-analysis of unsolved challenges by the baseline and propose our solutions. The challenges we identified include (1) a blind spot that is difficult to learn, and (2) a specific type of misevaluation in the standard setup. We propose a new generation system to effectively cover the training blind spot and suggest a new evaluation setup to avoid misevaluation. Our proposed system leads to significant improvements over existing systems and large language models such as GPT-4. Additionally, our analysis provides insights into the nature of user simulation to facilitate future work.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.
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